bayesm/0000755000176000001440000000000013134414120011553 5ustar ripleyusersbayesm/inst/0000755000176000001440000000000013123305446012540 5ustar ripleyusersbayesm/inst/doc/0000755000176000001440000000000013123305446013305 5ustar ripleyusersbayesm/inst/doc/bayesm_Overview_Vignette.html0000644000176000001440000654717713123305445021240 0ustar ripleyusers bayesm Overview

1 Introduction

bayesm is an R package that facilitates statistical analysis using Bayesian methods. The package provides a set of functions for commonly used models in applied microeconomics and quantitative marketing.

The goal of this vignette is to make it easier for users to adopt bayesm by providing a comprehensive overview of the package’s contents and detailed examples of certain functions. We begin with the overview, followed by a discussion of how to work with bayesm. The discussion covers the structure of function arguments, the required input data formats, and the various output formats. The final section provides detailed examples to demonstrate Bayesian inference with the linear normal, multinomial logit, and hierarchical multinomial logit regression models.

2 Package Contents

For ease of exposition, we have grouped the package contents into:

  • Posterior sampling functions
  • Utility functions
  • S3 methods1
  • Datasets

Because the first two groups contain many functions, we organize them into subgroups by purpose. Below, we display each group of functions in a table with one column per subgroup.

Posterior Sampling Functions
Linear Models Limited Dependent Variable Models Hierarchical Models Density Estimation
runireg* rbprobitGibbs** rhierLinearModel rnmixGibbs*
runiregGibbs rmnpGibbs rhierLinearMixture rDPGibbs
rsurGibbs* rmvpGibbs rhierMnlRwMixture*
rivGibbs rmnlIndepMetrop rhierMnlDP
rivDP rscaleUsage rbayesBLP

rnegbinRw rhierNegbinRw

rordprobitGibbs

*bayesm offers the utility function breg with a related but limited set of capabilities as runireg — similarly with rmultireg for rsurGibbs, rmixGibbs for rnmixGibbs, and rhierBinLogit for rhierMnlRwMixture.

**rbiNormGibbs provides a tutorial-like example of Gibbs Sampling from a bivariate normal distribution.

Utility Functions
Log-Likelihood 
(data vector)
Log Density (univariate) Random Draws Mixture-of-Normals Miscellaneous
llmnl lndIChisq rdirichlet clusterMix cgetC
llmnp lndIWishart rmixture eMixMargDen condMom
llnhlogit lndMvn rmvst mixDen createX

lndMvst rtrun mixDenBi ghkvec


rwishart momMix logMargDenNR




mnlHess




mnpProb




nmat




numEff




simnhlogit
S3 Methods
Plot Methods Summary Methods
plot.bayesm.mat summary.bayesm.mat
plot.bayesm.nmix summary.bayesm.nmix
plot.bayesm.hcoef summary.bayesm.var
Datasets
bank customerSat orangeJuice
camera detailing Scotch
cheese margarine tuna

Some discussion of the naming conventions may be warranted. All functions use CamelCase but begin lowercase. Posterior sampling functions begin with r to match R’s style of naming random number generation functions since these functions all draw from (posterior) distributions. Common abbreviations include DP for Dirichlet Process, IV for instrumental variables, MNL and MNP for multinomial logit and probit, SUR for seemingly unrelated regression, and hier for hierarchical. Utility functions that begin with ll calculate the log-likelihood of a data vector, while those that begin with lnd provide the log-density. Other abbreviations should be straighforward; please see the help file for a specific function if its name is unclear.

3 Working with bayesm

We expect most users of the package to interact primarily with the posterior sampling functions. These functions take a consistent set of arguments as inputs (Data, Prior, and Mcmc — each is a list) and they return output in a consistent format (always a list). summary and plot generic functions can then be used to facilitate analysis of the output because of the classes and methods defined in bayesm. The following subsections describe the format of the standardized function arguments as well as the required format of the data inputs and the format of the output from bayesm’s posterior sampling functions.

3.1 Input: Function Arguments

The posterior sampling functions take three arguments: Data, Prior, and Mcmc. Each argument is a list.

As a minimal example, assume you’d like to perform a linear regression and that you have in your work space y (a vector of length \(n\)) and X (a matrix of dimension \(n \times p\)). For this example, we utilize the default values for Prior and so we do not specify the Prior argument. These components (Data, Prior, and Mcmc as well as their arguments including R and nprint) are discussed in the subsections that follow. Then the bayesm syntax is simply:

mydata <- list(y = y, X = X)
mymcmc <- list(R = 1e6, nprint = 0)

out <- runireg(Data = mydata, Mcmc = mymcmc)

The list elements of Data, Prior, and Mcmc must be named. For example, you could not use the following code because the Data argument mydata2 has unnamed elements.

mydata2 <- list(y, X)
out <- runireg(Data = mydata2, Mcmc = mymcmc)

3.1.1 Data Argument

bayesm’s posterior sampling functions do not accept data stored in dataframes; data must be stored as vectors or matrices.

For non-hierarchical models, the list of input data simply contains the approprate data vectors or matrices from the set {y, X, w, z}2 and possibly a scalar (length one vector) from the set {k, p}.

  • For functions that require only a single data argument (such as the two density estimation functions, rnmixGibbs and rDPGibbs), y is that argument. More typically, y is used for LHS3 variable(s) and X for RHS variables. For estimation using instrumental variables, variables in the structural equation are separated into “exogenous†variables w and an “edogenous†variable x; z is a matrix of instruments.

  • For the scalars, p indicates the number of choice alternatives in discrete choice models and k is used as the maximum ordinate in models for ordinal data (e.g., rordprobitGibbs).

For hierarchical models, the input data has up to 3 components. We’ll discuss these components using the mixed logit model (rhierMnlRwMixture) as an example. For rhierMnlRwMixture, the Data argument is list(lgtdata, Z, p).

  1. The first component for all hierarchical models is required. It is a list of lists named either regdata or lgtdata, depending on the function. In rhierMnlRwMixture, lgtdata is a list of lists, with each interior list containing a vector or one-column matrix of multinomial outcomes y and a design matrix of covariates X. In Example 3 below, we show how to convert data from a data frame to this required list-of-lists format.

  2. The second component, Z, is present but optional for all hierarchical models. Z is a matrix of cross-sectional unit characteristics that drive the mean responses; that is, a matrix of covariates for the individual parameters (e.g. \(\beta_i\)’s). For example, the model (omitting the priors) for rhierMnlRwMixture is:

    \[ y_i \sim \text{MNL}(X_i'\beta_i) \hspace{1em} \text{with} \hspace{1em} \beta_i = Z \Delta_i + u_i \hspace{1em} \text{and} \hspace{1em} u_i \sim N(\mu_j, \Sigma_j) \]

    where \(i\) indexes individuals and \(j\) indexes cross-sectional unit characteristics.

  3. The third component (if accepted) is a scalar, such as p or k, and like the arguments by the same names in the non-hierarchical models, is used to indicate the size of the choice set or the maximum value of a scale or count variable. In rhierMnlRwMixture, the argument is p, which is used to indicate the number of choice alternatives.

Note that rbayesBLP (the hierarchical logit model with aggregate data as in Berry, Levinsohn, and Pakes (1995) and Jiang, Manchanda, and Rossi (2009)) deviates slightly from the standard data input. rbayesBLP uses j instead of p to be consistent with the literature and calls the LHS variable share rather than y to emphasize that aggregate (market share instead of individual choice) data are required.

3.1.2 Prior Argument

Specification of prior distributions is model-specific, so our discussion here is brief.

All posterior sampling functions offer default values for parameters of prior distributions. These defaults were selected to yield proper yet reasonably-diffuse prior distributions (assuming the data are in approximately unit scale). In addition, these defaults are consistent across functions. For example, normal priors have default values of mean 0 with value 0.01 for the scaling factor of the prior precision matrix.

Specification of the prior is important. Significantly more detail can be found in chapters 2–5 of BSM4 and the help files for the posterior sampling functions. We strongly recommend you consult them before accepting the default values.

3.1.3 Mcmc Argument

The Mcmc argument controls parameters of the sampling algorithm. The most common components of this list include:

  • R: the number of MCMC draws
  • keep: a thinning parameter indicating that every keep\(^\text{th}\) draw should be retained
  • nprint: an option to print the estimated time remaining to the console after each nprint\(^\text{th}\) draw

MCMC methods are non-iid. As a result, a large simulation size may be required to get reliable results. We recommend setting R large enough to yield an adequate effective sample size and letting keep default to the value 1 unless doing so imposes memory constraints. A careful reader of the bayesm help files will notice that many of the examples set R equal to 1000 or less. This low number of draws was chosen for speed, as the examples are meant to demonstrate how to run the code and do not necessarily suggest best practices for a proper statistical analysis.

nprint defaults to 100, but for large R, you may want to increase the nprint option. Alternatively, you can set nprint=0, in which case the priors will still be printed to the console, but the estimated time remaining will not.

Additional components of the Mcmc argument are function-specific, but typically include starting values for the algorithm. For example, the Mcmc argument for runiregGibbs takes sigmasq as a scalar element of the list. The Gibbs Sampler for runiregGibbs first draws \(\beta | \sigma^2\), then draws \(\sigma^2 | \beta\), and then repeats. For the first draw of \(\beta\) in the MCMC chain, a value of \(\sigma^2\) is required. The user can specify a value using Mcmc$sigmasq, or the user can omit the argument and the function will use its default (sigmasq = var(Data$y)).

3.2 Output: Returned Results

bayesm posterior sampling functions return a consistent set of results and output to the user. At a minimum, this output includes draws from the posterior distribution. bayesm provides a set of summary and plot methods to facilitate analysis of this output, but the user is free to analyze the results as he or she sees fit.

3.2.1 Output Formats

All bayesm posterior sampling functions return a list. The elements of that list include a set of vectors, matrices, and/or arrays (and possibly a list), the exact set of which depend on the function.

  • Vectors are returned for draws of parameters with no natural grouping. For example, runireg implements and iid sampler to draw from the posterior of a homoskedastic univariate regression with a conjugate prior (i.e., a Bayesian analog to OLS regression). One output list element is sigmasqdraw, a length R/keep vector for the scalar parameter \(\sigma^2\).

  • Matrices are returned for draws of parameters with a natural grouping. Again using runireg as the example, the output list includes betadraw, an R/keep \(\times\) ncol(X) matrix for the vector of \(\beta\) parameters.

    Contrary to the next bullet, draws for the parameters in a variance-covariance matrix are returned in matrix form. For example, rmnpGibbs implements a Gibbs Sampler for a multinomial probit model where one set of parameters is the \((p-1) \times (p-1)\) matrix \(\Sigma\). The output list for rmnpGibbs includes the list element sigmadraw, which is a matrix of dimension R/keep\(\times (p-1)*(p-1)\) with each row containing a draw (in vector form) for all the elements of the matrix \(\Sigma\). bayesm’s summary and plot methods (see below) are designed to handle this format.

  • Arrays are used when parameters have a natural matrix-grouping, such that the MCMC algorithm returns R/keep draws of the matrix. For example, rsurGibbs returns a list that includes Sigmadraw, an \(m \times m \times\)R/keep array, where \(m\) is the number of regression equations. As a second example, rhierLinearModel estimates a hierarchical linear regression model with a normal prior, and returns a list that includes betadraw, an \(n \times k \times\)R/keep array, where \(n\) signifies the number of individuals (each with their own \(\beta_i\)) and \(k\) signifies the number of covariates (ncol(X) = \(k\)).

  • For functions that use a mixture-of-normals or Dirichlet Process prior, the output list includes a list (nmix) pertaining to that prior. nmix is itself a list with 3 components: probdraw, zdraw, and compdraw. probdraw reports the probability that each draw came from a particular normal component; zdraw indicates which mixture-of-normals component each draw is assigned to; and compdraw provides draws for the mixture-of-normals components (i.e., mean vectors and Cholesky roots of covariance matrices). Note that if you specify a “mixture†with only one normal component, there will be no useful information in probdraw. Also note that zdraw is not relevant for density estimation and will be null except in rnmixGibbs and rDPGibbs.

3.2.2 Classes and Methods

In R generally, objects can be assigned a class and then a generic function can be used to run a method on an object with that class. The list elements in the output from bayesm posterior sampling functions are assigned special bayesm classes. The bayesm package includes summary and plot methods for use with these classes (see the table in Section 2 above). This means you can call the generic function (e.g., summary) on individual list elements of bayesm output and it will return specially-formatted summary results, including the effective sample size.

To see this, the code below provides an example using runireg. Here the generic function summary dispatches the method summary.bayesm.mat because the betadraw element of runireg’s output has class bayesm.mat. This example also shows the information about the prior that is printed to the console during the call to a posterior sampling function. Notice, however, that no remaining time is printed because nprint is set to zero.

set.seed(66)
R <- 2000
n <- 200
X <- cbind(rep(1,n), runif(n))
beta <- c(1,2)
sigsq <- 0.25
y <- X %*% beta + rnorm(n, sd = sqrt(sigsq))
out <- runireg(Data = list(y = y, X = X), Mcmc = list(R = R, nprint = 0))
##  
## Starting IID Sampler for Univariate Regression Model
##   with  200  observations
##  
## Prior Parms: 
## betabar
## [1] 0 0
## A
##      [,1] [,2]
## [1,] 0.01 0.00
## [2,] 0.00 0.01
## nu =  3  ssq=  0.5721252
##  
## MCMC parms: 
## R=  2000  keep=  1  nprint=  0
## 
summary(out$betadraw, tvalues = beta)
## Summary of Posterior Marginal Distributions 
## Moments 
##   tvalues mean std dev num se rel eff sam size
## 1       1  1.0    0.07 0.0015    0.85     1800
## 2       2  2.1    0.12 0.0029    1.01      900
## 
## Quantiles 
##   tvalues 2.5%  5% 50% 95% 97.5%
## 1       1 0.88 0.9 1.0 1.1   1.2
## 2       2 1.83 1.9 2.1 2.3   2.3
##    based on 1800 valid draws (burn-in=200)

3.3 Access to Code

bayesm was originally created as a companion to BSM, at which time most functions were written in R. The package has since been expanded to include additional functionality and most code has been converted to C++ via Rcpp for faster performance. However, for users interested in obtaining the original implementation of a posterior sampling function (in R instead of C++), you may still access the last version (2.2-5) of bayesm prior to the C++/Rcpp conversion from the package archive on CRAN.

To access the R code in the current version of bayesm, the user can simply call a function without parenthesis. For example, bayesm::runireg. However, most posterior sampling functions only perform basic checks in R and then call an unexported C++ function to do the heavy lifting (i.e., the MCMC draws). This C++ source code is not available to the user via the installed bayesm package because C++ code is compiled upon package installation on Linux machines and pre-compiled by CRAN for Mac and Windows. To access this source code, the user must download the “package source†from CRAN. This can be accomplished by clicking on the appropriate link at the bayesm package archive or by executing the R command download.packages(pkgs="bayesm", destdir=".", type="source"). Either of these methods will provide you with a compressed file “bayesm_version.tar.gz†that can be uncompressed. The C++ code can then be found in the “src†subdirectory.

4 Examples

We begin with a brief introduction to regression and Bayesian estimation. This will help set the notation and provide background for the examples that follow. We do not claim that this will be a sufficient introduction to the reader for which these ideas are new. We refer that reader to excellent texts on regression analysis by Cameron & Trivedi, Davidson & MacKinnon, Goldberger, Greene, Wasserman, and Wooldridge.5 For Bayesian methods, we recommend Gelman et al., Jackman, Marin & Robert, Rossi et al., and Zellner.6

4.1 What is Regression

Suppose you believe a variable \(y\) varies with (or is caused by) a set of variables \(x_1, x_2, \ldots, x_k\). For notational convenience, we’ll collect the set of \(x\) variables into \(X\). These variables \(y\) and \(X\) have a joint distribution \(f(y, X)\). Typically, interest will not fall on this joint distribution, but rather on the conditional distribution of the “outcome†variable \(y\) given the “explanatory†variables (or “covariatesâ€) \(x_1, x_2, \ldots, x_k\); this conditional distribution being \(f(y|X)\).

To carry out inference on the relationship between \(y\) and \(X\), the researcher then often focuses attention on one aspect of the conditional distribution, most commonly its expected value. This conditional mean is assumed to be a function \(g\) of the covariates such that \(\mathbb{E}[y|X] = g(X, \beta)\) where \(\beta\) is a vector of parameters. A function for the conditional mean is known as a “regression†function.

The canonical introductory regression model is the normal linear regression model, which assumes that \(y \sim N(X\beta, \sigma^2)\). Most students of regression will have first encountered this model as a combination of deterministic and stochastic components. There, the stochastic component is defined as deviations from the conditional mean, \(\varepsilon = y - \mathbb{E}[y|X]\), such that \(y = \mathbb{E}[y|X] + \varepsilon\) or that \(y = g(X, \beta) + \varepsilon\). The model is then augmented with the assumptions that \(g(X, \beta) = X \beta\) and \(\varepsilon \sim N(0,\sigma^2)\) so that the normal linear regression model is:

\[ y = X \beta + \varepsilon \text{ with } \varepsilon \sim N(0,\sigma^2) \hspace{1em} \text{or} \hspace{1em} y \sim N(X\beta, \sigma^2) \]

When taken to data, additional assumptions are made which include a full-rank condition on \(X\) and often that \(\varepsilon_i\) for \(i=1,\ldots,n\) are independent and identically distributed.

Our first example will demonstrate how to estimate the parameters of the normal linear regression model using Bayesian methods made available by the posterior sampling function runireg. We then provide an example to estimate the parameters of a model when \(y\) is a categorical variable. This second example is called a multinomial logit model and uses the logistic “link†function \(g(X, \beta) = [1 + exp(-X\beta)]^{-1}\). Our third and final example will extend the multinomial logit model to permit individual-level parameters. This is known as a hierarchical model and requires panel data to perform the estimation.

Before launching into the examples, we briefly introduce Bayesian methodology and contrast it with classical methods.

4.2 What is Bayesian Inference

Under classical econometric methods, \(\beta\) is most commonly estimated by minimizing the sum of squared residuals, maximizing the likelihood, or matching sample moments to population moments. The distribution of the estimators (e.g., \(\hat{\beta}\)) and test statistics derived from these methods rely on asymptotic concepts and are based on imaginary samples not observed.

In contrast, Bayesian inference provides the benefits of (a) exact sample results, (b) integration of descision-making, estimation, testing, and model selection, and (c) a full accounting of uncertainty. These benefits from Bayesian inference rely heavily on probability theory and, in particular, distributional theory, some elements of which we now briefly review.

Recall the relationship between the joint and conditional densities for random variables \(W\) and \(Z\):

\[ P_{A|B}(A=a|B=b) = \frac{P_{A,B}(A=a, B=b)}{P_B(B=b)} \]

This relationship can be used to derive Bayes’ Theorem, which we write with \(D\) for “data†and \(\theta\) as the parameters (and with implied subscripts):

\[ P(\theta|D) = \frac{P(D|\theta)P(\theta)}{P(D)} \]

Noticing that \(P(D)\) does not contain the parameters of interest (\(\theta\)) and is therefore simply a normalizing constant, we can instead write:

\[ P(\theta|D) \propto P(D|\theta)P(\theta) \]

Introducing Bayesian terminology, we have that the “Posterior†is proportional to the Likelihood times the Prior.

Thus, given (1) a dataset (\(D\)), (2) an assumption on the data generating process (the likelihood, \(P(D|\theta)\)), and (3) a specification of the prior distribution of the parameters (\(P(\theta)\)), we can find the exact (posterior) distribution of the parameters given the observed data. This is in stark contrast to classical econometric methods, which typically only provide the asymptotic distributions of estimators.

However, for any problem of practical interest, the posterior distribution is a high-dimensional object. Additionally, it may not be possible to analytically calculate the posterior or its features (e.g., marginal distributions or moments such as the mean). To handle these issues, the modern approach to Bayesian inference relies on simulation methods to sample from the (high-dimensional) posterior distribution and then construct marginal distributions (or their features) from the sampled draws of the posterior. As a result, simulation and summaries of the posterior play important roles in modern Bayesian statistics.

bayesm’s posterior sampling functions (as their name suggests) sample from posterior distributions. bayesm’s summary and plot methods can be used to analyze those draws. Unlike most classical econometric methods, the MCMC methods implemented in bayesm’s posterior sampling functions provide an estimate of the entire posterior distribution, not just a few moments. Given this “rich†result from Bayesian methods, it is best to summarize posterior distributions using histograms or quantiles. We advise that you resist the temptation to simply report the posterior mean and standard deviation; for non-normal distributions, those moments may have little meaning.

In the examples that follow, we will describe the data we use, present the model, demonstrate how to estimate it using the appropriate posterior sampling function, and provide various ways to summarize the output.

4.3 Example 1: Linear Normal Regression

4.3.1 Data

For our first example, we will use the cheese dataset, which provides 5,555 observations of weekly sales volume for a package of Borden sliced cheese, as well as a measure of promotional display activity and price. The data are aggregated to the “key†account (i.e., retailer-market) level.

data(cheese)
names(cheese) <- tolower(names(cheese))
str(cheese)
## 'data.frame':    5555 obs. of  4 variables:
##  $ retailer: Factor w/ 88 levels "ALBANY,NY - PRICE CHOPPER",..: 42 43 44 19 20 21 35 36 64 31 ...
##  $ volume  : int  21374 6427 17302 13561 42774 4498 6834 3764 5112 6676 ...
##  $ disp    : num  0.162 0.1241 0.102 0.0276 0.0906 ...
##  $ price   : num  2.58 3.73 2.71 2.65 1.99 ...

Suppose we want to assess the relationship between sales volume and price and promotional display activity. For this example, we will abstract from whether these relationships vary by retailer or whether prices are set endogenously. Simple statistics show a negative correlation between volume and price, and a positive correlation between volume and promotional activity, as we would expect.

options(digits=3)
cor(cheese$volume, cheese$price)
## [1] -0.227
cor(cheese$volume, cheese$disp)
## [1] 0.173

4.3.2 Model

We model the expected log sales volume as a linear function of log(price) and promotional activity. Specifically, we assume \(y_i\) to be iid with \(p(y_i|x_i,\beta)\) normally distributed with a mean linear in \(x\) and a variance of \(\sigma^2\). We will denote observations with the index \(i = 1, \ldots, n\) and covariates with the index \(j = 1, \ldots, k\). The model can be written as:

\[ y_i = \sum_{j=1}^k \beta_j x_{ij} + \varepsilon_i = x_i'\beta + \varepsilon_i \hspace{1em} \text{with} \hspace{1em} \varepsilon_i \sim iid\ N(0,\sigma^2) \]

or equivalently but more compactly as:

\[ y \sim MVN(X\beta,\ \sigma^2I_n) \]

Here, the notation \(N(0, \sigma^2)\) indicates a univariate normal distribution with mean \(0\) and variance \(\sigma^2\), while \(MVN(X\beta,\ \sigma^2I_n)\) indicates a multivariate normal distribution with mean vector \(X\beta\) and variance-covariance matrix \(\sigma^2I_n\). In addition, \(y_i\), \(x_{ij}\), \(\varepsilon_i\), and \(\sigma^2\) are scalars while \(x_i\) and \(\beta\) are \(k \times 1\) dimensional vectors. In the more compact notation, \(y\) is an \(n \times 1\) dimensional vector, \(X\) is an \(n \times k\) dimensional matrix with row \(x_i\), and \(I_n\) is an \(n \times n\) dimensional identity matrix. With regard to the cheese dataset, \(k = 2\) and \(n = 5,555\).

When employing Bayesian methods, the model is incomplete until the prior is specified. For our example, we elect to use natural conjugate priors, meaning the family of distributions for the prior is chosen such that, when combined with the likelihood, the posterior will be of the same distributional family. Specifically, we first factor the joint prior into marginal and conditional prior distributions:

\[ p(\beta,\sigma^2) = p(\beta|\sigma^2)p(\sigma^2) \]

We then specify the prior for \(\sigma^2\) as inverse-gamma (written in terms of a chi-squared random variable) and the prior for \(\beta|\sigma^2\) as multivariate normal:

\[ \sigma^2 \sim \frac{\nu s^2}{\chi^2_{\nu}} \hspace{1em} \text{and} \hspace{1em} \beta|\sigma^2 \sim MVN(\bar{\beta},\sigma^2A^{-1}) \]

Other than convenience, we have little reason to specify priors from these distributional families; however, we will select diffuse priors so as not to impose restrictions on the model. To do so, we must pick values for \(\nu\) and \(s^2\) (the degrees of freedom and scale parameters for the inverted chi-squared prior on \(\sigma^2\)) as well as \(\bar{\beta}\) and \(A^{-1}\) (the mean vector and variance-covariance matrix for the multivariate normal prior on the \(\beta\) vector). The bayesm posterior sampling function for this model, runireg, defaults to the following values:

  • \(\nu = 3\)
  • \(s^2 =\) var(y)
  • \(\bar{\beta} = 0\)
  • \(A = 0.01*I\)

We will use these defaults, as they are chosen to be diffuse for data with a unit scale. Thus, for each \(\beta_j | \sigma^2\) we have specified a normal prior with mean 0 and variance \(100\sigma^2\), and for \(\sigma^2\) we have specified an inverse-gamma prior with \(\nu = 3\) and \(s^2 = \text{var}(y)\). We graph these prior distributions below.

par(mfrow = c(1,2))

curve(dnorm(x,0,10), xlab = "", ylab = "", xlim = c(-30,30),
      main = expression(paste("Prior for ", beta[j])),
      col = "dodgerblue4")

nu  <- 3
ssq <- var(log(cheese$volume))
curve(nu*ssq/dchisq(x,nu), xlab = "", ylab = "", xlim = c(0,1),
      main = expression(paste("Prior for ", sigma^2)), 
      col = "darkred")

par(mfrow = c(1,1))

4.3.3 Bayesian Estimation

Although this model involves nontrivial natural conjugate priors, the posterior is available in closed form:

\[ p(\beta, \sigma^2 | y, X) \propto (\sigma^2)^{-k/2} \exp \left\{ -\frac{1}{2\sigma^2}(\beta - \bar{\beta})'(X'X+A)(\beta - \bar{\beta}) \right\} \times (\sigma^2)^{-((n+\nu_0)/2+1)} \exp \left\{ -\frac{\nu_0s_0^2 + ns^2}{2\sigma^2} \right\} \]

or

\[\begin{align*} \beta | \sigma^2, y, X &\sim N(\bar{\beta}, \sigma^2(X'X+A)^{-1}) \\ \\ \sigma^2 | y, X &\sim \frac{\nu_1s_1^2}{\chi^2_{\nu_1}}, \hspace{3em} \text{with} \> \nu_1 = \nu_0+n \hspace{1em} \text{and} \hspace{1em} s_1^2 = \frac{\nu_0s_0^2 + ns^2}{\nu_0+n} \end{align*}\]

The latter representation suggests a simulation strategy for making draws from the posterior. We draw a value of \(\sigma^2\) from its marginal posterior distribution, insert this value into the expression for the covariance matrix of the conditional normal distribution of \(\beta|\{\sigma^2,y\}\) and draw from this multivariate normal. This simulation strategy is implemented by runireg, using the defaults for Prior specified above. The code is quite simple.

dat <- list(y = log(cheese$volume), X = model.matrix( ~ price + disp, data = cheese))
out <- runireg(Data = dat, Mcmc = list(R=1e4, nprint=1e3))

Note that bayesm posterior sampling functions print out information about the prior and about MCMC progress during the function call (unless nprint is set to 0), but for presentation purposes we suppressed that output here.

runireg returns a list that we have saved in out. The list contains two elements, betadraw and sigmasqdraw, which you can verify by running str(out). betadraw is an R/keep \(\times\) ncol(X) (\(10,000 \times 3\) with a column for each of the intercept, price, and display) dimension matrix with class bayesm.mat. We can analyze or summarize the marginal posterior distributions for any \(\beta\) parameter or the \(\sigma^2\) parameter. For example, we can plot histograms of the price coefficient (even though it is known to follow a t-distrbution, see BSM Ch. 2.8) and for \(\sigma^2\). Notice how concentrated the posterior distributions are compared to their priors above.

B <- 1000+1 #burn in draws to discard 
R <- 10000

par(mfrow = c(1,2))
hist(out$betadraw[B:R,2], breaks = 30, 
     main = "Posterior Dist. of Price Coef.", 
     yaxt = "n", yaxs="i",
     xlab = "", ylab = "", 
     col = "dodgerblue4", border = "gray")
hist(out$sigmasqdraw[B:R], breaks = 30, 
     main = "Posterior Dist. of Sigma2", 
     yaxt = "n", yaxs="i",
     xlab = "", ylab = "", 
     col = "darkred", border = "gray")
par(mfrow = c(1,1))

Additionally, we can compute features of these posterior distributions. For example, the posterior means price and display are:

apply(out$betadraw[B:R,2:3], 2, mean)
## [1] -0.393  0.542

Conveniently, bayesm offers this functionality (and more) with its summary and plot methods. Notice that bayesm’s methods use a default burn-in length, calculated as trunc(0.1*nrow(X)). You can override the default by specifying the burnin argument. We see that the means for the first few retail fixed effects in the summary information below match those calculated “by hand†above.

summary(out$betadraw)
## Summary of Posterior Marginal Distributions 
## Moments 
##    mean std dev  num se rel eff sam size
## 1  9.19   0.059 0.00057    0.85     9000
## 2 -0.39   0.020 0.00019    0.87     9000
## 3  0.54   0.063 0.00072    1.18     4500
## 
## Quantiles 
##    2.5%    5%   50%   95% 97.5%
## 1  9.08  9.09  9.19  9.29  9.31
## 2 -0.43 -0.43 -0.39 -0.36 -0.35
## 3  0.42  0.44  0.54  0.64  0.66
##    based on 9000 valid draws (burn-in=1000)

The same can be done with the plot generic function. However, we reference the method directly (plot.bayesm.mat) to plot a subset of the bayesm output – specifically we plot the price coefficient. In the histogram, note that the green bars delimit a 95% Bayesian credibility interval, yellow bars shows +/- 2 numerical standard errors for the posterior mean, and the red bar indicates the posterior mean. Also notice that this pink histogram of the posterior distribution on price, which was created by calling the plot generic, matches the blue one we created “by hand†above.

The plot generic function also provides a trace plot and and ACF plot. In many applications (although not in this simple model), we cannot be certain that our draws from the posterior distribution adequately represent all areas of the posterior with nontrivial mass. This may occur, for instance, when using a “slow mixing†Markov Chain Monte Carlo (MCMC) algorithm to draw from the posterior. In such a case, we might see patterns in the trace plot and non-zero autocorrelations in the ACF plot; these will coincide with values for the Effective Sample Size less than R. (Effective Sample Size prints out with the summary generic function, as above.) Here, however, we are able to sample from the posterior distribution by taking iid draws, and so we see large Effective Sample Sizes in the summary output above, good mixing the trace plot below, and virtually no autocorrelation between draws in the ACF plot below.

plot.bayesm.mat(out$betadraw[,2])

4.4 Example 2: Multinomial Logistic Regression

4.4.1 Data

Linear regression models like the one in the previous example are best suited for continuous outcome variables. Different models (known as limited dependent variable models) have been developed for binary or multinomial outcome variables, the most popular of which — the multinomial logit — will be the subject of this section.

For this example, we analyze the margarine dataset, which provides panel data on purchases of margarine. The data are stored in two dataframes. The first, choicePrice, lists the outcome of 4,470 choice occasions as well as the choosing household and the prices of the 10 choice alternatives. The second, demos, provides demographic information about the choosing households, such as their income and family size. We begin by merging the information from these two dataframes:

data(margarine)
str(margarine)
marg <- merge(margarine$choicePrice, margarine$demos, by = "hhid")
## List of 2
##  $ choicePrice:'data.frame': 4470 obs. of  12 variables:
##   ..$ hhid    : int [1:4470] 2100016 2100016 2100016 2100016 2100016 2100016 2100016 2100024 2100024 2100024 ...
##   ..$ choice  : num [1:4470] 1 1 1 1 1 4 1 1 4 1 ...
##   ..$ PPk_Stk : num [1:4470] 0.66 0.63 0.29 0.62 0.5 0.58 0.29 0.66 0.66 0.66 ...
##   ..$ PBB_Stk : num [1:4470] 0.67 0.67 0.5 0.61 0.58 0.45 0.51 0.45 0.59 0.67 ...
##   ..$ PFl_Stk : num [1:4470] 1.09 0.99 0.99 0.99 0.99 0.99 0.99 1.08 1.08 1.09 ...
##   ..$ PHse_Stk: num [1:4470] 0.57 0.57 0.57 0.57 0.45 0.45 0.29 0.57 0.57 0.57 ...
##   ..$ PGen_Stk: num [1:4470] 0.36 0.36 0.36 0.36 0.33 0.33 0.33 0.36 0.36 0.36 ...
##   ..$ PImp_Stk: num [1:4470] 0.93 1.03 0.69 0.75 0.72 0.72 0.72 0.93 0.93 0.93 ...
##   ..$ PSS_Tub : num [1:4470] 0.85 0.85 0.79 0.85 0.85 0.85 0.85 0.85 0.85 0.85 ...
##   ..$ PPk_Tub : num [1:4470] 1.09 1.09 1.09 1.09 1.07 1.07 1.07 1.09 1.09 1.09 ...
##   ..$ PFl_Tub : num [1:4470] 1.19 1.19 1.19 1.19 1.19 1.19 1.19 1.19 1.34 1.19 ...
##   ..$ PHse_Tub: num [1:4470] 0.33 0.37 0.59 0.59 0.59 0.59 0.59 0.33 0.33 0.33 ...
##  $ demos      :'data.frame': 516 obs. of  8 variables:
##   ..$ hhid     : num [1:516] 2100016 2100024 2100495 2100560 2100610 ...
##   ..$ Income   : num [1:516] 32.5 17.5 37.5 17.5 87.5 12.5 17.5 17.5 27.5 67.5 ...
##   ..$ Fs3_4    : int [1:516] 0 1 0 0 0 0 0 0 0 0 ...
##   ..$ Fs5.     : int [1:516] 0 0 0 0 0 0 0 0 1 0 ...
##   ..$ Fam_Size : int [1:516] 2 3 2 1 1 2 2 2 5 2 ...
##   ..$ college  : int [1:516] 1 1 0 0 1 0 1 0 1 1 ...
##   ..$ whtcollar: int [1:516] 0 1 0 1 1 0 0 0 1 1 ...
##   ..$ retired  : int [1:516] 1 1 1 0 0 1 0 1 0 0 ...

Compared to the standard \(n \times k\) rectangular format for data to be used in a linear regression model, choice data may be stored in various formats, including a rectangular format where the \(p\) choice alternatives are allocated across columns or rows, or a list-of-lists format as used in bayesm’s hierarchical models, which we demonstrate in Example 3 below. For all functions — and notably those that implement multinomial logit and probit models — the data must be in the format expected by the function, and bayesm’s posterior sampling funtions are no exception.

In this example, we will implement a multinomial logit model using rmnlIndepMetrop. This posterior sampling function requires y to be a length-\(n\) vector (or an \(n \times 1\) matrix) of multinomial outcomes (\(1, \dots, p\)). That is, each element of y corresponds to a choice occasion \(i\) with the value of the element \(y_i\) indicating the choice that was made. So if the fourth alternative was chosen on the seventh choice occasion, then \(y_7 = 4\). The margarine data are stored in that format, and so we easily specify y with the following code:

y <- marg[,2]

rmnlIndepMetrop requires X to be an \(np \times k\) matrix. That is, each alternative is listed on its own row, with a group of \(p\) rows together corresponding to the alternatives available on one choice occasion. However, the margarine data are stored with the various choice alternatives in columns rather than rows, so reformatting is necessary. bayesm provides the utility function createX to assist with the conversion. createX requires the user to specify the number of choice alternatives p as well as the number of alternative-specific variables na and an \(n \times\) na matrix of alternative-specific data Xa (“a†for alternative-specific). Here, we have \(p=10\) choice alternatives with na \(=1\) alternative-specific variable (price). If we were only interested in using price as a covariate, we would code:

X1 <- createX(p=10, na=1, Xa=marg[,3:12], nd=NULL, Xd=NULL, base=1)
colnames(X1) <- c(names(marg[,3:11]), "price")
head(X1, n=10)
##       PPk_Stk PBB_Stk PFl_Stk PHse_Stk PGen_Stk PImp_Stk PSS_Tub PPk_Tub
##  [1,]       0       0       0        0        0        0       0       0
##  [2,]       1       0       0        0        0        0       0       0
##  [3,]       0       1       0        0        0        0       0       0
##  [4,]       0       0       1        0        0        0       0       0
##  [5,]       0       0       0        1        0        0       0       0
##  [6,]       0       0       0        0        1        0       0       0
##  [7,]       0       0       0        0        0        1       0       0
##  [8,]       0       0       0        0        0        0       1       0
##  [9,]       0       0       0        0        0        0       0       1
## [10,]       0       0       0        0        0        0       0       0
##       PFl_Tub price
##  [1,]       0  0.66
##  [2,]       0  0.67
##  [3,]       0  1.09
##  [4,]       0  0.57
##  [5,]       0  0.36
##  [6,]       0  0.93
##  [7,]       0  0.85
##  [8,]       0  1.09
##  [9,]       0  1.19
## [10,]       1  0.33

Notice that createX uses \(p-1\) dummy variables to distinguish the \(p\) choice alternatives. As with factor variables in linear regression, one factor must be the base; the coefficients on the other factors report deviations from the base. The user may specify the base alternative using the base argument (as we have done above), or let it default to the alternative with the highest index.

For our example, we might also like to include some “demographic†variables. These are variables that do not vary with the choice alternatives. For example, with the margarine data we might want to include family size. Here again we turn to createX, this time specifying the nd and Xd arguments (“d†for demographic):

X2 <- createX(p=10, na=NULL, Xa=NULL, nd=2, Xd=as.matrix(marg[,c(13,16)]), base=1)
print(X2[1:10,1:9]); cat("\n")
print(X2[1:10,10:18])
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
##  [1,]    0    0    0    0    0    0    0    0    0
##  [2,]    1    0    0    0    0    0    0    0    0
##  [3,]    0    1    0    0    0    0    0    0    0
##  [4,]    0    0    1    0    0    0    0    0    0
##  [5,]    0    0    0    1    0    0    0    0    0
##  [6,]    0    0    0    0    1    0    0    0    0
##  [7,]    0    0    0    0    0    1    0    0    0
##  [8,]    0    0    0    0    0    0    1    0    0
##  [9,]    0    0    0    0    0    0    0    1    0
## [10,]    0    0    0    0    0    0    0    0    1
## 
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
##  [1,]  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
##  [2,] 32.5  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
##  [3,]  0.0 32.5  0.0  0.0  0.0  0.0  0.0  0.0  0.0
##  [4,]  0.0  0.0 32.5  0.0  0.0  0.0  0.0  0.0  0.0
##  [5,]  0.0  0.0  0.0 32.5  0.0  0.0  0.0  0.0  0.0
##  [6,]  0.0  0.0  0.0  0.0 32.5  0.0  0.0  0.0  0.0
##  [7,]  0.0  0.0  0.0  0.0  0.0 32.5  0.0  0.0  0.0
##  [8,]  0.0  0.0  0.0  0.0  0.0  0.0 32.5  0.0  0.0
##  [9,]  0.0  0.0  0.0  0.0  0.0  0.0  0.0 32.5  0.0
## [10,]  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0 32.5

Notice that createX again uses \(p-1\) dummy variables to distinguish the \(p\) choice alternatives. However, for demographic variables, the value of the demographic variable is spread across \(p-1\) columns and \(p-1\) rows.

4.4.2 Model

The logit specification was originally derived by Luce (1959) from assumptions on characteristics of choice probabilities. McFadden (1974) tied the model to rational economic theory by showing how the multinomial logit specification models choices made by a utility-maximizing consumer, assuming that the unobserved utility component is distributed Type I Extreme Value. We motivate use of this model following McFadden by assuming the decision maker chooses the alternative providing him with the highest utility, where the utility \(U_{ij}\) from the choice \(y_{ij}\) made by a decision maker in choice situation \(i\) for product \(j = 1, \ldots, p\) is modeled as the sum of a deterministic and a stochastic component:

\[ U_{ij} = V_{ij} + \varepsilon_{ij} \hspace{2em} \text{with } \varepsilon_{ij}\ \sim \text{ iid T1EV} \]

Regressors (both demographic and alternative-specific) are included in the model by assuming \(V_{ij} = x_{ij}'\beta\). These assumptions result in choice probabilities of:

\[ \text{Pr}(y_i=j) = \frac{\exp \{x_{ij}'\beta\}}{\sum_{k=1}^p\exp\{x_{ik}'\beta\}} \]

Independent priors for the components of the beta vector are specified as normal distributions. Using notation for the multivariate normal distribution, we have:

\[ \beta \sim MVN(\bar{\beta},\ A^{-1}) \]

We use bayesm’s default values for the parameters of the priors: \(\bar{\beta} = 0\) and \(A = 0.01I\).

4.4.3 Bayesian Estimation

Experience with the MNL likelihood is that the asymptotic normal approximation is excellent. rmnlIndepMetrop implements an independent Metropolis algorithm to sample from the normal approximation to the posterior distribution of \(\beta\):

\[ p(\beta | X, y) \overset{\cdot}{\propto} |H|^{1/2} \exp \left\{ \frac{1}{2}(\beta - \hat{\beta})'H(\beta - \hat{\beta}) \right\} \]

where \(\hat{\beta}\) is the MLE, \(H = \sum_i x_i A_i x_i'\), and the candidate distribution used in the Metropolis algorithm is the multivariate student t. For more detail, see Section 11 of BSM Chapter 3.

We sample from the normal approximation to the posterior as follows:

X <- cbind(X1, X2[,10:ncol(X2)])
out <- rmnlIndepMetrop(Data = list(y=y, X=X, p=10), 
                       Mcmc = list(R=1e4, nprint=1e3))

rmnlIndepMetrop returns a list that we have saved in out. The list contains 3 elements, betadraw, loglike, and acceptr, which you can verify by running str(out). betadraw is a \(10,000 \times 28\) dimension matrix with class bayesm.mat. As with the linear regression of Example 1 above, we can plot or summarize features of the the posterior distribution in many ways. For information on each marginal posterior distribution, call summary(out) or plot(out). Because we have 28 covariates (intercepts and demographic variables make up 9 columns each and there is one column for the price variable) we omit the full set of results to save space and instead, we only present summary statistics for the marginal posterior distribution for \(\beta_\text{price}\):

summary.bayesm.mat(out$betadraw[,10], names = "Price")
## Summary of Posterior Marginal Distributions 
## Moments 
##       mean std dev num se rel eff sam size
## Price -6.7    0.18 0.0039     4.5     1800
## 
## Quantiles 
##       2.5% 5%  50%  95% 97.5%
## Price   -7 -7 -6.7 -6.4  -6.3
##    based on 9000 valid draws (burn-in=1000)

In addition to summary information for a marginal posterior distribution, we can plot it. We use bayesm’s plot generic function (calling plot(out$betadraw) would provide the same plots for all 28 \(X\) variables). In the histogram, the green bars delimit a 95% Bayesian credibility interval, yellow bars shows +/- 2 numerical standard errors for the posterior mean, and the red bar indicates the posterior mean. The subsequent two plots are a trace plot and and ACF plot.

plot.bayesm.mat(out$betadraw[,10], names = "Price")

We see that the posterior is approximately normally distributed with a mean of -6.7 and a standard deviation of 0.17. The trace plot shows good mixing. The ACF plot shows a fair amount of correlation such that, even though the algorithm took R = 10,000 draws, the Effective Sample Size (as reported in the summary stats above) is only 1,800.

Because of the nonlinearity in this model, interpreting the results is more difficult than with linear regression models. We do not elaborate further on the interpretation of coefficients and methods of displaying results from multinomial logit models, but for the uninitiated reader, we refer you to excellent sources for this information authored by Kenneth Train and Gary King.7

4.5 Example 3: Hierarchical Logit

4.5.1 Data

While we could add individual-specific parameters to the previous model and use the same dataset, we elect to provide the reader with greater variety. For this example, we use the camera dataset in bayesm, which contains conjoint choice data for 332 respondents who evaluated digital cameras. These data have already been processed to exclude respondents that always answered “noneâ€, always picked the same brand, always selected the highest priced offering, or who appeared to be answering randomly.

data(camera)
length(camera)
## [1] 332
str(camera[[1]])
## List of 2
##  $ y: int [1:16] 1 2 2 4 2 2 1 1 1 2 ...
##  $ X: num [1:80, 1:10] 0 1 0 0 0 0 1 0 0 0 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:80] "1" "2" "3" "4" ...
##   .. ..$ : chr [1:10] "canon" "sony" "nikon" "panasonic" ...
colnames(camera[[1]]$X)
##  [1] "canon"     "sony"      "nikon"     "panasonic" "pixels"   
##  [6] "zoom"      "video"     "swivel"    "wifi"      "price"

The camera data is stored in a list-of-lists format, which is the format required by bayesm’s posterior sampling functions for hierarchical models. This format has one list per individual with each list containing a vector y of choice outcomes and a matrix X of covariates. As with the multinomial logit model of the last example, y is a length-\(n_i\) vector (or one-column matrix) and X has dimensions \(n_ij \times k\) where \(n_i\) is the number of choice occasions faced by individual \(i\), \(j\) is the number of choice alternatives, and \(k\) is the number of covariates. For the camera data, \(N=332\), \(n_i=16\) for all \(i\), \(j=5\), and \(k=10\).

If your data were not in this format, it could be easily converted with a for loop and createX. For example, we can format margarine data from Example 2 above into a list-of-lists format with the following code, which simply loops over individuals, extracting and storing their y and X data one individual at a time:

data(margarine)
chpr <- margarine$choicePrice
chpr$hhid <- as.factor(chpr$hhid)
N <- nlevels(chpr$hhid)
dat <- vector(mode = "list", length = N)
for (i in 1:N) {
  dat[[i]]$y <- chpr[chpr$hhid==levels(chpr$hhid)[i], "choice"]
  dat[[i]]$X <- createX(p=10, na=1, Xa=chpr[chpr$hhid==levels(chpr$hhid)[i],3:12], nd=NULL, Xd=NULL)
}

Returning to the camera data, the first 4 covariates are binary indicators for the brands Canon, Sony, Nikon, and Panasonic. These correspond to choice (y) values of 1, 2, 3, and 4. y can also take the value 5, indicating that the respondent chose “noneâ€. The data include binary indicators for two levels of pixel count, zoom strength, swivel video display capability, and wifi connectivity. The last covaritate is price, recorded in hundreds of U.S. dollars (we leave price in these units so that we do not need to adjust the default prior settings).

When we look at overall choice outcomes, we see that the brands and the outside alternative (“noneâ€) are chosen roughly in fifths, with specific implied market shares ranging from 17%–25%:

N <- length(camera)
dat <- matrix(NA, N*16, 2)
for (i in 1:length(camera)) {
  Ni <- length(camera[[i]]$y)
  dat[((i-1)*Ni+1):(i*Ni),1] <- i
  dat[((i-1)*Ni+1):(i*Ni),2] <- camera[[i]]$y
}
round(prop.table(table(dat[,2])), 3)
## 
##     1     2     3     4     5 
## 0.207 0.176 0.195 0.169 0.253

However, when we look at a few individuals’ choices, we see much greater variability:

round(prop.table(table(dat[,1], dat[,2])[41:50,], 1), 3)
##     
##          1     2     3     4     5
##   41 0.188 0.000 0.312 0.500 0.000
##   42 0.250 0.125 0.312 0.312 0.000
##   43 0.312 0.188 0.125 0.125 0.250
##   44 0.000 0.000 0.188 0.188 0.625
##   45 0.312 0.250 0.125 0.125 0.188
##   46 0.375 0.250 0.062 0.062 0.250
##   47 0.188 0.062 0.062 0.250 0.438
##   48 0.125 0.500 0.188 0.125 0.062
##   49 0.062 0.125 0.500 0.188 0.125
##   50 0.000 0.125 0.375 0.250 0.250

It is this heterogeneity in individual choice that motivates us to employ a hierarchical model.

4.5.2 Model

Hierarchical (also known as multi-level, random-coefficient, or mixed) models allow each respondent to have his or her own coefficients. Different people have different preferences, and models that estimate individual-level coefficients can fit data better and make more accurate predictions than single-level models. These models are quite popular in marketing, as they allow, for example, promotions to be targeted to individuals with high promotional part worths — meaning those inviduals who are most likely to respond to the promotion. For more information, see Rossi et al. (1996).8

The model follows the multinomial logit specification given in Example 2 above where individuals are assumed to be rational economic agents that make utility-maximizing choices. Now, however, the model includes individual-level parameters (\(\beta_i\)) assumed to be drawn from a normal distribution and with mean values driven by cross-sectional unit characteristics \(Z\):

\[ y_i \sim \text{MNL}(x_i'\beta_i) \hspace{1em} \text{with} \hspace{1em} \beta_i = z_i' \Delta + u_i \hspace{1em} \text{and} \hspace{1em} u_i \sim MVN(\mu, \Sigma) \]

\(x_i\) is \(n_i \times k\) and \(i = 1, \ldots, N\).

We can alternatively write the middle equation as \(B=Z\Delta + U\) where \(\beta_i\), \(z_i\), and \(u_i\) are the \(i^\text{th}\) rows of \(B\), \(Z\), and \(U\). \(B\) is \(N \times k\), \(Z\) is \(N \times m\), \(\Delta\) is \(m \times k\), and \(U\) is \(N \times k\).

Note that we do not have any cross-sectional unit characteristics in the camera dataset and thus \(Z\) will be omitted.

The priors are:

\[ \text{vec}(\Delta) = \delta \sim MVN(\bar{\delta}, A_\delta^{-1}) \hspace{2em} \mu \sim MVN(\bar{\mu}, \Sigma \otimes a^{-1}) \hspace{2em} \Sigma \sim IW(\nu, V) \]

This specification of priors assumes that, conditional on the hyperparameters (that is, the parameters of the prior distribution), the \(\beta\)’s are a priori independent. This means that inference for each unit can be conducted independently of all other units, conditional on the hyperparameters, which is the Bayesian analogue of the fixed effects approach in classical statistics.

Note also that we have assumed a normal “first-stage†prior distribution over the \(\beta\)’s. rhierMnlRwMixture permits a more-flexible mixture-of-normals first-stage prior (hence the “mixture†in the function name). However, for our example, we will not include this added flexibility (Prior$ncomp = 1 below).

4.5.3 Bayesian Estimation

Although the model is more complex than the models used in the two previous examples, the increased programming difficulty for the researcher is minimal. As before, we specify Data, Prior, and Mcmc arguments, and call the posterior sampling function:

data  <- list(lgtdata = camera, p = 5)
prior <- list(ncomp = 1)
mcmc  <- list(R = 1e4, nprint = 0)

out <- rhierMnlRwMixture(Data = data, Prior = prior, Mcmc = mcmc)
## Z not specified
## Table of Y values pooled over all units
## ypooled
##    1    2    3    4    5 
## 1100  936 1035  898 1343 
##  
## Starting MCMC Inference for Hierarchical Logit:
##    Normal Mixture with 1 components for first stage prior
##    5  alternatives;  10  variables in X
##    for  332  cross-sectional units
##  
## Prior Parms: 
## nu = 13
## V 
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]   13    0    0    0    0    0    0    0    0     0
##  [2,]    0   13    0    0    0    0    0    0    0     0
##  [3,]    0    0   13    0    0    0    0    0    0     0
##  [4,]    0    0    0   13    0    0    0    0    0     0
##  [5,]    0    0    0    0   13    0    0    0    0     0
##  [6,]    0    0    0    0    0   13    0    0    0     0
##  [7,]    0    0    0    0    0    0   13    0    0     0
##  [8,]    0    0    0    0    0    0    0   13    0     0
##  [9,]    0    0    0    0    0    0    0    0   13     0
## [10,]    0    0    0    0    0    0    0    0    0    13
## mubar 
##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,]    0    0    0    0    0    0    0    0    0     0
## Amu 
##      [,1]
## [1,] 0.01
## a 
## [1] 5
##  
## MCMC Parms: 
## s= 0.753  w=  0.1  R=  10000  keep=  1  nprint=  0
## 
## initializing Metropolis candidate densities for  332  units ...
##   completed unit # 50
##   completed unit # 100
##   completed unit # 150
##   completed unit # 200
##   completed unit # 250
##   completed unit # 300

We store the results in out, which is a list of length 4. The list elements are betadraw, nmix, loglike, and SignRes.

  • betadraw is a \(332 \times 10 \times 10,000\) array. These dimensions correspond to the number of individuals, the number of covariates, and the number of MCMC draws.

  • nmix is a list with elements probdraw, zdraw, and compdraw.

    • probdraw tells us the probability that each draw came from a particular normal component. This is relevant when there is a mixture-of-normals first-stage prior. However, since our specified prior over the \(\beta\) vector is one normal distribution, probdraw is a \(10,000 \times 1\) vector of all 1’s.

    • zdraw is NULL as it is not relevant for this function.

    • compdraw provides draws for the mixture-of-normals components. Here, compdraw is a list of 10,000 lists. The \(r^\text{th}\) of the 10,000 lists contains the \(r^\text{th}\) draw of the \(\mu\) vector (dim \(1 \times 10\)) and the Cholesky root of the \(r^\text{th}\) draw for the \(10 \times 10\) covariance matrix.

  • loglike is a \(10,000 \times 1\) vector that provides the log-likelihood of each draw.

  • SignRes relates to whether any sign restrictions were placed on the model. This is discussed in detail in a separate vignette detailing a contrainsted hierarchical multinomial logit model; it is not relevant here.

We can summarize results as before. plot(out$betadraw) provides plots for each variable that summarize the distributions of the individual parameters. For brevity, we provide just a histogram of posterior means for the 332 individual coefficients on wifi capability.

hist(apply(out$betadraw, 1:2, mean)[,9], col = "dodgerblue4", 
     xlab = "", ylab = "", yaxt="n", xlim = c(-4,6), breaks = 20,
     main = "Histogram of Posterior Means For Individual Wifi Coefs")

We see that the distribution of individual posterior means is skewed, suggesting that our assumption of a normal first-stage prior may be incorrect. We could improve this model by using the more flexible mixture-of-normals prior or, if we believe all consumers value wifi connectivity positively, we could impose a sign constraint on that set of parameters — both of which are demonstrated in the vignette for sign-constrained hierarchical multinomial logit.

5 Conclusion

We hope that this vignette has provided the reader with a thorough introduction to the bayesm package and is sufficient to enable immediate use of its posterior sampling functions for bayesian estimation. Comments or edits can be sent to the vignette authors at the email addresses below.


Authored by Dan Yavorsky and Peter Rossi. Last updated June 2017.


  1. For example, calling the generic function summary(x) on an object x with class bayesm.mat actually dispatches the method summary.bayesm.mat on x, which is equivalent to calling summary.bayes.mat(x). For a nice introduction, see Advanced R by Hadley Wickham, available online.↩

  2. Functions such as rivGibbs only permit one endogenous variable and so the function argument is lowercase: x.↩

  3. LHS and RHS stand for left-hand side and right-hand side.↩

  4. Rossi, Peter, Greg Allenby and Robert McCulloch, Bayesian Statistics and Marketing, John Wiley & Sons, 2005. Website.↩

  5. Cameron, Colin and Pravin Trivedi, Microeconometrics: Methods and Applications, Cambridge University Press, 2005.

    Davidson, Russell and James MacKinnon, Estimation and Inference in Econometrics, Oxford University Press, 1993.

    Goldberger, Arthur, A Course in Econometrics, Harvard University Press, 1991.

    Greene, William, Econometric Analysis, Prentice Hall, 2012 (7th edition).

    Wasserman, Larry, All of Statistics: A Concise Course in Statistical Inferece, Springer, 2004.

    Wooldridge, Jeffrey, Econometric Analysis of Cross Section and Panel Data, MIT Press, 2010 (2nd edition).↩

  6. Gelman, Andrew, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin, Bayesian Data Analysis, CRC Press, 2013 (3rd edition).

    Jackman, Simon, Bayesian Analysis for the Social Sciences, Wiley, 2009.

    Marin, Jean-Michel and Christian Robert, Bayesian Essentials with R, Springer, 2014 (2nd edition).

    Rossi, Peter, Greg Allenby, and Robert McCulloch, Bayesian Statistics and Marketing, Wiley, 2005.

    Zellner, Arnold, An Introduction to Bayesian Inference in Economics, Wiley, 1971.↩

  7. Train, Kenneth, Discrete Choice Models with Simulation Cambridge University Press, 2009.

    King, Gary Unifying Political Methodlogy: The Likelihood Theory of Statistical Inference, University of Michigan Press (1998) p. 108.

    King, Gary, Michael Tomz, and Jason Wittenberg, “Making the Most of Statistical Analyses: Improving Interpretation and Presentation†American Journal of Political Science, Vol. 44 (April 2000) pp. 347–361 at p. 355.↩

  8. Rossi, McCulloch, and Allenby “The Value of Purchase History Data in Target Marketing†Marketing Science (1996).↩

bayesm/inst/doc/Constrained_MNL_Vignette.R0000644000176000001440000001353313123305371020256 0ustar ripleyusers## ---- echo = FALSE------------------------------------------------------- library(bayesm) knitr::opts_chunk$set(fig.align = "center", fig.height = 3.5, warning = FALSE, error = FALSE, message = FALSE) ## ------------------------------------------------------------------------ # define function drawprior <- function (mubar_betak, nvar, ncomp, a, nu, Amu, V, ndraw) { betakstar <- double(ndraw) betak <- double(ndraw) otherbeta <- double(ndraw) mubar <- c(rep(0, nvar-1), mubar_betak) for(i in 1:ndraw) { comps=list() for(k in 1:ncomp) { Sigma <- rwishart(nu,chol2inv(chol(V)))$IW comps[[k]] <- list(mubar + t(chol(Sigma/Amu)) %*% rnorm(nvar), backsolve(chol(Sigma), diag(1,nvar)) ) } pvec <- rdirichlet(a) beta <- rmixture(1,pvec,comps)$x betakstar[i] <- beta[nvar] betak[i] <- -exp(beta[nvar]) otherbeta[i] <- beta[1] } return(list(betakstar=betakstar, betak=betak, otherbeta=otherbeta)) } set.seed(1234) ## ------------------------------------------------------------------------ # specify rhierMnlRwMixture defaults mubar_betak <- 0 nvar <- 10 ncomp <- 3 a <- rep(5, ncomp) nu <- nvar + 3 Amu <- 0.01 V <- nu*diag(c(rep(1,nvar-1),1)) ndraw <- 10000 defaultprior <- drawprior(mubar_betak, nvar, ncomp, a, nu, Amu, V, ndraw) ## ---- fig.align='center', fig.height=3.5, results='hold'----------------- # plot priors under defaults par(mfrow=c(1,3)) trimhist <- -20 hist(defaultprior$betakstar, breaks=40, col="magenta", main="Beta_k_star", xlab="", ylab="", yaxt="n") hist(defaultprior$betak[defaultprior$betak>trimhist], breaks=40, col="magenta", main="Beta_k", xlab="", ylab="", yaxt="n", xlim=c(trimhist,0)) hist(defaultprior$otherbeta, breaks=40, col="magenta", main="Other Beta", xlab="", ylab="", yaxt="n") ## ------------------------------------------------------------------------ # adjust priors for constraints mubar_betak <- 2 nvar <- 10 ncomp <- 3 a <- rep(5, ncomp) nu <- nvar + 15 Amu <- 0.1 V <- nu*diag(c(rep(4,nvar-1),0.1)) ndraw <- 10000 tightprior <- drawprior(mubar_betak, nvar, ncomp, a, nu, Amu, V, ndraw) ## ---- fig.align='center', fig.height=3.5, results='hold'----------------- # plot priors under adjusted values par(mfrow=c(1,3)) trimhist <- -20 hist(tightprior$betakstar, breaks=40, col="magenta", main="Beta_k_star", xlab="", ylab="", yaxt="n") hist(tightprior$betak[tightprior$betak>trimhist], breaks=40, col="magenta", main="Beta_k", xlab="", ylab="", yaxt="n", xlim=c(trimhist,0)) hist(tightprior$otherbeta, breaks=40, col="magenta", main="Other Beta", xlab="", ylab="", yaxt="n") ## ------------------------------------------------------------------------ library(bayesm) data(camera) length(camera) str(camera[[1]]) ## ------------------------------------------------------------------------ str(camera[[1]]$y) str(as.data.frame(camera[[1]]$X)) ## ---- echo = FALSE------------------------------------------------------- nvar <- 10 mubar <- c(rep(0,nvar-1),2) Amu <- 0.1 ncomp <- 5 a <- rep(5, ncomp) nu <- 25 V <- nu*diag(c(rep(4,nvar-1),0.1)) ## ---- eval = FALSE------------------------------------------------------- # SignRes <- c(rep(0,nvar-1),-1) # # data <- list(lgtdata=camera, p=5) # prior <- list(mubar=mubar, Amu=Amu, ncomp=ncomp, a=a, nu=nu, V=V, SignRes=SignRes) # mcmc <- list(R=1e4, nprint=0) # # out <- rhierMnlRwMixture(Data=data, Prior=prior, Mcmc=mcmc) ## ---- echo = FALSE------------------------------------------------------- temp <- capture.output( {SignRes <- c(rep(0,nvar-1),-1); data <- list(lgtdata = camera, p = 5); prior <- list(mubar=mubar, Amu=Amu, ncomp=ncomp, a=a, nu=nu, V=V, SignRes=SignRes); mcmc <- list(R = 1e4, nprint = 0); out <- rhierMnlRwMixture(Data = data, Prior = prior, Mcmc = mcmc)}, file = NULL) ## ------------------------------------------------------------------------ par(mfrow=c(1,3)) ind_hist <- function(mod, i) { hist(mod$betadraw[i , 10, ], breaks = seq(-14,0,0.5), col = "dodgerblue3", border = "grey", yaxt = "n", xlim = c(-14,0), xlab = "", ylab = "", main = paste("Ind.",i)) } ind_hist(out,1) ind_hist(out,2) ind_hist(out,3) ## ------------------------------------------------------------------------ par(mfrow=c(1,1)) hist(apply(out$betadraw[ , 10, ], 1, mean), xlim = c(-20,0), breaks = 20, col = "firebrick2", border = "gray", xlab = "", ylab = "", main = "Posterior Means for Ind. Price Params, With Sign Constraint") ## ------------------------------------------------------------------------ data0 <- list(lgtdata = camera, p = 5) prior0 <- list(ncomp = 5) mcmc0 <- list(R = 1e4, nprint = 0) ## ---- eval = FALSE------------------------------------------------------- # out0 <- rhierMnlRwMixture(Data = data0, Prior = prior0, Mcmc = mcmc0) ## ---- echo = FALSE------------------------------------------------------- temp <- capture.output( {out0 <- rhierMnlRwMixture(Data = data0, Prior = prior0, Mcmc = mcmc0)}, file = NULL) ## ------------------------------------------------------------------------ par(mfrow=c(1,3)) ind_hist <- function(mod, i) { hist(mod$betadraw[i , 10, ], breaks = seq(-12,2,0.5), col = "dodgerblue4", border = "grey", yaxt = "n", xlim = c(-12,2), xlab = "", ylab = "", main = paste("Ind.",i)) } ind_hist(out0,1) ind_hist(out0,2) ind_hist(out0,3) ## ------------------------------------------------------------------------ par(mfrow=c(1,1)) hist(apply(out0$betadraw[ , 10, ], 1, mean), xlim = c(-15,5), breaks = 20, col = "firebrick3", border = "gray", xlab = "", ylab = "", main = "Posterior Means for Ind. Price Params, No Sign Constraint") bayesm/inst/doc/Constrained_MNL_Vignette.html0000644000176000001440000566557213123305372021047 0ustar ripleyusers Hierarchical Multinomial Logit with Sign Constraints

Introduction

bayesm’s posterior sampling function rhierMnlRwMixture permits the imposition of sign constraints on the individual-specific parameters of a hierarchical multinomial logit model. This may be desired if, for example, the researcher believes there are heterogenous effects from, say, price, but that all responses should be negative (i.e., sign-constrained). This vignette provides exposition of the model, discussion of prior specification, and an example.

Model

The model follows the hierarchical multinomial logit specification given in Example 3 of the “bayesm Overview†Vignette, but will be repeated here succinctly. Individuals are assumed to be rational economic agents that make utility-maximizing choices. Utility is modeled as the sum of deterministic and stochastic components, where the inverse-logit of the probability of chosing an alternative is linear in the parameters and the error is assumed to follow a Type I Extreme Value distribution:

\[ U_{ij} = X_{ij}\beta_i + \varepsilon_{ij} \hspace{0.8em} \text{with} \hspace{0.8em} \varepsilon_{ij}\ \sim \text{ iid Type I EV} \]

These assumptions yield choice probabilities of:

\[ \text{Pr}(y_i=j) = \frac{\exp \{x_{ij}'\beta_i\}}{\sum_{k=1}^p\exp\{x_{ik}'\beta_i\}} \]

\(x_i\) is \(n_i \times k\) and \(i = 1, \ldots, N\). There are \(p\) alternatives, \(j = 1, \ldots, p\). An outside option, often denoted \(j=0\) can be introduced by assigning \(0\)’s to that option’s covariate (\(x\)) values.

We impose sign constraints by defining a \(k\)-length constraint vector SignRes that takes values from the set \(\{-1, 0, 1\}\) to define \(\beta_{ik} = f(\beta_{ik}^*)\) where \(f(\cdot)\) is as follows:

\[ \beta_{ik} = f(\beta_{ik}^*) = \left\{ \begin{array}{lcl} \exp(\beta_{ik}^*) & \text{if} & \texttt{SignRes[k]} = 1 \\ \beta_{ik}^* & \text{if} & \texttt{SignRes[k]} = 0 \\ -\exp(\beta_{ik}^*) & \text{if} & \texttt{SignRes[k]} = -1 \\ \end{array} \right. \]

The “deep†individual-specific parameters (\(\beta_i^*\)) are assumed to be drawn from a mixture of \(M\) normal distributions with mean values driven by cross-sectional unit characteristics \(Z\). That is, \(\beta_i^* = z_i' \Delta + u_i\) where \(u_i\) has a mixture-of-normals distribution.1

Considering \(\beta_i^*\) a length-\(k\) row vector, we will stack the \(N\) \(\beta_i^*\)’s vertically and write:

\[ B=Z\Delta + U \] Thus we have \(\beta_i\), \(z_i\), and \(u_i\) as the \(i^\text{th}\) rows of \(B\), \(Z\), and \(U\). \(B\) is \(N \times k\), \(Z\) is \(N \times M\), \(\Delta\) is \(M \times k\), and \(U\) is \(N \times k\) where the distribution on \(U\) is such that:

\[ \Pr(\beta_{ik}^*) = \sum_{m=1}^M \pi_m \phi(z_i' \Delta \vert \mu_j, \Sigma_j) \]

\(\phi\) is the normal pdf.

Priors

Natural conjugate priors are specified:

\[ \pi \sim \text{Dirichlet}(a) \] \[ \text{vec}(\Delta) = \delta \sim MVN(\bar{\delta}, A_\delta^{-1}) \] \[ \mu_m \sim MVN(\bar{\mu}, \Sigma_m \otimes a_\mu^{-1}) \] \[ \Sigma_m \sim IW(\nu, V) \]

This specification of priors assumes that \(\mu_m\) is independent of \(\Sigma_m\) and that, conditional on the hyperparameters, the \(\beta_i\)’s are a priori independent.

\(a\) implements prior beliefs on the number of normal components in the mixture with a default of 5. \(\nu\) is a “tightness†parameter of the inverted-Wishart distribution and \(V\) is its location matrix. Without sign constraints, they default to \(\nu=k+3\) and \(V=\nu I\), which has the effect of centering the prior on \(I\) and making it “barely properâ€. \(a_\mu\) is a tightness parameter for the priors on \(\mu\), and when no sign constraints are imposed it defaults to an extremely diffuse prior of 0.01.

These defaults assume the logit coefficients (\(\beta_{ik}\)’s) are on the order of approximately 1 and, if so, are typically reasonable hyperprior values. However, when sign constraints are imposed, say, SignRes[k]=-1 such that \(\beta_{ik} = -\exp\{\beta_{ik}^*\}\), then these hyperprior defults pile up mass near zero — a result that follows from the nature of the exponential function and the fact that the \(\beta_{ik}^*\)’s are on the log scale. Let’s show this graphically.

# define function
drawprior <- function (mubar_betak, nvar, ncomp, a, nu, Amu, V, ndraw) {
  betakstar <- double(ndraw)
  betak     <- double(ndraw)
  otherbeta <- double(ndraw)
  mubar     <- c(rep(0, nvar-1), mubar_betak)
  
  for(i in 1:ndraw) {
    comps=list()
    for(k in 1:ncomp) {
      Sigma <- rwishart(nu,chol2inv(chol(V)))$IW
      comps[[k]] <- list(mubar + t(chol(Sigma/Amu)) %*% rnorm(nvar), 
                         backsolve(chol(Sigma), diag(1,nvar)) )
    }
    pvec         <- rdirichlet(a)
    beta         <- rmixture(1,pvec,comps)$x
    betakstar[i] <- beta[nvar]
    betak[i]     <- -exp(beta[nvar])
    otherbeta[i] <- beta[1]
  }
  
  return(list(betakstar=betakstar, betak=betak, otherbeta=otherbeta))
}
set.seed(1234)
# specify rhierMnlRwMixture defaults
mubar_betak <- 0
nvar  <- 10
ncomp <- 3
a     <- rep(5, ncomp)
nu    <- nvar + 3
Amu   <- 0.01
V     <- nu*diag(c(rep(1,nvar-1),1))
ndraw <- 10000
defaultprior <- drawprior(mubar_betak, nvar, ncomp, a, nu, Amu, V, ndraw)
# plot priors under defaults
par(mfrow=c(1,3))
trimhist <- -20
hist(defaultprior$betakstar, breaks=40, col="magenta", 
     main="Beta_k_star", xlab="", ylab="", yaxt="n")
hist(defaultprior$betak[defaultprior$betak>trimhist],
     breaks=40, col="magenta", main="Beta_k",
     xlab="", ylab="", yaxt="n", xlim=c(trimhist,0))
hist(defaultprior$otherbeta, breaks=40, col="magenta",
     main="Other Beta", xlab="", ylab="", yaxt="n")

We see that the hyperprior values for constrained logit parameters are far from uninformative. As a result, rhierMnlRwMixture implements different default priors for parameters when sign constraints are imposed. In particular, \(a_\mu=0.1\), \(\nu = k + 15\), and \(V = \nu*\text{diag}(d)\) where \(d_i=4\) if \(\beta_{ik}\) is unconstrained and \(d_i=0.1\) if \(\beta_{ik}\) is constrained. Additionally, \(\bar{\mu}_m = 0\) if unconstrained and \(\bar{\mu}_m = 2\) otherwise. As the following plots show, this yields substantially less informative hyperpriors on \(\beta_{ik}^*\) without significantly affecting the hyperpriors on \(\beta_{ik}\) or \(\beta_{ij}\) (\(j \ne k\)).

# adjust priors for constraints
mubar_betak <- 2
nvar  <- 10
ncomp <- 3 
a     <- rep(5, ncomp)
nu    <- nvar + 15
Amu   <- 0.1 
V     <- nu*diag(c(rep(4,nvar-1),0.1))
ndraw <- 10000
tightprior <- drawprior(mubar_betak, nvar, ncomp, a, nu, Amu, V, ndraw)
# plot priors under adjusted values
par(mfrow=c(1,3))
trimhist <- -20
hist(tightprior$betakstar, breaks=40, col="magenta", 
     main="Beta_k_star", xlab="", ylab="", yaxt="n")
hist(tightprior$betak[tightprior$betak>trimhist],
     breaks=40, col="magenta", main="Beta_k",
     xlab="", ylab="", yaxt="n", xlim=c(trimhist,0))
hist(tightprior$otherbeta, breaks=40, col="magenta", 
     main="Other Beta", xlab="", ylab="", yaxt="n")

Example

Here we demonstrate the implementation of the hierarchical multinomial logit model with sign-constrained parameters. We return to the camera data used in Example 3 of the “bayesm Overview†Vignette. This dataset contains conjoint choice data for 332 respondents who evaluated digital cameras. The data are stored in a lists-of-lists format with one list per respondent, and each respondent’s list having two elements: a vector of choices (y) and a matrix of covariates (X). Notice the dimensions: there is one value for each choice occasion in each individual’s y vector but one row per alternative in each individual’s X matrix, making nrow(x) = 5 \(\times\) length(y) because there are 5 alternatives per choice occasion.

library(bayesm)
data(camera)
length(camera)
## [1] 332
str(camera[[1]])
## List of 2
##  $ y: int [1:16] 1 2 2 4 2 2 1 1 1 2 ...
##  $ X: num [1:80, 1:10] 0 1 0 0 0 0 1 0 0 0 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:80] "1" "2" "3" "4" ...
##   .. ..$ : chr [1:10] "canon" "sony" "nikon" "panasonic" ...

As shown next, the first 4 covariates are binary indicators for the brands Canon, Sony, Nikon, and Panasonic. These correspond to choice (y) values of 1, 2, 3, and 4. y can also take the value 5, indicating that the respondent chose “noneâ€. The data include binary indicators for two levels of pixel count, zoom strength, swivel video display capability, and wifi connectivity. The last covaritate is price, recorded in hundreds of U.S. dollars so that the magnitude of the expected price coefficient is such that the default prior settings in rhierMnlRwMixture do not need to be adjusted.

str(camera[[1]]$y)
##  int [1:16] 1 2 2 4 2 2 1 1 1 2 ...
str(as.data.frame(camera[[1]]$X))
## 'data.frame':    80 obs. of  10 variables:
##  $ canon    : num  0 1 0 0 0 0 1 0 0 0 ...
##  $ sony     : num  0 0 0 1 0 0 0 1 0 0 ...
##  $ nikon    : num  1 0 0 0 0 0 0 0 1 0 ...
##  $ panasonic: num  0 0 1 0 0 1 0 0 0 0 ...
##  $ pixels   : num  0 1 0 0 0 1 1 1 1 0 ...
##  $ zoom     : num  1 1 0 1 0 0 0 0 0 0 ...
##  $ video    : num  0 0 0 0 0 0 1 1 1 0 ...
##  $ swivel   : num  1 1 0 1 0 1 0 0 1 0 ...
##  $ wifi     : num  0 1 1 0 0 0 1 1 1 0 ...
##  $ price    : num  0.79 2.29 1.29 2.79 0 2.79 0.79 1.79 1.29 0 ...

Let’s say we would like to estimate the part-worths of the various attributes of these digital cameras using a multinomial logit model. To incorporate individual-level heterogeneous effects, we elect to use a hierarchical (i.e., random coefficient) specification. Further, we believe that despite the heterogeneity, each consumer’s estimate price response (\(\beta_{i,\text{price}}\)) should be negative, which we will impose with a sign constraint. Following the above discussion, we use the default priors, which “adjust†automatically when sign constraints are imposed.

SignRes <- c(rep(0,nvar-1),-1)

data  <- list(lgtdata=camera, p=5)
prior <- list(mubar=mubar, Amu=Amu, ncomp=ncomp, a=a, nu=nu, V=V, SignRes=SignRes)
mcmc  <- list(R=1e4, nprint=0)

out <- rhierMnlRwMixture(Data=data, Prior=prior, Mcmc=mcmc)

While much can be done to analyze the output, we will focus here on the constrained parameters on price. We first plot the posterior distributions for the price parameter for individuals \(i=1,2,3\). Notice that the posterior distributions for the selected individual’s price parameters lie entirely below zero.

par(mfrow=c(1,3))
ind_hist <- function(mod, i) {
  hist(mod$betadraw[i , 10, ], breaks = seq(-14,0,0.5), 
     col = "dodgerblue3", border = "grey", yaxt = "n",
     xlim = c(-14,0), xlab = "", ylab = "", main = paste("Ind.",i))
}
ind_hist(out,1)
ind_hist(out,2)
ind_hist(out,3)

Next we plot a histogram of the posterior means for the 332 individual price paramters (\(\beta_{i,\text{price}}\)):

par(mfrow=c(1,1))
hist(apply(out$betadraw[ , 10, ], 1, mean), 
     xlim = c(-20,0), breaks = 20, 
     col = "firebrick2", border = "gray", xlab = "", ylab = "",
     main = "Posterior Means for Ind. Price Params, 
             With Sign Constraint")

As a point of comparison, we re-run the model without the sign constraint using the default priors (output omitted) and provide the same set of plots. Note now that the right tail of the posterior distribution of \(\beta_2^\text{price}\) extends to the right of zero.

data0  <- list(lgtdata = camera, p = 5)
prior0 <- list(ncomp = 5)
mcmc0  <- list(R = 1e4, nprint = 0)
out0 <- rhierMnlRwMixture(Data = data0, Prior = prior0, Mcmc = mcmc0)
par(mfrow=c(1,3))
ind_hist <- function(mod, i) {
  hist(mod$betadraw[i , 10, ], breaks = seq(-12,2,0.5), 
     col = "dodgerblue4", border = "grey", yaxt = "n",
     xlim = c(-12,2), xlab = "", ylab = "", main = paste("Ind.",i))
}
ind_hist(out0,1)
ind_hist(out0,2)
ind_hist(out0,3)

par(mfrow=c(1,1))
hist(apply(out0$betadraw[ , 10, ], 1, mean), 
     xlim = c(-15,5), breaks = 20, 
     col = "firebrick3", border = "gray", 
     xlab = "", ylab = "",
     main = "Posterior Means for Ind. Price Params, 
             No Sign Constraint")


Authored by Dan Yavorsky and Peter Rossi. Last updated June 2017.


  1. As documented in the helpfile for this function (accessible by ?bayesm::rhierMnlRwMixture), draws from the posterior of the constrained parameters (\(\beta\)) can be found in the output $betadraw while draws from the posterior of the unconstrained parameters (\(\beta^*\)) are available in $nmix$compdraw.↩

bayesm/inst/doc/Constrained_MNL_Vignette.Rmd0000644000176000001440000003260313117570164020605 0ustar ripleyusers--- title: "Hierarchical Multinomial Logit with Sign Constraints" output: rmarkdown::html_document: theme: spacelab highlight: pygments toc: true toc_float: true toc_depth: 3 number_sections: no fig_caption: yes vignette: > %\VignetteIndexEntry{Hierarchical Multinomial Logit with Sign Constraints} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r, echo = FALSE} library(bayesm) knitr::opts_chunk$set(fig.align = "center", fig.height = 3.5, warning = FALSE, error = FALSE, message = FALSE) ``` ***** # Introduction `bayesm`'s posterior sampling function `rhierMnlRwMixture` permits the imposition of sign constraints on the individual-specific parameters of a hierarchical multinomial logit model. This may be desired if, for example, the researcher believes there are heterogenous effects from, say, price, but that all responses should be negative (i.e., sign-constrained). This vignette provides exposition of the model, discussion of prior specification, and an example. # Model The model follows the hierarchical multinomial logit specification given in Example 3 of the "`bayesm` Overview" Vignette, but will be repeated here succinctly. Individuals are assumed to be rational economic agents that make utility-maximizing choices. Utility is modeled as the sum of deterministic and stochastic components, where the inverse-logit of the probability of chosing an alternative is linear in the parameters and the error is assumed to follow a Type I Extreme Value distribution: $$ U_{ij} = X_{ij}\beta_i + \varepsilon_{ij} \hspace{0.8em} \text{with} \hspace{0.8em} \varepsilon_{ij}\ \sim \text{ iid Type I EV} $$ These assumptions yield choice probabilities of: $$ \text{Pr}(y_i=j) = \frac{\exp \{x_{ij}'\beta_i\}}{\sum_{k=1}^p\exp\{x_{ik}'\beta_i\}} $$ $x_i$ is $n_i \times k$ and $i = 1, \ldots, N$. There are $p$ alternatives, $j = 1, \ldots, p$. An outside option, often denoted $j=0$ can be introduced by assigning $0$'s to that option's covariate ($x$) values. We impose sign constraints by defining a $k$-length constraint vector `SignRes` that takes values from the set $\{-1, 0, 1\}$ to define $\beta_{ik} = f(\beta_{ik}^*)$ where $f(\cdot)$ is as follows: $$ \beta_{ik} = f(\beta_{ik}^*) = \left\{ \begin{array}{lcl} \exp(\beta_{ik}^*) & \text{if} & \texttt{SignRes[k]} = 1 \\ \beta_{ik}^* & \text{if} & \texttt{SignRes[k]} = 0 \\ -\exp(\beta_{ik}^*) & \text{if} & \texttt{SignRes[k]} = -1 \\ \end{array} \right. $$ The "deep" individual-specific parameters ($\beta_i^*$) are assumed to be drawn from a mixture of $M$ normal distributions with mean values driven by cross-sectional unit characteristics $Z$. That is, $\beta_i^* = z_i' \Delta + u_i$ where $u_i$ has a mixture-of-normals distribution.^[As documented in the helpfile for this function (accessible by `?bayesm::rhierMnlRwMixture`), draws from the posterior of the constrained parameters ($\beta$) can be found in the output `$betadraw` while draws from the posterior of the unconstrained parameters ($\beta^*$) are available in `$nmix$compdraw`.] Considering $\beta_i^*$ a length-$k$ row vector, we will stack the $N$ $\beta_i^*$'s vertically and write: $$ B=Z\Delta + U $$ Thus we have $\beta_i$, $z_i$, and $u_i$ as the $i^\text{th}$ rows of $B$, $Z$, and $U$. $B$ is $N \times k$, $Z$ is $N \times M$, $\Delta$ is $M \times k$, and $U$ is $N \times k$ where the distribution on $U$ is such that: $$ \Pr(\beta_{ik}^*) = \sum_{m=1}^M \pi_m \phi(z_i' \Delta \vert \mu_j, \Sigma_j) $$ $\phi$ is the normal pdf. # Priors Natural conjugate priors are specified: $$ \pi \sim \text{Dirichlet}(a) $$ $$ \text{vec}(\Delta) = \delta \sim MVN(\bar{\delta}, A_\delta^{-1}) $$ $$ \mu_m \sim MVN(\bar{\mu}, \Sigma_m \otimes a_\mu^{-1}) $$ $$ \Sigma_m \sim IW(\nu, V) $$ This specification of priors assumes that $\mu_m$ is independent of $\Sigma_m$ and that, conditional on the hyperparameters, the $\beta_i$'s are _a priori_ independent. $a$ implements prior beliefs on the number of normal components in the mixture with a default of 5. $\nu$ is a "tightness" parameter of the inverted-Wishart distribution and $V$ is its location matrix. Without sign constraints, they default to $\nu=k+3$ and $V=\nu I$, which has the effect of centering the prior on $I$ and making it "barely proper". $a_\mu$ is a tightness parameter for the priors on $\mu$, and when no sign constraints are imposed it defaults to an extremely diffuse prior of 0.01. These defaults assume the logit coefficients ($\beta_{ik}$'s) are on the order of approximately 1 and, if so, are typically reasonable hyperprior values. However, when sign constraints are imposed, say, `SignRes[k]=-1` such that $\beta_{ik} = -\exp\{\beta_{ik}^*\}$, then these hyperprior defults pile up mass near zero --- a result that follows from the nature of the exponential function and the fact that the $\beta_{ik}^*$'s are on the log scale. Let's show this graphically. ```{r} # define function drawprior <- function (mubar_betak, nvar, ncomp, a, nu, Amu, V, ndraw) { betakstar <- double(ndraw) betak <- double(ndraw) otherbeta <- double(ndraw) mubar <- c(rep(0, nvar-1), mubar_betak) for(i in 1:ndraw) { comps=list() for(k in 1:ncomp) { Sigma <- rwishart(nu,chol2inv(chol(V)))$IW comps[[k]] <- list(mubar + t(chol(Sigma/Amu)) %*% rnorm(nvar), backsolve(chol(Sigma), diag(1,nvar)) ) } pvec <- rdirichlet(a) beta <- rmixture(1,pvec,comps)$x betakstar[i] <- beta[nvar] betak[i] <- -exp(beta[nvar]) otherbeta[i] <- beta[1] } return(list(betakstar=betakstar, betak=betak, otherbeta=otherbeta)) } set.seed(1234) ``` ```{r} # specify rhierMnlRwMixture defaults mubar_betak <- 0 nvar <- 10 ncomp <- 3 a <- rep(5, ncomp) nu <- nvar + 3 Amu <- 0.01 V <- nu*diag(c(rep(1,nvar-1),1)) ndraw <- 10000 defaultprior <- drawprior(mubar_betak, nvar, ncomp, a, nu, Amu, V, ndraw) ``` ```{r, fig.align='center', fig.height=3.5, results='hold'} # plot priors under defaults par(mfrow=c(1,3)) trimhist <- -20 hist(defaultprior$betakstar, breaks=40, col="magenta", main="Beta_k_star", xlab="", ylab="", yaxt="n") hist(defaultprior$betak[defaultprior$betak>trimhist], breaks=40, col="magenta", main="Beta_k", xlab="", ylab="", yaxt="n", xlim=c(trimhist,0)) hist(defaultprior$otherbeta, breaks=40, col="magenta", main="Other Beta", xlab="", ylab="", yaxt="n") ``` We see that the hyperprior values for constrained logit parameters are far from uninformative. As a result, `rhierMnlRwMixture` implements different default priors for parameters when sign constraints are imposed. In particular, $a_\mu=0.1$, $\nu = k + 15$, and $V = \nu*\text{diag}(d)$ where $d_i=4$ if $\beta_{ik}$ is unconstrained and $d_i=0.1$ if $\beta_{ik}$ is constrained. Additionally, $\bar{\mu}_m = 0$ if unconstrained and $\bar{\mu}_m = 2$ otherwise. As the following plots show, this yields substantially less informative hyperpriors on $\beta_{ik}^*$ without significantly affecting the hyperpriors on $\beta_{ik}$ or $\beta_{ij}$ ($j \ne k$). ```{r} # adjust priors for constraints mubar_betak <- 2 nvar <- 10 ncomp <- 3 a <- rep(5, ncomp) nu <- nvar + 15 Amu <- 0.1 V <- nu*diag(c(rep(4,nvar-1),0.1)) ndraw <- 10000 tightprior <- drawprior(mubar_betak, nvar, ncomp, a, nu, Amu, V, ndraw) ``` ```{r, fig.align='center', fig.height=3.5, results='hold'} # plot priors under adjusted values par(mfrow=c(1,3)) trimhist <- -20 hist(tightprior$betakstar, breaks=40, col="magenta", main="Beta_k_star", xlab="", ylab="", yaxt="n") hist(tightprior$betak[tightprior$betak>trimhist], breaks=40, col="magenta", main="Beta_k", xlab="", ylab="", yaxt="n", xlim=c(trimhist,0)) hist(tightprior$otherbeta, breaks=40, col="magenta", main="Other Beta", xlab="", ylab="", yaxt="n") ``` # Example Here we demonstrate the implementation of the hierarchical multinomial logit model with sign-constrained parameters. We return to the `camera` data used in Example 3 of the "`bayesm` Overview" Vignette. This dataset contains conjoint choice data for 332 respondents who evaluated digital cameras. The data are stored in a lists-of-lists format with one list per respondent, and each respondent's list having two elements: a vector of choices (`y`) and a matrix of covariates (`X`). Notice the dimensions: there is one value for each choice occasion in each individual's `y` vector but one row per alternative in each individual's `X` matrix, making `nrow(x)` = 5 $\times$ `length(y)` because there are 5 alternatives per choice occasion. ```{r} library(bayesm) data(camera) length(camera) str(camera[[1]]) ``` As shown next, the first 4 covariates are binary indicators for the brands Canon, Sony, Nikon, and Panasonic. These correspond to choice (`y`) values of 1, 2, 3, and 4. `y` can also take the value 5, indicating that the respondent chose "none". The data include binary indicators for two levels of pixel count, zoom strength, swivel video display capability, and wifi connectivity. The last covaritate is price, recorded in hundreds of U.S. dollars so that the magnitude of the expected price coefficient is such that the default prior settings in `rhierMnlRwMixture` do not need to be adjusted. ```{r} str(camera[[1]]$y) str(as.data.frame(camera[[1]]$X)) ``` Let's say we would like to estimate the part-worths of the various attributes of these digital cameras using a multinomial logit model. To incorporate individual-level heterogeneous effects, we elect to use a hierarchical (i.e., random coefficient) specification. Further, we believe that despite the heterogeneity, each consumer's estimate price response ($\beta_{i,\text{price}}$) should be negative, which we will impose with a sign constraint. Following the above discussion, we use the default priors, which "adjust" automatically when sign constraints are imposed. ```{r, echo = FALSE} nvar <- 10 mubar <- c(rep(0,nvar-1),2) Amu <- 0.1 ncomp <- 5 a <- rep(5, ncomp) nu <- 25 V <- nu*diag(c(rep(4,nvar-1),0.1)) ``` ```{r, eval = FALSE} SignRes <- c(rep(0,nvar-1),-1) data <- list(lgtdata=camera, p=5) prior <- list(mubar=mubar, Amu=Amu, ncomp=ncomp, a=a, nu=nu, V=V, SignRes=SignRes) mcmc <- list(R=1e4, nprint=0) out <- rhierMnlRwMixture(Data=data, Prior=prior, Mcmc=mcmc) ``` ```{r, echo = FALSE} temp <- capture.output( {SignRes <- c(rep(0,nvar-1),-1); data <- list(lgtdata = camera, p = 5); prior <- list(mubar=mubar, Amu=Amu, ncomp=ncomp, a=a, nu=nu, V=V, SignRes=SignRes); mcmc <- list(R = 1e4, nprint = 0); out <- rhierMnlRwMixture(Data = data, Prior = prior, Mcmc = mcmc)}, file = NULL) ``` While much can be done to analyze the output, we will focus here on the constrained parameters on price. We first plot the posterior distributions for the price parameter for individuals $i=1,2,3$. Notice that the posterior distributions for the selected individual's price parameters lie entirely below zero. \begin{center} \textbf{Posterior Distributions for beta\_price} \end{center} ```{r} par(mfrow=c(1,3)) ind_hist <- function(mod, i) { hist(mod$betadraw[i , 10, ], breaks = seq(-14,0,0.5), col = "dodgerblue3", border = "grey", yaxt = "n", xlim = c(-14,0), xlab = "", ylab = "", main = paste("Ind.",i)) } ind_hist(out,1) ind_hist(out,2) ind_hist(out,3) ``` Next we plot a histogram of the posterior means for the 332 individual price paramters ($\beta_{i,\text{price}}$): ```{r} par(mfrow=c(1,1)) hist(apply(out$betadraw[ , 10, ], 1, mean), xlim = c(-20,0), breaks = 20, col = "firebrick2", border = "gray", xlab = "", ylab = "", main = "Posterior Means for Ind. Price Params, With Sign Constraint") ``` As a point of comparison, we re-run the model without the sign constraint using the default priors (output omitted) and provide the same set of plots. Note now that the right tail of the posterior distribution of $\beta_2^\text{price}$ extends to the right of zero. ```{r} data0 <- list(lgtdata = camera, p = 5) prior0 <- list(ncomp = 5) mcmc0 <- list(R = 1e4, nprint = 0) ``` ```{r, eval = FALSE} out0 <- rhierMnlRwMixture(Data = data0, Prior = prior0, Mcmc = mcmc0) ``` ```{r, echo = FALSE} temp <- capture.output( {out0 <- rhierMnlRwMixture(Data = data0, Prior = prior0, Mcmc = mcmc0)}, file = NULL) ``` ```{r} par(mfrow=c(1,3)) ind_hist <- function(mod, i) { hist(mod$betadraw[i , 10, ], breaks = seq(-12,2,0.5), col = "dodgerblue4", border = "grey", yaxt = "n", xlim = c(-12,2), xlab = "", ylab = "", main = paste("Ind.",i)) } ind_hist(out0,1) ind_hist(out0,2) ind_hist(out0,3) ``` ```{r} par(mfrow=c(1,1)) hist(apply(out0$betadraw[ , 10, ], 1, mean), xlim = c(-15,5), breaks = 20, col = "firebrick3", border = "gray", xlab = "", ylab = "", main = "Posterior Means for Ind. Price Params, No Sign Constraint") ``` ***** _Authored by [Dan Yavorsky](dyavorsky@gmail.com) and [Peter Rossi](perossichi@gmail.com). Last updated June 2017._ bayesm/inst/doc/bayesm_Overview_Vignette.R0000644000176000001440000001401413123305445020442 0ustar ripleyusers## ---- echo = FALSE------------------------------------------------------- library(bayesm) knitr::opts_chunk$set(fig.align = "center", fig.height = 3.5, warning = FALSE, error = FALSE, message = FALSE) ## ---- eval = FALSE------------------------------------------------------- # mydata <- list(y = y, X = X) # mymcmc <- list(R = 1e6, nprint = 0) # # out <- runireg(Data = mydata, Mcmc = mymcmc) ## ---- eval=FALSE--------------------------------------------------------- # mydata2 <- list(y, X) # out <- runireg(Data = mydata2, Mcmc = mymcmc) ## ------------------------------------------------------------------------ set.seed(66) R <- 2000 n <- 200 X <- cbind(rep(1,n), runif(n)) beta <- c(1,2) sigsq <- 0.25 y <- X %*% beta + rnorm(n, sd = sqrt(sigsq)) out <- runireg(Data = list(y = y, X = X), Mcmc = list(R = R, nprint = 0)) summary(out$betadraw, tvalues = beta) ## ------------------------------------------------------------------------ data(cheese) names(cheese) <- tolower(names(cheese)) str(cheese) ## ------------------------------------------------------------------------ options(digits=3) cor(cheese$volume, cheese$price) cor(cheese$volume, cheese$disp) ## ----fig.show = "hold"--------------------------------------------------- par(mfrow = c(1,2)) curve(dnorm(x,0,10), xlab = "", ylab = "", xlim = c(-30,30), main = expression(paste("Prior for ", beta[j])), col = "dodgerblue4") nu <- 3 ssq <- var(log(cheese$volume)) curve(nu*ssq/dchisq(x,nu), xlab = "", ylab = "", xlim = c(0,1), main = expression(paste("Prior for ", sigma^2)), col = "darkred") par(mfrow = c(1,1)) ## ---- eval = FALSE------------------------------------------------------- # dat <- list(y = log(cheese$volume), X = model.matrix( ~ price + disp, data = cheese)) # out <- runireg(Data = dat, Mcmc = list(R=1e4, nprint=1e3)) ## ---- echo = FALSE------------------------------------------------------- temp <- capture.output( {set.seed(1234); dat <- list(y = log(cheese$volume), X = model.matrix( ~ price + disp, data = cheese)); out <- runireg(Data = dat, Mcmc = list(R=1e4, nprint=1e3))}, file = NULL) ## ---- fig.show = "hold"-------------------------------------------------- B <- 1000+1 #burn in draws to discard R <- 10000 par(mfrow = c(1,2)) hist(out$betadraw[B:R,2], breaks = 30, main = "Posterior Dist. of Price Coef.", yaxt = "n", yaxs="i", xlab = "", ylab = "", col = "dodgerblue4", border = "gray") hist(out$sigmasqdraw[B:R], breaks = 30, main = "Posterior Dist. of Sigma2", yaxt = "n", yaxs="i", xlab = "", ylab = "", col = "darkred", border = "gray") par(mfrow = c(1,1)) ## ------------------------------------------------------------------------ apply(out$betadraw[B:R,2:3], 2, mean) ## ------------------------------------------------------------------------ summary(out$betadraw) ## ------------------------------------------------------------------------ plot.bayesm.mat(out$betadraw[,2]) ## ---- results = "hold"--------------------------------------------------- data(margarine) str(margarine) marg <- merge(margarine$choicePrice, margarine$demos, by = "hhid") ## ------------------------------------------------------------------------ y <- marg[,2] ## ------------------------------------------------------------------------ X1 <- createX(p=10, na=1, Xa=marg[,3:12], nd=NULL, Xd=NULL, base=1) colnames(X1) <- c(names(marg[,3:11]), "price") head(X1, n=10) ## ---- results = "hold"--------------------------------------------------- X2 <- createX(p=10, na=NULL, Xa=NULL, nd=2, Xd=as.matrix(marg[,c(13,16)]), base=1) print(X2[1:10,1:9]); cat("\n") print(X2[1:10,10:18]) ## ---- eval = FALSE------------------------------------------------------- # X <- cbind(X1, X2[,10:ncol(X2)]) # out <- rmnlIndepMetrop(Data = list(y=y, X=X, p=10), # Mcmc = list(R=1e4, nprint=1e3)) ## ---- echo = FALSE------------------------------------------------------- temp <- capture.output( {set.seed(1234); X <- cbind(X1, X2[,10:ncol(X2)]); out <- rmnlIndepMetrop(Data = list(y=y, X=X, p=10), Mcmc = list(R=1e4, nprint=1e3))}, file = NULL) ## ------------------------------------------------------------------------ summary.bayesm.mat(out$betadraw[,10], names = "Price") ## ------------------------------------------------------------------------ plot.bayesm.mat(out$betadraw[,10], names = "Price") ## ------------------------------------------------------------------------ data(camera) length(camera) str(camera[[1]]) colnames(camera[[1]]$X) ## ---- eval = FALSE------------------------------------------------------- # data(margarine) # chpr <- margarine$choicePrice # chpr$hhid <- as.factor(chpr$hhid) # N <- nlevels(chpr$hhid) # dat <- vector(mode = "list", length = N) # for (i in 1:N) { # dat[[i]]$y <- chpr[chpr$hhid==levels(chpr$hhid)[i], "choice"] # dat[[i]]$X <- createX(p=10, na=1, Xa=chpr[chpr$hhid==levels(chpr$hhid)[i],3:12], nd=NULL, Xd=NULL) # } ## ------------------------------------------------------------------------ N <- length(camera) dat <- matrix(NA, N*16, 2) for (i in 1:length(camera)) { Ni <- length(camera[[i]]$y) dat[((i-1)*Ni+1):(i*Ni),1] <- i dat[((i-1)*Ni+1):(i*Ni),2] <- camera[[i]]$y } round(prop.table(table(dat[,2])), 3) ## ------------------------------------------------------------------------ round(prop.table(table(dat[,1], dat[,2])[41:50,], 1), 3) ## ------------------------------------------------------------------------ data <- list(lgtdata = camera, p = 5) prior <- list(ncomp = 1) mcmc <- list(R = 1e4, nprint = 0) out <- rhierMnlRwMixture(Data = data, Prior = prior, Mcmc = mcmc) ## ------------------------------------------------------------------------ hist(apply(out$betadraw, 1:2, mean)[,9], col = "dodgerblue4", xlab = "", ylab = "", yaxt="n", xlim = c(-4,6), breaks = 20, main = "Histogram of Posterior Means For Individual Wifi Coefs") bayesm/inst/doc/bayesm_Overview_Vignette.Rmd0000644000176000001440000015530213117606056020776 0ustar ripleyusers--- title: "bayesm Overview" output: rmarkdown::html_document : theme: spacelab highlight: pygments toc: true toc_float: true toc_depth: 3 number_sections: yes fig_caption: yes vignette: > %\VignetteIndexEntry{bayesm Overview} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r, echo = FALSE} library(bayesm) knitr::opts_chunk$set(fig.align = "center", fig.height = 3.5, warning = FALSE, error = FALSE, message = FALSE) ``` ***** # Introduction `bayesm` is an R package that facilitates statistical analysis using Bayesian methods. The package provides a set of functions for commonly used models in applied microeconomics and quantitative marketing. The goal of this vignette is to make it easier for users to adopt `bayesm` by providing a comprehensive overview of the package's contents and detailed examples of certain functions. We begin with the overview, followed by a discussion of how to work with `bayesm`. The discussion covers the structure of function arguments, the required input data formats, and the various output formats. The final section provides detailed examples to demonstrate Bayesian inference with the linear normal, multinomial logit, and hierarchical multinomial logit regression models. # Package Contents For ease of exposition, we have grouped the package contents into: - Posterior sampling functions - Utility functions - S3 methods^[For example, calling the generic function `summary(x)` on an object `x` with class `bayesm.mat` actually dispatches the method `summary.bayesm.mat` on `x`, which is equivalent to calling `summary.bayes.mat(x)`. For a nice introduction, see _Advanced R_ by Hadley Wickham, available [online](http://adv-r.had.co.nz/OO-essentials.html).] - Datasets Because the first two groups contain many functions, we organize them into subgroups by purpose. Below, we display each group of functions in a table with one column per subgroup. ----------------------------------------------------------------------------- Linear Models Limited Dependent Hierarchical Models Density Estimation \ Variable Models \ \ --------------- -------------------- -------------------- ------------------- `runireg`* `rbprobitGibbs`** `rhierLinearModel` `rnmixGibbs`* `runiregGibbs` `rmnpGibbs` `rhierLinearMixture` `rDPGibbs` `rsurGibbs`* `rmvpGibbs` `rhierMnlRwMixture`* \ `rivGibbs` `rmnlIndepMetrop` `rhierMnlDP` \ `rivDP` `rscaleUsage` `rbayesBLP` \ \ `rnegbinRw` `rhierNegbinRw` \ \ `rordprobitGibbs` ----------------------------------------------------------------------------- Table: Posterior Sampling Functions *`bayesm` offers the utility function `breg` with a related but limited set of capabilities as `runireg` --- similarly with `rmultireg` for `rsurGibbs`, `rmixGibbs` for `rnmixGibbs`, and `rhierBinLogit` for `rhierMnlRwMixture`. **`rbiNormGibbs` provides a tutorial-like example of Gibbs Sampling from a bivariate normal distribution. ------------------------------------------------------------------------------------ Log-Likelihood\ \ Log Density Random Draws Mixture-of-Normals Miscellaneous (data vector) (univariate) \ \ \ ------------------ --------------- ------------- ------------------- --------------- `llmnl` `lndIChisq` `rdirichlet` `clusterMix` `cgetC` `llmnp` `lndIWishart` `rmixture` `eMixMargDen` `condMom` `llnhlogit` `lndMvn` `rmvst` `mixDen` `createX` \ `lndMvst` `rtrun` `mixDenBi` `ghkvec` \ \ `rwishart` `momMix` `logMargDenNR` \ \ \ \ `mnlHess` \ \ \ \ `mnpProb` \ \ \ \ `nmat` \ \ \ \ `numEff` \ \ \ \ `simnhlogit` ------------------------------------------------------------------------------------ Table: Utility Functions ------------------------------------------- Plot Methods Summary Methods -------------------- ---------------------- `plot.bayesm.mat` `summary.bayesm.mat` `plot.bayesm.nmix` `summary.bayesm.nmix` `plot.bayesm.hcoef` `summary.bayesm.var` ------------------------------------------- Table: S3 Methods --------------------------------------- \ \ \ --------- -------------- -------------- `bank` `customerSat` `orangeJuice` `camera` `detailing` `Scotch` `cheese` `margarine` `tuna` --------------------------------------- Table: Datasets Some discussion of the naming conventions may be warranted. All functions use CamelCase but begin lowercase. Posterior sampling functions begin with `r` to match R's style of naming random number generation functions since these functions all draw from (posterior) distributions. Common abbreviations include _DP_ for Dirichlet Process, _IV_ for instrumental variables, _MNL_ and _MNP_ for multinomial logit and probit, _SUR_ for seemingly unrelated regression, and _hier_ for hierarchical. Utility functions that begin with `ll` calculate the log-likelihood of a data vector, while those that begin with `lnd` provide the log-density. Other abbreviations should be straighforward; please see the help file for a specific function if its name is unclear. # Working with `bayesm` We expect most users of the package to interact primarily with the posterior sampling functions. These functions take a consistent set of arguments as inputs (`Data`, `Prior`, and `Mcmc` --- each is a list) and they return output in a consistent format (always a list). `summary` and `plot` generic functions can then be used to facilitate analysis of the output because of the classes and methods defined in `bayesm`. The following subsections describe the format of the standardized function arguments as well as the required format of the data inputs and the format of the output from `bayesm`'s posterior sampling functions. ## Input: Function Arguments The posterior sampling functions take three arguments: `Data`, `Prior`, and `Mcmc`. Each argument is a **list**. As a minimal example, assume you'd like to perform a linear regression and that you have in your work space `y` (a vector of length $n$) and `X` (a matrix of dimension $n \times p$). For this example, we utilize the default values for `Prior` and so we do not specify the `Prior` argument. These components (`Data`, `Prior`, and `Mcmc` as well as their arguments including `R` and `nprint`) are discussed in the subsections that follow. Then the `bayesm` syntax is simply: ```{r, eval = FALSE} mydata <- list(y = y, X = X) mymcmc <- list(R = 1e6, nprint = 0) out <- runireg(Data = mydata, Mcmc = mymcmc) ``` The list elements of `Data`, `Prior`, and `Mcmc` must be named. For example, you could not use the following code because the `Data` argument `mydata2` has unnamed elements. ```{r, eval=FALSE} mydata2 <- list(y, X) out <- runireg(Data = mydata2, Mcmc = mymcmc) ``` ### `Data` Argument `bayesm`'s posterior sampling functions do not accept data stored in dataframes; data must be stored as vectors or matrices. For **non-hierarchical** models, the list of input data simply contains the approprate data vectors or matrices from the set \{`y`, `X`, `w`, `z`\}^[Functions such as `rivGibbs` only permit one endogenous variable and so the function argument is lowercase: `x`.] and possibly a scalar (length one vector) from the set \{`k`, `p`\}. - For functions that require only a single data argument (such as the two density estimation functions, `rnmixGibbs` and `rDPGibbs`), `y` is that argument. More typically, `y` is used for LHS^[LHS and RHS stand for left-hand side and right-hand side.] variable(s) and `X` for RHS variables. For estimation using instrumental variables, variables in the structural equation are separated into "exogenous" variables `w` and an "edogenous" variable `x`; `z` is a matrix of instruments. - For the scalars, `p` indicates the number of choice alternatives in discrete choice models and `k` is used as the maximum ordinate in models for ordinal data (e.g., `rordprobitGibbs`). For **hierarchical** models, the input data has up to 3 components. We'll discuss these components using the mixed logit model (`rhierMnlRwMixture`) as an example. For `rhierMnlRwMixture`, the `Data` argument is `list(lgtdata, Z, p)`. 1. The first component for all hierarchical models is required. It is a list of lists named either `regdata` or `lgtdata`, depending on the function. In `rhierMnlRwMixture`, `lgtdata` is a list of lists, with each interior list containing a vector or one-column matrix of multinomial outcomes `y` and a design matrix of covariates `X`. In Example 3 below, we show how to convert data from a data frame to this required list-of-lists format. 1. The second component, `Z`, is present but optional for all hierarchical models. `Z` is a matrix of cross-sectional unit characteristics that drive the mean responses; that is, a matrix of covariates for the individual parameters (e.g. $\beta_i$'s). For example, the model (omitting the priors) for `rhierMnlRwMixture` is: $$ y_i \sim \text{MNL}(X_i'\beta_i) \hspace{1em} \text{with} \hspace{1em} \beta_i = Z \Delta_i + u_i \hspace{1em} \text{and} \hspace{1em} u_i \sim N(\mu_j, \Sigma_j) $$ where $i$ indexes individuals and $j$ indexes cross-sectional unit characteristics. 1. The third component (if accepted) is a scalar, such as `p` or `k`, and like the arguments by the same names in the non-hierarchical models, is used to indicate the size of the choice set or the maximum value of a scale or count variable. In `rhierMnlRwMixture`, the argument is `p`, which is used to indicate the number of choice alternatives. Note that `rbayesBLP` (the hierarchical logit model with _aggregate_ data as in Berry, Levinsohn, and Pakes (1995) and Jiang, Manchanda, and Rossi (2009)) deviates slightly from the standard data input. `rbayesBLP` uses `j` instead of `p` to be consistent with the literature and calls the LHS variable `share` rather than `y` to emphasize that aggregate (market share instead of individual choice) data are required. ### `Prior` Argument Specification of prior distributions is model-specific, so our discussion here is brief. All posterior sampling functions offer default values for parameters of prior distributions. These defaults were selected to yield proper yet reasonably-diffuse prior distributions (assuming the data are in approximately unit scale). In addition, these defaults are consistent across functions. For example, normal priors have default values of mean 0 with value 0.01 for the scaling factor of the prior precision matrix. Specification of the prior is important. Significantly more detail can be found in chapters 2--5 of BSM[^BSM] and the help files for the posterior sampling functions. We strongly recommend you consult them before accepting the default values. [^BSM]: Rossi, Peter, Greg Allenby and Robert McCulloch, _Bayesian Statistics and Marketing_, John Wiley \& Sons, 2005. [Website](http://www.perossi.org/home/bsm-1). ### `Mcmc` Argument {#mcmcarg} The `Mcmc` argument controls parameters of the sampling algorithm. The most common components of this list include: - `R`: the number of MCMC draws - `keep`: a thinning parameter indicating that every `keep`$^\text{th}$ draw should be retained - `nprint`: an option to print the estimated time remaining to the console after each `nprint`$^\text{th}$ draw MCMC methods are non-iid. As a result, a large simulation size may be required to get reliable results. We recommend setting `R` large enough to yield an adequate effective sample size and letting `keep` default to the value 1 unless doing so imposes memory constraints. A careful reader of the `bayesm` help files will notice that many of the examples set `R` equal to 1000 or less. This low number of draws was chosen for speed, as the examples are meant to demonstrate _how_ to run the code and do not necessarily suggest best practices for a proper statistical analysis. `nprint` defaults to 100, but for large `R`, you may want to increase the `nprint` option. Alternatively, you can set `nprint=0`, in which case the priors will still be printed to the console, but the estimated time remaining will not. Additional components of the `Mcmc` argument are function-specific, but typically include starting values for the algorithm. For example, the `Mcmc` argument for `runiregGibbs` takes `sigmasq` as a scalar element of the list. The Gibbs Sampler for `runiregGibbs` first draws $\beta | \sigma^2$, then draws $\sigma^2 | \beta$, and then repeats. For the first draw of $\beta$ in the MCMC chain, a value of $\sigma^2$ is required. The user can specify a value using `Mcmc$sigmasq`, or the user can omit the argument and the function will use its default (`sigmasq = var(Data$y)`). ## Output: Returned Results `bayesm` posterior sampling functions return a consistent set of results and output to the user. At a minimum, this output includes draws from the posterior distribution. `bayesm` provides a set of `summary` and `plot` methods to facilitate analysis of this output, but the user is free to analyze the results as he or she sees fit. ### Output Formats All `bayesm` posterior sampling functions return a list. The elements of that list include a set of vectors, matrices, and/or arrays (and possibly a list), the exact set of which depend on the function. - Vectors are returned for draws of parameters with no natural grouping. For example, `runireg` implements and iid sampler to draw from the posterior of a homoskedastic univariate regression with a conjugate prior (i.e., a Bayesian analog to OLS regression). One output list element is `sigmasqdraw`, a length `R/keep` vector for the scalar parameter $\sigma^2$. - Matrices are returned for draws of parameters with a natural grouping. Again using `runireg` as the example, the output list includes `betadraw`, an `R/keep` $\times$ `ncol(X)` matrix for the vector of $\beta$ parameters. Contrary to the next bullet, draws for the parameters in a variance-covariance matrix are returned in matrix form. For example, `rmnpGibbs` implements a Gibbs Sampler for a multinomial probit model where one set of parameters is the $(p-1) \times (p-1)$ matrix $\Sigma$. The output list for `rmnpGibbs` includes the list element `sigmadraw`, which is a matrix of dimension `R/keep`$\times (p-1)*(p-1)$ with each row containing a draw (in vector form) for all the elements of the matrix $\Sigma$. `bayesm`'s `summary` and `plot` methods (see below) are designed to handle this format. - Arrays are used when parameters have a natural matrix-grouping, such that the MCMC algorithm returns `R/keep` draws of the matrix. For example, `rsurGibbs` returns a list that includes `Sigmadraw`, an $m \times m \times$`R/keep` array, where $m$ is the number of regression equations. As a second example, `rhierLinearModel` estimates a hierarchical linear regression model with a normal prior, and returns a list that includes `betadraw`, an $n \times k \times$`R/keep` array, where $n$ signifies the number of individuals (each with their own $\beta_i$) and $k$ signifies the number of covariates (`ncol(X)` = $k$). - For functions that use a mixture-of-normals or Dirichlet Process prior, the output list includes a list (`nmix`) pertaining to that prior. `nmix` is itself a list with 3 components: `probdraw`, `zdraw`, and `compdraw`. `probdraw` reports the probability that each draw came from a particular normal component; `zdraw` indicates which mixture-of-normals component each draw is assigned to; and `compdraw` provides draws for the mixture-of-normals components (i.e., mean vectors and Cholesky roots of covariance matrices). Note that if you specify a "mixture" with only one normal component, there will be no useful information in `probdraw`. Also note that `zdraw` is not relevant for density estimation and will be null except in `rnmixGibbs` and `rDPGibbs`. ### Classes and Methods In R generally, objects can be assigned a _class_ and then a _generic_ function can be used to run a _method_ on an object with that class. The list elements in the output from `bayesm` posterior sampling functions are assigned special `bayesm` classes. The `bayesm` package includes `summary` and `plot` methods for use with these classes (see the table in Section 2 above). This means you can call the generic function (e.g., `summary`) on individual list elements of `bayesm` output and it will return specially-formatted summary results, including the effective sample size. To see this, the code below provides an example using `runireg`. Here the generic function `summary` dispatches the method `summary.bayesm.mat` because the `betadraw` element of `runireg`'s output has class `bayesm.mat`. This example also shows the information about the prior that is printed to the console during the call to a posterior sampling function. Notice, however, that no remaining time is printed because `nprint` is set to zero. ```{r} set.seed(66) R <- 2000 n <- 200 X <- cbind(rep(1,n), runif(n)) beta <- c(1,2) sigsq <- 0.25 y <- X %*% beta + rnorm(n, sd = sqrt(sigsq)) out <- runireg(Data = list(y = y, X = X), Mcmc = list(R = R, nprint = 0)) summary(out$betadraw, tvalues = beta) ``` ## Access to Code `bayesm` was originally created as a companion to BSM, at which time most functions were written in R. The package has since been expanded to include additional functionality and most code has been converted to C++ via `Rcpp` for faster performance. However, for users interested in obtaining the original implementation of a posterior sampling function (in R instead of C++), you may still access the last version (2.2-5) of `bayesm` prior to the C++/`Rcpp` conversion from the [package archive](https://cran.r-project.org/src/contrib/Archive/bayesm/) on CRAN. To access the `R` code in the current version of `bayesm`, the user can simply call a function without parenthesis. For example, `bayesm::runireg`. However, most posterior sampling functions only perform basic checks in `R` and then call an unexported C++ function to do the heavy lifting (i.e., the MCMC draws). This C++ source code is not available to the user via the installed `bayesm` package because C++ code is compiled upon package installation on Linux machines and pre-compiled by CRAN for Mac and Windows. To access this source code, the user must download the "package source" from CRAN. This can be accomplished by clicking on the appropriate link at the `bayesm` [package archive](https://cran.r-project.org/src/contrib/Archive/bayesm/) or by executing the `R` command `download.packages(pkgs="bayesm", destdir=".", type="source")`. Either of these methods will provide you with a compressed file "bayesm_version.tar.gz" that can be uncompressed. The C++ code can then be found in the "src" subdirectory. # Examples We begin with a brief introduction to regression and Bayesian estimation. This will help set the notation and provide background for the examples that follow. We do not claim that this will be a sufficient introduction to the reader for which these ideas are new. We refer that reader to excellent texts on regression analysis by Cameron \& Trivedi, Davidson \& MacKinnon, Goldberger, Greene, Wasserman, and Wooldridge.[^1] For Bayesian methods, we recommend Gelman et al., Jackman, Marin \& Robert, Rossi et al., and Zellner.[^2] [^1]: Cameron, Colin and Pravin Trivedi, _Microeconometrics: Methods and Applications_, Cambridge University Press, 2005. Davidson, Russell and James MacKinnon, _Estimation and Inference in Econometrics_, Oxford University Press, 1993. Goldberger, Arthur, _A Course in Econometrics_, Harvard University Press, 1991. Greene, William, _Econometric Analysis_, Prentice Hall, 2012 (7th edition). Wasserman, Larry, _All of Statistics: A Concise Course in Statistical Inferece_, Springer, 2004. Wooldridge, Jeffrey, _Econometric Analysis of Cross Section and Panel Data_, MIT Press, 2010 (2nd edition). [^2]: Gelman, Andrew, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin, _Bayesian Data Analysis_, CRC Press, 2013 (3rd edition). Jackman, Simon, _Bayesian Analysis for the Social Sciences_, Wiley, 2009. Marin, Jean-Michel and Christian Robert, _Bayesian Essentials with R_, Springer, 2014 (2nd edition). Rossi, Peter, Greg Allenby, and Robert McCulloch, _Bayesian Statistics and Marketing_, Wiley, 2005. Zellner, Arnold, _An Introduction to Bayesian Inference in Economics_, Wiley, 1971. ## What is Regression Suppose you believe a variable $y$ varies with (or is caused by) a set of variables $x_1, x_2, \ldots, x_k$. For notational convenience, we'll collect the set of $x$ variables into $X$. These variables $y$ and $X$ have a joint distribution $f(y, X)$. Typically, interest will not fall on this joint distribution, but rather on the conditional distribution of the "outcome" variable $y$ given the "explanatory" variables (or "covariates") $x_1, x_2, \ldots, x_k$; this conditional distribution being $f(y|X)$. To carry out inference on the relationship between $y$ and $X$, the researcher then often focuses attention on one aspect of the conditional distribution, most commonly its expected value. This conditional mean is assumed to be a function $g$ of the covariates such that $\mathbb{E}[y|X] = g(X, \beta)$ where $\beta$ is a vector of parameters. A function for the conditional mean is known as a "regression" function. The canonical introductory regression model is the normal linear regression model, which assumes that $y \sim N(X\beta, \sigma^2)$. Most students of regression will have first encountered this model as a combination of deterministic and stochastic components. There, the stochastic component is defined as deviations from the conditional mean, $\varepsilon = y - \mathbb{E}[y|X]$, such that $y = \mathbb{E}[y|X] + \varepsilon$ or that $y = g(X, \beta) + \varepsilon$. The model is then augmented with the assumptions that $g(X, \beta) = X \beta$ and $\varepsilon \sim N(0,\sigma^2)$ so that the normal linear regression model is: $$ y = X \beta + \varepsilon \text{ with } \varepsilon \sim N(0,\sigma^2) \hspace{1em} \text{or} \hspace{1em} y \sim N(X\beta, \sigma^2) $$ When taken to data, additional assumptions are made which include a full-rank condition on $X$ and often that $\varepsilon_i$ for $i=1,\ldots,n$ are independent and identically distributed. Our first example will demonstrate how to estimate the parameters of the normal linear regression model using Bayesian methods made available by the posterior sampling function `runireg`. We then provide an example to estimate the parameters of a model when $y$ is a categorical variable. This second example is called a multinomial logit model and uses the logistic "link" function $g(X, \beta) = [1 + exp(-X\beta)]^{-1}$. Our third and final example will extend the multinomial logit model to permit individual-level parameters. This is known as a hierarchical model and requires panel data to perform the estimation. Before launching into the examples, we briefly introduce Bayesian methodology and contrast it with classical methods. ## What is Bayesian Inference Under classical econometric methods, $\beta$ is most commonly estimated by minimizing the sum of squared residuals, maximizing the likelihood, or matching sample moments to population moments. The distribution of the estimators (e.g., $\hat{\beta}$) and test statistics derived from these methods rely on asymptotic concepts and are based on imaginary samples not observed. In contrast, Bayesian inference provides the benefits of (a) exact sample results, (b) integration of descision-making, estimation, testing, and model selection, and (c) a full accounting of uncertainty. These benefits from Bayesian inference rely heavily on probability theory and, in particular, distributional theory, some elements of which we now briefly review. Recall the relationship between the joint and conditional densities for random variables $W$ and $Z$: $$ P_{A|B}(A=a|B=b) = \frac{P_{A,B}(A=a, B=b)}{P_B(B=b)} $$ This relationship can be used to derive Bayes' Theorem, which we write with $D$ for "data" and $\theta$ as the parameters (and with implied subscripts): $$ P(\theta|D) = \frac{P(D|\theta)P(\theta)}{P(D)} $$ Noticing that $P(D)$ does not contain the parameters of interest ($\theta$) and is therefore simply a normalizing constant, we can instead write: $$ P(\theta|D) \propto P(D|\theta)P(\theta) $$ Introducing Bayesian terminology, we have that the "Posterior" is proportional to the Likelihood times the Prior. Thus, given (1) a dataset ($D$), (2) an assumption on the data generating process (the likelihood, $P(D|\theta)$), and (3) a specification of the prior distribution of the parameters ($P(\theta)$), we can find the _exact_ (posterior) distribution of the parameters given the observed data. This is in stark contrast to classical econometric methods, which typically only provide the _asymptotic_ distributions of estimators. However, for any problem of practical interest, the posterior distribution is a high-dimensional object. Additionally, it may not be possible to analytically calculate the posterior or its features (e.g., marginal distributions or moments such as the mean). To handle these issues, the modern approach to Bayesian inference relies on simulation methods to sample from the (high-dimensional) posterior distribution and then construct marginal distributions (or their features) from the sampled draws of the posterior. As a result, simulation and summaries of the posterior play important roles in modern Bayesian statistics. `bayesm`'s posterior sampling functions (as their name suggests) sample from posterior distributions. `bayesm`'s `summary` and `plot` methods can be used to analyze those draws. Unlike most classical econometric methods, the MCMC methods implemented in `bayesm`'s posterior sampling functions provide an estimate of the entire posterior distribution, not just a few moments. Given this "rich" result from Bayesian methods, it is best to summarize posterior distributions using histograms or quantiles. We advise that you resist the temptation to simply report the posterior mean and standard deviation; for non-normal distributions, those moments may have little meaning. In the examples that follow, we will describe the data we use, present the model, demonstrate how to estimate it using the appropriate posterior sampling function, and provide various ways to summarize the output. ## Example 1: Linear Normal Regression ### Data For our first example, we will use the `cheese` dataset, which provides `r data(cheese); format(nrow(cheese), big.mark=",")` observations of weekly sales volume for a package of Borden sliced cheese, as well as a measure of promotional display activity and price. The data are aggregated to the "key" account (i.e., retailer-market) level. ```{r} data(cheese) names(cheese) <- tolower(names(cheese)) str(cheese) ``` Suppose we want to assess the relationship between sales volume and price and promotional display activity. For this example, we will abstract from whether these relationships vary by retailer or whether prices are set endogenously. Simple statistics show a negative correlation between volume and price, and a positive correlation between volume and promotional activity, as we would expect. ```{r} options(digits=3) cor(cheese$volume, cheese$price) cor(cheese$volume, cheese$disp) ``` ### Model We model the expected log sales volume as a linear function of log(price) and promotional activity. Specifically, we assume $y_i$ to be iid with $p(y_i|x_i,\beta)$ normally distributed with a mean linear in $x$ and a variance of $\sigma^2$. We will denote observations with the index $i = 1, \ldots, n$ and covariates with the index $j = 1, \ldots, k$. The model can be written as: $$ y_i = \sum_{j=1}^k \beta_j x_{ij} + \varepsilon_i = x_i'\beta + \varepsilon_i \hspace{1em} \text{with} \hspace{1em} \varepsilon_i \sim iid\ N(0,\sigma^2) $$ or equivalently but more compactly as: $$ y \sim MVN(X\beta,\ \sigma^2I_n) $$ Here, the notation $N(0, \sigma^2)$ indicates a univariate normal distribution with mean $0$ and variance $\sigma^2$, while $MVN(X\beta,\ \sigma^2I_n)$ indicates a multivariate normal distribution with mean vector $X\beta$ and variance-covariance matrix $\sigma^2I_n$. In addition, $y_i$, $x_{ij}$, $\varepsilon_i$, and $\sigma^2$ are scalars while $x_i$ and $\beta$ are $k \times 1$ dimensional vectors. In the more compact notation, $y$ is an $n \times 1$ dimensional vector, $X$ is an $n \times k$ dimensional matrix with row $x_i$, and $I_n$ is an $n \times n$ dimensional identity matrix. With regard to the `cheese` dataset, $k = 2$ and $n = 5,555$. When employing Bayesian methods, the model is incomplete until the prior is specified. For our example, we elect to use natural conjugate priors, meaning the family of distributions for the prior is chosen such that, when combined with the likelihood, the posterior will be of the same distributional family. Specifically, we first factor the joint prior into marginal and conditional prior distributions: $$ p(\beta,\sigma^2) = p(\beta|\sigma^2)p(\sigma^2) $$ We then specify the prior for $\sigma^2$ as inverse-gamma (written in terms of a chi-squared random variable) and the prior for $\beta|\sigma^2$ as multivariate normal: $$ \sigma^2 \sim \frac{\nu s^2}{\chi^2_{\nu}} \hspace{1em} \text{and} \hspace{1em} \beta|\sigma^2 \sim MVN(\bar{\beta},\sigma^2A^{-1}) $$ Other than convenience, we have little reason to specify priors from these distributional families; however, we will select diffuse priors so as not to impose restrictions on the model. To do so, we must pick values for $\nu$ and $s^2$ (the degrees of freedom and scale parameters for the inverted chi-squared prior on $\sigma^2$) as well as $\bar{\beta}$ and $A^{-1}$ (the mean vector and variance-covariance matrix for the multivariate normal prior on the $\beta$ vector). The `bayesm` posterior sampling function for this model, `runireg`, defaults to the following values: - $\nu = 3$ - $s^2 =$ `var(y)` - $\bar{\beta} = 0$ - $A = 0.01*I$ We will use these defaults, as they are chosen to be diffuse for data with a unit scale. Thus, for each $\beta_j | \sigma^2$ we have specified a normal prior with mean 0 and variance $100\sigma^2$, and for $\sigma^2$ we have specified an inverse-gamma prior with $\nu = 3$ and $s^2 = \text{var}(y)$. We graph these prior distributions below. ```{r fig.show = "hold"} par(mfrow = c(1,2)) curve(dnorm(x,0,10), xlab = "", ylab = "", xlim = c(-30,30), main = expression(paste("Prior for ", beta[j])), col = "dodgerblue4") nu <- 3 ssq <- var(log(cheese$volume)) curve(nu*ssq/dchisq(x,nu), xlab = "", ylab = "", xlim = c(0,1), main = expression(paste("Prior for ", sigma^2)), col = "darkred") par(mfrow = c(1,1)) ``` ### Bayesian Estimation Although this model involves nontrivial natural conjugate priors, the posterior is available in closed form: $$ p(\beta, \sigma^2 | y, X) \propto (\sigma^2)^{-k/2} \exp \left\{ -\frac{1}{2\sigma^2}(\beta - \bar{\beta})'(X'X+A)(\beta - \bar{\beta}) \right\} \times (\sigma^2)^{-((n+\nu_0)/2+1)} \exp \left\{ -\frac{\nu_0s_0^2 + ns^2}{2\sigma^2} \right\} $$ or \begin{align*} \beta | \sigma^2, y, X &\sim N(\bar{\beta}, \sigma^2(X'X+A)^{-1}) \\ \\ \sigma^2 | y, X &\sim \frac{\nu_1s_1^2}{\chi^2_{\nu_1}}, \hspace{3em} \text{with} \> \nu_1 = \nu_0+n \hspace{1em} \text{and} \hspace{1em} s_1^2 = \frac{\nu_0s_0^2 + ns^2}{\nu_0+n} \end{align*} The latter representation suggests a simulation strategy for making draws from the posterior. We draw a value of $\sigma^2$ from its marginal posterior distribution, insert this value into the expression for the covariance matrix of the conditional normal distribution of $\beta|\{\sigma^2,y\}$ and draw from this multivariate normal. This simulation strategy is implemented by `runireg`, using the defaults for `Prior` specified above. The code is quite simple. ```{r, eval = FALSE} dat <- list(y = log(cheese$volume), X = model.matrix( ~ price + disp, data = cheese)) out <- runireg(Data = dat, Mcmc = list(R=1e4, nprint=1e3)) ``` ```{r, echo = FALSE} temp <- capture.output( {set.seed(1234); dat <- list(y = log(cheese$volume), X = model.matrix( ~ price + disp, data = cheese)); out <- runireg(Data = dat, Mcmc = list(R=1e4, nprint=1e3))}, file = NULL) ``` Note that `bayesm` posterior sampling functions print out information about the prior and about MCMC progress during the function call (unless `nprint` is set to 0), but for presentation purposes we suppressed that output here. `runireg` returns a list that we have saved in `out`. The list contains two elements, `betadraw` and `sigmasqdraw`, which you can verify by running `str(out)`. `betadraw` is an `R/keep` $\times$ `ncol(X)` ($10,000 \times 3$ with a column for each of the intercept, price, and display) dimension matrix with class `bayesm.mat`. We can analyze or summarize the marginal posterior distributions for any $\beta$ parameter or the $\sigma^2$ parameter. For example, we can plot histograms of the price coefficient (even though it is known to follow a t-distrbution, see BSM Ch. 2.8) and for $\sigma^2$. Notice how concentrated the posterior distributions are compared to their priors above. ```{r, fig.show = "hold"} B <- 1000+1 #burn in draws to discard R <- 10000 par(mfrow = c(1,2)) hist(out$betadraw[B:R,2], breaks = 30, main = "Posterior Dist. of Price Coef.", yaxt = "n", yaxs="i", xlab = "", ylab = "", col = "dodgerblue4", border = "gray") hist(out$sigmasqdraw[B:R], breaks = 30, main = "Posterior Dist. of Sigma2", yaxt = "n", yaxs="i", xlab = "", ylab = "", col = "darkred", border = "gray") par(mfrow = c(1,1)) ``` Additionally, we can compute features of these posterior distributions. For example, the posterior means price and display are: ```{r} apply(out$betadraw[B:R,2:3], 2, mean) ``` Conveniently, `bayesm` offers this functionality (and more) with its `summary` and `plot` methods. Notice that `bayesm`'s methods use a default burn-in length, calculated as `trunc(0.1*nrow(X))`. You can override the default by specifying the `burnin` argument. We see that the means for the first few retail fixed effects in the summary information below match those calculated "by hand" above. ```{r} summary(out$betadraw) ``` The same can be done with the `plot` generic function. However, we reference the method directly (`plot.bayesm.mat`) to plot a subset of the `bayesm` output -- specifically we plot the price coefficient. In the histogram, note that the green bars delimit a 95\% Bayesian credibility interval, yellow bars shows +/- 2 numerical standard errors for the posterior mean, and the red bar indicates the posterior mean. Also notice that this pink histogram of the posterior distribution on price, which was created by calling the `plot` generic, matches the blue one we created "by hand" above. The `plot` generic function also provides a trace plot and and ACF plot. In many applications (although not in this simple model), we cannot be certain that our draws from the posterior distribution adequately represent all areas of the posterior with nontrivial mass. This may occur, for instance, when using a "slow mixing" Markov Chain Monte Carlo (MCMC) algorithm to draw from the posterior. In such a case, we might see patterns in the trace plot and non-zero autocorrelations in the ACF plot; these will coincide with values for the Effective Sample Size less than `R`. (Effective Sample Size prints out with the `summary` generic function, as above.) Here, however, we are able to sample from the posterior distribution by taking iid draws, and so we see large Effective Sample Sizes in the `summary` output above, good mixing the trace plot below, and virtually no autocorrelation between draws in the ACF plot below. ```{r} plot.bayesm.mat(out$betadraw[,2]) ``` ## Example 2: Multinomial Logistic Regression ### Data Linear regression models like the one in the previous example are best suited for continuous outcome variables. Different models (known as limited dependent variable models) have been developed for binary or multinomial outcome variables, the most popular of which --- the multinomial logit --- will be the subject of this section. For this example, we analyze the `margarine` dataset, which provides panel data on purchases of margarine. The data are stored in two dataframes. The first, `choicePrice`, lists the outcome of `r data(margarine); format(nrow(margarine$choicePrice), big.mark=",")` choice occasions as well as the choosing household and the prices of the `r max(margarine$choicePrice[,2])` choice alternatives. The second, `demos`, provides demographic information about the choosing households, such as their income and family size. We begin by merging the information from these two dataframes: ```{r, results = "hold"} data(margarine) str(margarine) marg <- merge(margarine$choicePrice, margarine$demos, by = "hhid") ``` Compared to the standard $n \times k$ rectangular format for data to be used in a linear regression model, choice data may be stored in various formats, including a rectangular format where the $p$ choice alternatives are allocated across columns or rows, or a list-of-lists format as used in `bayesm`'s hierarchical models, which we demonstrate in Example 3 below. For all functions --- and notably those that implement multinomial logit and probit models --- the data must be in the format expected by the function, and `bayesm`'s posterior sampling funtions are no exception. In this example, we will implement a multinomial logit model using `rmnlIndepMetrop`. This posterior sampling function requires `y` to be a length-$n$ vector (or an $n \times 1$ matrix) of multinomial outcomes ($1, \dots, p$). That is, each element of `y` corresponds to a choice occasion $i$ with the value of the element $y_i$ indicating the choice that was made. So if the fourth alternative was chosen on the seventh choice occasion, then $y_7 = 4$. The `margarine` data are stored in that format, and so we easily specify `y` with the following code: ```{r} y <- marg[,2] ``` `rmnlIndepMetrop` requires `X` to be an $np \times k$ matrix. That is, each alternative is listed on its own row, with a group of $p$ rows together corresponding to the alternatives available on one choice occasion. However, the `margarine` data are stored with the various choice alternatives in columns rather than rows, so reformatting is necessary. `bayesm` provides the utility function `createX` to assist with the conversion. `createX` requires the user to specify the number of choice alternatives `p` as well as the number of alternative-specific variables `na` and an $n \times$ `na` matrix of alternative-specific data `Xa` ("a" for alternative-specific). Here, we have $p=10$ choice alternatives with `na` $=1$ alternative-specific variable (price). If we were only interested in using price as a covariate, we would code: ```{r} X1 <- createX(p=10, na=1, Xa=marg[,3:12], nd=NULL, Xd=NULL, base=1) colnames(X1) <- c(names(marg[,3:11]), "price") head(X1, n=10) ``` Notice that `createX` uses $p-1$ dummy variables to distinguish the $p$ choice alternatives. As with factor variables in linear regression, one factor must be the base; the coefficients on the other factors report deviations from the base. The user may specify the base alternative using the `base` argument (as we have done above), or let it default to the alternative with the highest index. For our example, we might also like to include some "demographic" variables. These are variables that do not vary with the choice alternatives. For example, with the `margarine` data we might want to include family size. Here again we turn to `createX`, this time specifying the `nd` and `Xd` arguments ("d" for demographic): ```{r, results = "hold"} X2 <- createX(p=10, na=NULL, Xa=NULL, nd=2, Xd=as.matrix(marg[,c(13,16)]), base=1) print(X2[1:10,1:9]); cat("\n") print(X2[1:10,10:18]) ``` Notice that `createX` again uses $p-1$ dummy variables to distinguish the $p$ choice alternatives. However, for demographic variables, the value of the demographic variable is spread across $p-1$ columns and $p-1$ rows. ### Model The logit specification was originally derived by Luce (1959) from assumptions on characteristics of choice probabilities. McFadden (1974) tied the model to rational economic theory by showing how the multinomial logit specification models choices made by a utility-maximizing consumer, assuming that the unobserved utility component is distributed Type I Extreme Value. We motivate use of this model following McFadden by assuming the decision maker chooses the alternative providing him with the highest utility, where the utility $U_{ij}$ from the choice $y_{ij}$ made by a decision maker in choice situation $i$ for product $j = 1, \ldots, p$ is modeled as the sum of a deterministic and a stochastic component: \[ U_{ij} = V_{ij} + \varepsilon_{ij} \hspace{2em} \text{with } \varepsilon_{ij}\ \sim \text{ iid T1EV} \] Regressors (both demographic and alternative-specific) are included in the model by assuming $V_{ij} = x_{ij}'\beta$. These assumptions result in choice probabilities of: $$ \text{Pr}(y_i=j) = \frac{\exp \{x_{ij}'\beta\}}{\sum_{k=1}^p\exp\{x_{ik}'\beta\}} $$ Independent priors for the components of the `beta` vector are specified as normal distributions. Using notation for the multivariate normal distribution, we have: $$ \beta \sim MVN(\bar{\beta},\ A^{-1}) $$ We use `bayesm`'s default values for the parameters of the priors: $\bar{\beta} = 0$ and $A = 0.01I$. ### Bayesian Estimation Experience with the MNL likelihood is that the asymptotic normal approximation is excellent. `rmnlIndepMetrop` implements an independent Metropolis algorithm to sample from the normal approximation to the posterior distribution of $\beta$: $$ p(\beta | X, y) \overset{\cdot}{\propto} |H|^{1/2} \exp \left\{ \frac{1}{2}(\beta - \hat{\beta})'H(\beta - \hat{\beta}) \right\} $$ where $\hat{\beta}$ is the MLE, $H = \sum_i x_i A_i x_i'$, and the candidate distribution used in the Metropolis algorithm is the multivariate student t. For more detail, see Section 11 of BSM Chapter 3. We sample from the normal approximation to the posterior as follows: ```{r, eval = FALSE} X <- cbind(X1, X2[,10:ncol(X2)]) out <- rmnlIndepMetrop(Data = list(y=y, X=X, p=10), Mcmc = list(R=1e4, nprint=1e3)) ``` ```{r, echo = FALSE} temp <- capture.output( {set.seed(1234); X <- cbind(X1, X2[,10:ncol(X2)]); out <- rmnlIndepMetrop(Data = list(y=y, X=X, p=10), Mcmc = list(R=1e4, nprint=1e3))}, file = NULL) ``` `rmnlIndepMetrop` returns a list that we have saved in `out`. The list contains 3 elements, `betadraw`, `loglike`, and `acceptr`, which you can verify by running `str(out)`. `betadraw` is a $10,000 \times 28$ dimension matrix with class `bayesm.mat`. As with the linear regression of Example 1 above, we can plot or summarize features of the the posterior distribution in many ways. For information on each marginal posterior distribution, call `summary(out)` or `plot(out)`. Because we have 28 covariates (intercepts and demographic variables make up 9 columns each and there is one column for the price variable) we omit the full set of results to save space and instead, we only present summary statistics for the marginal posterior distribution for $\beta_\text{price}$: ```{r} summary.bayesm.mat(out$betadraw[,10], names = "Price") ``` In addition to summary information for a marginal posterior distribution, we can plot it. We use `bayesm`'s `plot` generic function (calling `plot(out$betadraw)` would provide the same plots for all 28 $X$ variables). In the histogram, the green bars delimit a 95\% Bayesian credibility interval, yellow bars shows +/- 2 numerical standard errors for the posterior mean, and the red bar indicates the posterior mean. The subsequent two plots are a trace plot and and ACF plot. ```{r} plot.bayesm.mat(out$betadraw[,10], names = "Price") ``` We see that the posterior is approximately normally distributed with a mean of `r format(round(mean(out$betadraw[,10]),1), big.mark=",")` and a standard deviation of `r round(sd(out$betadraw[,10]), 2)`. The trace plot shows good mixing. The ACF plot shows a fair amount of correlation such that, even though the algorithm took `R = 10,000` draws, the Effective Sample Size (as reported in the summary stats above) is only `r format(round(summary.bayesm.mat(out$betadraw[,10])[1,5],0), big.mark = ",")`. Because of the nonlinearity in this model, interpreting the results is more difficult than with linear regression models. We do not elaborate further on the interpretation of coefficients and methods of displaying results from multinomial logit models, but for the uninitiated reader, we refer you to excellent sources for this information authored by Kenneth Train and Gary King.[^3] [^3]: Train, Kenneth, _Discrete Choice Models with Simulation_ Cambridge University Press, 2009. King, Gary _Unifying Political Methodlogy: The Likelihood Theory of Statistical Inference_, University of Michigan Press (1998) p. 108. King, Gary, Michael Tomz, and Jason Wittenberg, "Making the Most of Statistical Analyses: Improving Interpretation and Presentation" American Journal of Political Science, Vol. 44 (April 2000) pp. 347--361 at p. 355. ## Example 3: Hierarchical Logit ### Data While we could add individual-specific parameters to the previous model and use the same dataset, we elect to provide the reader with greater variety. For this example, we use the `camera` dataset in `bayesm`, which contains conjoint choice data for 332 respondents who evaluated digital cameras. These data have already been processed to exclude respondents that always answered "none", always picked the same brand, always selected the highest priced offering, or who appeared to be answering randomly. ```{r} data(camera) length(camera) str(camera[[1]]) colnames(camera[[1]]$X) ``` The `camera` data is stored in a list-of-lists format, which is the format required by `bayesm`'s posterior sampling functions for hierarchical models. This format has one list per individual with each list containing a vector `y` of choice outcomes and a matrix `X` of covariates. As with the multinomial logit model of the last example, `y` is a length-$n_i$ vector (or one-column matrix) and `X` has dimensions $n_ij \times k$ where $n_i$ is the number of choice occasions faced by individual $i$, $j$ is the number of choice alternatives, and $k$ is the number of covariates. For the `camera` data, $N=332$, $n_i=16$ for all $i$, $j=5$, and $k=10$. If your data were not in this format, it could be easily converted with a `for` loop and `createX`. For example, we can format `margarine` data from Example 2 above into a list-of-lists format with the following code, which simply loops over individuals, extracting and storing their `y` and `X` data one individual at a time: ```{r, eval = FALSE} data(margarine) chpr <- margarine$choicePrice chpr$hhid <- as.factor(chpr$hhid) N <- nlevels(chpr$hhid) dat <- vector(mode = "list", length = N) for (i in 1:N) { dat[[i]]$y <- chpr[chpr$hhid==levels(chpr$hhid)[i], "choice"] dat[[i]]$X <- createX(p=10, na=1, Xa=chpr[chpr$hhid==levels(chpr$hhid)[i],3:12], nd=NULL, Xd=NULL) } ``` Returning to the `camera` data, the first 4 covariates are binary indicators for the brands Canon, Sony, Nikon, and Panasonic. These correspond to choice (`y`) values of 1, 2, 3, and 4. `y` can also take the value 5, indicating that the respondent chose "none". The data include binary indicators for two levels of pixel count, zoom strength, swivel video display capability, and wifi connectivity. The last covaritate is price, recorded in hundreds of U.S. dollars (we leave price in these units so that we do not need to adjust the default prior settings). When we look at overall choice outcomes, we see that the brands and the outside alternative ("none") are chosen roughly in fifths, with specific implied market shares ranging from 17\%--25\%: ```{r} N <- length(camera) dat <- matrix(NA, N*16, 2) for (i in 1:length(camera)) { Ni <- length(camera[[i]]$y) dat[((i-1)*Ni+1):(i*Ni),1] <- i dat[((i-1)*Ni+1):(i*Ni),2] <- camera[[i]]$y } round(prop.table(table(dat[,2])), 3) ``` However, when we look at a few individuals' choices, we see much greater variability: ```{r} round(prop.table(table(dat[,1], dat[,2])[41:50,], 1), 3) ``` It is this heterogeneity in individual choice that motivates us to employ a hierarchical model. ### Model Hierarchical (also known as multi-level, random-coefficient, or mixed) models allow each respondent to have his or her own coefficients. Different people have different preferences, and models that estimate individual-level coefficients can fit data better and make more accurate predictions than single-level models. These models are quite popular in marketing, as they allow, for example, promotions to be targeted to individuals with high promotional part worths --- meaning those inviduals who are most likely to respond to the promotion. For more information, see Rossi et al. (1996).^[Rossi, McCulloch, and Allenby "The Value of Purchase History Data in Target Marketing" Marketing Science (1996).] The model follows the multinomial logit specification given in Example 2 above where individuals are assumed to be rational economic agents that make utility-maximizing choices. Now, however, the model includes individual-level parameters ($\beta_i$) assumed to be drawn from a normal distribution and with mean values driven by cross-sectional unit characteristics $Z$: $$ y_i \sim \text{MNL}(x_i'\beta_i) \hspace{1em} \text{with} \hspace{1em} \beta_i = z_i' \Delta + u_i \hspace{1em} \text{and} \hspace{1em} u_i \sim MVN(\mu, \Sigma) $$ $x_i$ is $n_i \times k$ and $i = 1, \ldots, N$. We can alternatively write the middle equation as $B=Z\Delta + U$ where $\beta_i$, $z_i$, and $u_i$ are the $i^\text{th}$ rows of $B$, $Z$, and $U$. $B$ is $N \times k$, $Z$ is $N \times m$, $\Delta$ is $m \times k$, and $U$ is $N \times k$. Note that we do not have any cross-sectional unit characteristics in the `camera` dataset and thus $Z$ will be omitted. The priors are: $$ \text{vec}(\Delta) = \delta \sim MVN(\bar{\delta}, A_\delta^{-1}) \hspace{2em} \mu \sim MVN(\bar{\mu}, \Sigma \otimes a^{-1}) \hspace{2em} \Sigma \sim IW(\nu, V) $$ This specification of priors assumes that, conditional on the hyperparameters (that is, the parameters of the prior distribution), the $\beta$'s are _a priori_ independent. This means that inference for each unit can be conducted independently of all other units, conditional on the hyperparameters, which is the Bayesian analogue of the fixed effects approach in classical statistics. Note also that we have assumed a normal "first-stage" prior distribution over the $\beta$'s. `rhierMnlRwMixture` permits a more-flexible mixture-of-normals first-stage prior (hence the "mixture" in the function name). However, for our example, we will not include this added flexibility (`Prior$ncomp = 1` below). ### Bayesian Estimation Although the model is more complex than the models used in the two previous examples, the increased programming difficulty for the researcher is minimal. As before, we specify `Data`, `Prior`, and `Mcmc` arguments, and call the posterior sampling function: ```{r} data <- list(lgtdata = camera, p = 5) prior <- list(ncomp = 1) mcmc <- list(R = 1e4, nprint = 0) out <- rhierMnlRwMixture(Data = data, Prior = prior, Mcmc = mcmc) ``` We store the results in `out`, which is a list of length 4. The list elements are `betadraw`, `nmix`, `loglike`, and `SignRes`. - `betadraw` is a $332 \times 10 \times 10,000$ array. These dimensions correspond to the number of individuals, the number of covariates, and the number of MCMC draws. - `nmix` is a list with elements `probdraw`, `zdraw`, and `compdraw`. - `probdraw` tells us the probability that each draw came from a particular normal component. This is relevant when there is a mixture-of-normals first-stage prior. However, since our specified prior over the $\beta$ vector is one normal distribution, `probdraw` is a $10,000 \times 1$ vector of all 1's. - `zdraw` is `NULL` as it is not relevant for this function. - `compdraw` provides draws for the mixture-of-normals components. Here, `compdraw` is a list of 10,000 lists. The $r^\text{th}$ of the 10,000 lists contains the $r^\text{th}$ draw of the $\mu$ vector (dim $1 \times 10$) and the Cholesky root of the $r^\text{th}$ draw for the $10 \times 10$ covariance matrix. - `loglike` is a $10,000 \times 1$ vector that provides the log-likelihood of each draw. - `SignRes` relates to whether any sign restrictions were placed on the model. This is discussed in detail in a separate vignette detailing a contrainsted hierarchical multinomial logit model; it is not relevant here. We can summarize results as before. `plot(out$betadraw)` provides plots for each variable that summarize the distributions of the individual parameters. For brevity, we provide just a histogram of posterior means for the 332 individual coefficients on wifi capability. ```{r} hist(apply(out$betadraw, 1:2, mean)[,9], col = "dodgerblue4", xlab = "", ylab = "", yaxt="n", xlim = c(-4,6), breaks = 20, main = "Histogram of Posterior Means For Individual Wifi Coefs") ``` We see that the distribution of individual posterior means is skewed, suggesting that our assumption of a normal first-stage prior may be incorrect. We could improve this model by using the more flexible mixture-of-normals prior or, if we believe all consumers value wifi connectivity positively, we could impose a sign constraint on that set of parameters --- both of which are demonstrated in the vignette for sign-constrained hierarchical multinomial logit. # Conclusion We hope that this vignette has provided the reader with a thorough introduction to the `bayesm` package and is sufficient to enable immediate use of its posterior sampling functions for bayesian estimation. Comments or edits can be sent to the vignette authors at the email addresses below. ***** _Authored by [Dan Yavorsky](dyavorsky@gmail.com) and [Peter Rossi](perossichi@gmail.com). Last updated June 2017._ bayesm/inst/include/0000755000176000001440000000000013123305446014163 5ustar ripleyusersbayesm/inst/include/bayesm.h0000644000176000001440000001236413114117322015614 0ustar ripleyusers#ifndef __BAYESM_H__ #define __BAYESM_H__ #include #include #include #include using namespace arma; using namespace Rcpp; //CUSTOM STRUCTS-------------------------------------------------------------------------------------------------- //Used in rhierLinearMixture, rhierLinearModel, rhierMnlDP, rhierMnlRwMixture, rhierNegbinRw, and rsurGibbs struct moments{ vec y; mat X; mat XpX; vec Xpy; mat hess; }; //Used in rhierLinearMixture, rhierLinearModel, rhierMnlRWMixture, and utilityFunctions.cpp struct unireg{ vec beta; double sigmasq; }; //Used in rhierMnlDP, rhierMnlRwMixture, and utilityFunctions.cpp struct mnlMetropOnceOut{ vec betadraw; int stay; double oldll; }; //Used in rDPGibbs, rhierMnlDP, rivDP, and utilityFunctions.cpp struct lambda{ vec mubar; double Amu; double nu; mat V; }; //Used in rDPGibbs, rhierMnlDP, rivDP, and utilityFunctions.cpp struct priorAlpha{ double power; double alphamin; double alphamax; int n; }; //Used in rDPGibbs, rhierMnlDP, rivDP, and utilityFunctions.cpp struct murooti{ vec mu; mat rooti; }; //Used in rDPGibbs, rhierMnlDP, rivDP, and utilityFunctions.cpp struct thetaStarIndex{ ivec indic; std::vector thetaStar_vector; }; //Used in rhierMnlDP, rivDP struct DPOut{ ivec indic; std::vector thetaStar_vector; std::vector thetaNp1_vector; double alpha; int Istar; lambda lambda_struct; }; //EXPOSED FUNCTIONS----------------------------------------------------------------------------------------------- List rwishart(double nu, mat const& V); List rmultireg(mat const& Y, mat const& X, mat const& Bbar, mat const& A, double nu, mat const& V); vec rdirichlet(vec const& alpha); double llmnl(vec const& beta, vec const& y, mat const& X); mat lndIChisq(double nu, double ssq, mat const& X); double lndMvst(vec const& x, double nu, vec const& mu, mat const& rooti, bool NORMC); double lndMvn(vec const& x, vec const& mu, mat const& rooti); double lndIWishart(double nu, mat const& V, mat const& IW); vec rmvst(double nu, vec const& mu, mat const& root); vec breg(vec const& y, mat const& X, vec const& betabar, mat const& A); vec cgetC(double e, int k); List rmixGibbs( mat const& y, mat const& Bbar, mat const& A, double nu, mat const& V, vec const& a, vec const& p, vec const& z); //rmixGibbs contains the following support functions, which are called ONLY THROUGH rmixGibbs: drawCompsFromLabels, drawLabelsFromComps, and drawPFromLabels //SUPPORT FUNCTIONS (contained in utilityFunctions.cpp and trunNorm.cpp)----------------------------------------------------------- //Used in rmvpGibbs and rmnpGibbs vec condmom(vec const& x, vec const& mu, mat const& sigmai, int p, int j); //double rtrun1(double mu, double sigma,double trunpt, int above); <--NO LONGER USED double trunNorm(double mu,double sig, double trunpt, int above); //Used in rhierLinearModel, rhierLinearMixture and rhierMnlRWMixture mat drawDelta(mat const& x,mat const& y,vec const& z,List const& comps,vec const& deltabar,mat const& Ad); unireg runiregG(vec const& y, mat const& X, mat const& XpX, vec const& Xpy, double sigmasq, mat const& A, vec const& Abetabar, double nu, double ssq); //Used in rnegbinRW and rhierNegbinRw double llnegbin(vec const& y, vec const& lambda, double alpha, bool constant); double lpostbeta(double alpha, vec const& beta, mat const& X, vec const& y, vec const& betabar, mat const& rootA); double lpostalpha(double alpha, vec const& beta, mat const& X, vec const& y, double a, double b); //Used in rbprobitGibbs (uses breg1 and trunNorm_vec) and rordprobitGibbs (uses breg1 and rtrunVec) vec breg1(mat const& root, mat const& X, vec const& y, vec const& Abetabar); vec rtrunVec(vec const& mu,vec const& sigma, vec const& a, vec const& b); vec trunNorm_vec(vec const& mu, vec const& sig, vec const& trunpt, vec const& above); //Used in rhierMnlDP and rhierMnlRwMixture mnlMetropOnceOut mnlMetropOnce(vec const& y, mat const& X, vec const& oldbeta, double oldll,double s, mat const& incroot, vec const& betabar, mat const& rootpi); //Used in rDPGibbs, rhierMnlDP, rivDP int rmultinomF(vec const& p); mat yden(std::vector const& thetaStar, mat const& y); ivec numcomp(ivec const& indic, int k); murooti thetaD(mat const& y, lambda const& lambda_struct); thetaStarIndex thetaStarDraw(ivec indic, std::vector thetaStar_vector, mat const& y, mat ydenmat, vec const& q0v, double alpha, lambda const& lambda_struct, int maxuniq); vec q0(mat const& y, lambda const& lambda_struct); vec seq_rcpp(double from, double to, int len); //kept _rcpp due to conflict with base seq function double alphaD(priorAlpha const& priorAlpha_struct, int Istar, int gridsize); murooti GD(lambda const& lambda_struct); lambda lambdaD(lambda const& lambda_struct, std::vector const& thetaStar_vector, vec const& alim, vec const& nulim, vec const& vlim, int gridsize); //FUNCTION TIMING (contained in functionTiming.cpp)--------------------------------------------------------------- void startMcmcTimer(); void infoMcmcTimer(int rep, int R); void endMcmcTimer(); #endif bayesm/src/0000755000176000001440000000000013134410677012357 5ustar ripleyusersbayesm/src/rmixGibbs_rcpp.cpp0000644000176000001440000001303213134410700016017 0ustar ripleyusers#include "bayesm.h" //W. Taylor: we considered moving the output to struct formats but the efficiency // gains were limited and the conversions back and forth between Lists and struct were cumbersome List drawCompsFromLabels(mat const& y, mat const& Bbar, mat const& A, double nu, mat const& V, int ncomp, vec const& z){ // Wayne Taylor 3/18/2015 // Function to draw the components based on the z labels vec b, r, mu; mat yk, Xk, Ck, sigma, rooti, S, IW, CI; List temp, rw, comps(ncomp); int n = z.n_rows; vec nobincomp = zeros(ncomp); //Determine the number of observations in each component for(int i = 0; i 0) { // If there are observations in this component, draw from the posterior yk = y.rows(find(z==(k+1))); //Note k starts at 0 and z starts at 1 Xk = ones(nobincomp[k], 1); temp = rmultireg(yk, Xk, Bbar, A, nu, V); sigma = as(temp["Sigma"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> rooti = solve(trimatu(chol(sigma)),eye(sigma.n_rows,sigma.n_cols)); //trimatu interprets the matrix as upper triangular and makes solve more efficient mu = as(temp["B"]); comps(k) = List::create( Named("mu") = NumericVector(mu.begin(),mu.end()), //converts to a NumericVector, otherwise it will be interpretted as a matrix Named("rooti") = rooti ); } else { // If there are no obervations in this component, draw from the prior S = solve(trimatu(chol(V)),eye(V.n_rows,V.n_cols)); S = S * trans(S); rw = rwishart(nu, S); IW = as(rw["IW"]); CI = as(rw["CI"]); rooti = solve(trimatu(chol(IW)),eye(IW.n_rows,IW.n_cols)); b = vectorise(Bbar); r = rnorm(b.n_rows,0,1); mu = b + (CI * r) / sqrt(A(0,0)); comps(k) = List::create( Named("mu") = NumericVector(mu.begin(),mu.end()), //converts to a NumericVector, otherwise it will be interpretted as a matrix Named("rooti") = rooti); } } return(comps); } vec drawLabelsFromComps(mat const& y, vec const& p, List comps) { // Wayne Taylor 3/18/2015 // Function to determine which label is associated with each y value double logprod; vec mu, u; mat rooti; List compsk; int n = y.n_rows; vec res = zeros(n); int ncomp = comps.size(); mat prob(n,ncomp); for(int k = 0; k(compsk["mu"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> rooti = as(compsk["rooti"]); //Find log of MVN density using matrices logprod = log(prod(diagvec(rooti))); mat z(y); z.each_row() -= trans(mu); //subtracts mu from each row in z z = trans(rooti) * trans(z); z = -(y.n_cols/2.0) * log(2*M_PI) + logprod - .5 * sum(z % z, 0); // operator % performs element-wise multiplication prob.col(k) = trans(z); } prob = exp(prob); prob.each_row() %= trans(p); //element-wise multiplication // Cumulatively add each row and take a uniform draw between 0 and the cumulative sum prob = cumsum(prob, 1); u = as(runif(n)) % prob.col(ncomp-1); // Evaluative each column of "prob" until the uniform draw is less than the cumulative value for(int i = 0; i prob(i, res[i]++)); } return(res); } vec drawPFromLabels(vec const& a, vec const& z) { // Wayne Taylor 9/10/2014 // Function to draw the probabilities based on the label proportions vec a2 = a; int n = z.n_rows; //Count number of observations in each component for(int i = 0; i(n); std::vector thetaStar_vector(1); murooti thetaStar0_struct; thetaStar0_struct.mu = zeros(dimy); thetaStar0_struct.rooti = eye(dimy,dimy); thetaStar_vector[0] = thetaStar0_struct; //convert Prioralpha from List to struct priorAlpha priorAlpha_struct; priorAlpha_struct.power = PrioralphaList["power"]; priorAlpha_struct.alphamin = PrioralphaList["alphamin"]; priorAlpha_struct.alphamax = PrioralphaList["alphamax"]; priorAlpha_struct.n = PrioralphaList["n"]; //initialize lambda lambda lambda_struct; lambda_struct.mubar = zeros(dimy); lambda_struct.Amu = BayesmConstantA; lambda_struct.nu = dimy+BayesmConstantnuInc; lambda_struct.V = lambda_struct.nu*eye(dimy,dimy); //initialize alpha double alpha = BayesmConstantDPalpha; //intialize remaining variables thetaStarIndex thetaStarDrawOut_struct; std::vector new_utheta_vector(1), thetaNp1_vector(1); murooti thetaNp10_struct, out_struct; mat ydenmat; vec q0v, probs; uvec ind; int nunique, indsize; uvec spanall(dimy); for(int i = 0; i(R/keep); vec Istardraw = zeros(R/keep); vec adraw = zeros(R/keep); vec nudraw = zeros(R/keep); vec vdraw = zeros(R/keep); List thetaNp1draw(R/keep); imat inddraw = zeros(R/keep,n); //do scaling rowvec dvec, ybar; if(SCALE){ dvec = 1/sqrt(var(y,0,0)); //norm_type=0 performs normalisation using N-1, dim=0 is by column ybar = mean(y,0); y.each_row() -= ybar; //subtract ybar from each row y.each_row() %= dvec; //divide each row by dvec } //note on scaling //we model scaled y, z_i=D(y_i-ybar) D=diag(1/sigma1, ..., 1/sigma_dimy) //if p_z= 1/R sum(phi(z|mu,Sigma)) // p_y=1/R sum(phi(y|D^-1mu+ybar,D^-1SigmaD^-1) // rooti_y=Drooti_z //you might want to use quantiles instead, like median and (10,90) // start main iteration loop int mkeep = 0; if(nprint>0) startMcmcTimer(); for(int rep = 0; rep maxuniq) stop("maximum number of unique thetas exceeded"); //ydenmat is a length(thetaStar) x n array of density values given f(y[j,] | thetaStar[[i]] // note: due to remix step (below) we must recompute ydenmat each time! ydenmat = zeros(maxuniq,n); ydenmat(span(0,nunique-1),span::all) = yden(thetaStar_vector,y); thetaStarDrawOut_struct = thetaStarDraw(indic, thetaStar_vector, y, ydenmat, q0v, alpha, lambda_struct, maxuniq); thetaStar_vector = thetaStarDrawOut_struct.thetaStar_vector; indic = thetaStarDrawOut_struct.indic; nunique = thetaStar_vector.size(); //thetaNp1 and remix probs = zeros(nunique+1); for(int j = 0; j < nunique; j++){ ind = find(indic == (j+1)); indsize = ind.size(); probs[j] = indsize/(alpha+n+0.0); new_utheta_vector[0] = thetaD(y(ind,spanall),lambda_struct); thetaStar_vector[j] = new_utheta_vector[0]; } probs[nunique] = alpha/(alpha+n+0.0); int ind = rmultinomF(probs); int probssize = probs.size(); if(ind == probssize) { out_struct = GD(lambda_struct); thetaNp10_struct.mu = out_struct.mu; thetaNp10_struct.rooti = out_struct.rooti; thetaNp1_vector[0] = thetaNp10_struct; } else { out_struct = thetaStar_vector[ind-1]; thetaNp10_struct.mu = out_struct.mu; thetaNp10_struct.rooti = out_struct.rooti; thetaNp1_vector[0] = thetaNp10_struct; } //draw alpha alpha = alphaD(priorAlpha_struct,nunique,gridsize); //draw lambda lambda_struct = lambdaD(lambda_struct,thetaStar_vector,lambda_hyper["alim"],lambda_hyper["nulim"],lambda_hyper["vlim"],gridsize); //print time to completion if (nprint>0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); //save every keepth draw if((rep+1)%keep==0){ mkeep = (rep+1)/keep; alphadraw[mkeep-1] = alpha; Istardraw[mkeep-1] = nunique; adraw[mkeep-1] = lambda_struct.Amu; nu = lambda_struct.nu; nudraw[mkeep-1] = nu; mat V = lambda_struct.V; vdraw[mkeep-1] = V(0,0)/nu; inddraw(mkeep-1,span::all) = trans(indic); thetaNp10_struct = thetaNp1_vector[0]; if(SCALE){ thetaNp10_struct.mu = thetaNp10_struct.mu/trans(dvec)+trans(ybar); thetaNp10_struct.rooti = diagmat(dvec)*thetaNp10_struct.rooti; } //here we put the draws into the list of lists of list format useful for finite mixture of normals utilities //we have to convetr to a NumericVector for the plotting functions to work thetaNp1draw[mkeep-1] = List::create(List::create(Named("mu") = NumericVector(thetaNp10_struct.mu.begin(),thetaNp10_struct.mu.end()),Named("rooti") = thetaNp10_struct.rooti)); } } if(nprint>0) endMcmcTimer(); return List::create( Named("inddraw") = inddraw, Named("thetaNp1draw") = thetaNp1draw, Named("alphadraw") = alphadraw, Named("Istardraw") = Istardraw, Named("adraw") = adraw, Named("nudraw") = nudraw, Named("vdraw") = vdraw); } bayesm/src/Makevars0000644000176000001440000000012213134410700014031 0ustar ripleyusersPKG_LIBS = $(LAPACK_LIBS) $(BLAS_LIBS) $(FLIBS) PKG_CPPFLAGS = -I../inst/include/ bayesm/src/rmvst_rcpp.cpp0000644000176000001440000000070113134410700015243 0ustar ripleyusers#include "bayesm.h" // [[Rcpp::export]] vec rmvst(double nu, vec const& mu, mat const& root){ // Wayne Taylor 9/7/2014 // function to draw from MV s-t with nu df, mean mu, Sigma=t(root)%*%root // root is upper triangular cholesky root vec rnormd = rnorm(mu.size()); vec nvec = trans(root)*rnormd; return(nvec/sqrt(rchisq(1,nu)[0]/nu) + mu); //rchisq returns a vectorized object, so using [0] allows for the conversion to double } bayesm/src/rmnpGibbs_rcpp_loop.cpp0000644000176000001440000000774213134410700017060 0ustar ripleyusers#include "bayesm.h" //EXTRA FUNCTIONS SPECIFIC TO THE MAIN FUNCTION-------------------------------------------- vec drawwi(vec const& w, vec const& mu, mat const& sigmai, int p, int y){ // Wayne Taylor 9/8/2014 //function to draw w_i by Gibbing thru p vector int above; double bound; vec outwi = w; vec maxInd(2); for(int i = 0; i(w.n_rows); for(int i = 0; i(R/keep, pm1*pm1); mat betadraw = zeros(R/keep,k); vec wnew = zeros(Xrows); //set initial values of w,beta, sigma (or root of inv) vec wold = wnew; vec betaold = beta0; mat C = chol(solve(trimatu(sigma0),eye(sigma0.n_cols,sigma0.n_cols))); //trimatu interprets the matrix as upper triangular and makes solve more efficient //C is upper triangular root of sigma^-1 (G) = C'C mat sigmai, zmat, epsilon, S, IW, ucholinv, VSinv; vec betanew; List W; // start main iteration loop int mkeep = 0; if(nprint>0) startMcmcTimer(); for(int rep = 0; rep(W["C"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> //print time to completion if (nprint>0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); //save every keepth draw if((rep+1)%keep==0){ mkeep = (rep+1)/keep; betadraw(mkeep-1,span::all) = trans(betanew); IW = as(W["IW"]); sigmadraw(mkeep-1,span::all) = trans(vectorise(IW)); } wold = wnew; betaold = betanew; } if(nprint>0) endMcmcTimer(); return List::create( Named("betadraw") = betadraw, Named("sigmadraw") = sigmadraw); } bayesm/src/runireg_rcpp_loop.cpp0000644000176000001440000000414413134410700016601 0ustar ripleyusers#include "bayesm.h" // [[Rcpp::export]] List runireg_rcpp_loop(vec const& y, mat const& X, vec const& betabar, mat const& A, double nu, double ssq, int R, int keep, int nprint) { // Keunwoo Kim 09/09/2014 // Purpose: perform iid draws from posterior of regression model using conjugate prior // Arguments: // y,X // betabar,A prior mean, prior precision // nu, ssq prior on sigmasq // R number of draws // keep thinning parameter // Output: list of beta, sigmasq // Model: // y = Xbeta + e e ~N(0,sigmasq) // y is n x 1 // X is n x k // beta is k x 1 vector of coefficients // Prior: // beta ~ N(betabar,sigmasq*A^-1) // sigmasq ~ (nu*ssq)/chisq_nu int mkeep; double s, sigmasq; mat RA, W, IR; vec z, btilde, res, beta; int nvar = X.n_cols; int nobs = y.size(); vec sigmasqdraw(R/keep); mat betadraw(R/keep, nvar); if (nprint>0) startMcmcTimer(); for (int rep=0; rep0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); if ((rep+1)%keep==0){ mkeep = (rep+1)/keep; betadraw(mkeep-1, span::all) = trans(beta); sigmasqdraw[mkeep-1] = sigmasq; } } if (nprint>0) endMcmcTimer(); return List::create( Named("betadraw") = betadraw, Named("sigmasqdraw") = NumericVector(sigmasqdraw.begin(),sigmasqdraw.end())); } bayesm/src/rhierLinearMixture_rcpp_loop.cpp0000644000176000001440000001023013134410700020741 0ustar ripleyusers#include "bayesm.h" //[[Rcpp::export]] List rhierLinearMixture_rcpp_loop(List const& regdata, mat const& Z, vec const& deltabar, mat const& Ad, mat const& mubar, mat const& Amu, double nu, mat const& V, double nu_e, vec const& ssq, int R, int keep, int nprint, bool drawdelta, mat olddelta, vec const& a, vec oldprob, vec ind, vec tau){ // Wayne Taylor 10/02/2014 int nreg = regdata.size(); int nvar = V.n_cols; int nz = Z.n_cols; mat rootpi, betabar, Abeta, Abetabar; int mkeep; unireg runiregout_struct; List regdatai, nmix; // convert List to std::vector of type "moments" std::vector regdata_vector; moments regdatai_struct; // store vector with struct for (int reg = 0; reg(regdatai["y"]); regdatai_struct.X = as(regdatai["X"]); regdatai_struct.XpX = as(regdatai["XpX"]); regdatai_struct.Xpy = as(regdatai["Xpy"]); regdata_vector.push_back(regdatai_struct); } // allocate space for draws mat oldbetas = zeros(nreg,nvar); mat taudraw(R/keep, nreg); cube betadraw(nreg, nvar, R/keep); mat probdraw(R/keep, oldprob.size()); mat Deltadraw(1,1); if(drawdelta) Deltadraw.zeros(R/keep, nz*nvar);//enlarge Deltadraw only if the space is required List compdraw(R/keep); if (nprint>0) startMcmcTimer(); for (int rep = 0; rep(mgout["p"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> ind = as(mgout["z"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> //now draw delta | {beta_i}, ind, comps if(drawdelta) olddelta = drawDelta(Z,oldbetas,ind,oldcomp,deltabar,Ad); //loop over all regression equations drawing beta_i | ind[i],z[i,],mu[ind[i]],rooti[ind[i]] for(int reg = 0; reg(oldcompreg[1]); //note: beta_i = Delta*z_i + u_i Delta is nvar x nz if(drawdelta){ olddelta.reshape(nvar,nz); betabar = as(oldcompreg[0])+olddelta*vectorise(Z(reg,span::all)); } else { betabar = as(oldcompreg[0]); } Abeta = trans(rootpi)*rootpi; Abetabar = Abeta*betabar; runiregout_struct = runiregG(regdata_vector[reg].y, regdata_vector[reg].X, regdata_vector[reg].XpX, regdata_vector[reg].Xpy, tau[reg], Abeta, Abetabar, nu_e, ssq[reg]); oldbetas(reg,span::all) = trans(runiregout_struct.beta); tau[reg] = runiregout_struct.sigmasq; } //print time to completion and draw # every nprint'th draw if (nprint>0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; taudraw(mkeep-1, span::all) = trans(tau); betadraw.slice(mkeep-1) = oldbetas; probdraw(mkeep-1, span::all) = trans(oldprob); if(drawdelta) Deltadraw(mkeep-1, span::all) = trans(vectorise(olddelta)); compdraw[mkeep-1] = oldcomp; } } if (nprint>0) endMcmcTimer(); nmix = List::create(Named("probdraw") = probdraw, Named("zdraw") = R_NilValue, //sets the value to NULL in R Named("compdraw") = compdraw); if(drawdelta){ return(List::create( Named("taudraw") = taudraw, Named("Deltadraw") = Deltadraw, Named("betadraw") = betadraw, Named("nmix") = nmix)); } else { return(List::create( Named("taudraw") = taudraw, Named("betadraw") = betadraw, Named("nmix") = nmix)); } } bayesm/src/lndMvn_rcpp.cpp0000644000176000001440000000114013134410700015324 0ustar ripleyusers#include "bayesm.h" // [[Rcpp::export]] double lndMvn(vec const& x, vec const& mu, mat const& rooti){ //Wayne Taylor 9/7/2014 // function to evaluate log of MV Normal density with mean mu, var Sigma // Sigma=t(root)%*%root (root is upper tri cholesky root) // Sigma^-1=rooti%*%t(rooti) // rooti is in the inverse of upper triangular chol root of sigma // note: this is the UL decomp of sigmai not LU! // Sigma=root'root root=inv(rooti) vec z = vectorise(trans(rooti)*(x-mu)); return((-(x.size()/2.0)*log(2*M_PI) -.5*(trans(z)*z) + sum(log(diagvec(rooti))))[0]); } bayesm/src/llmnl_rcpp.cpp0000644000176000001440000000075113134410700015213 0ustar ripleyusers#include "bayesm.h" //[[Rcpp::export]] double llmnl(vec const& beta, vec const& y, mat const& X){ // Wayne Taylor 9/7/2014 // Evaluates log-likelihood for the multinomial logit model int n = y.size(); int j = X.n_rows/n; mat Xbeta = X*beta; vec xby = zeros(n); vec denom = zeros(n); for(int i = 0; i const& thetaStar_vector){ // Wayne Taylor 3/14/2015 int dimz = z.n_cols; int dimx = x.n_cols; //variable type initializaion double sig; mat wk, zk, xk, rooti, Sigma, xt; vec yk, mu, e1, ee2, yt; uvec ind, colAllw, colAllz(dimz), colAllx(dimx); //Create the index vectors, the colAll vectors are equal to span::all but with uvecs (as required by .submat) for(int i = 0; i0){ if(isw) wk = w.submat(ind,colAllw); zk = z.submat(ind,colAllz); yk = y(ind); xk = x.submat(ind,colAllx); murooti thetaStark_struct = thetaStar_vector[k]; mu = thetaStark_struct.mu; rooti = thetaStark_struct.rooti; Sigma = solve(rooti,eye(2,2)); Sigma = trans(Sigma)*Sigma; e1 = xk-zk*delta; ee2 = mu[1] + (Sigma(0,1)/Sigma(0,0))*(e1-mu[0]); sig = sqrt(Sigma(1,1)-pow(Sigma(0,1),2.0)/Sigma(0,0)); yt = join_cols(yt,(yk-ee2)/sig); //analogous to rbind() if(isw) { xt = join_cols(xt,join_rows(xk,wk)/sig); } else { xt = join_cols(xt,xk/sig); } } } ytxtxtd out_struct; out_struct.yt = yt; out_struct.xt = xt; return(out_struct); } ytxtxtd get_ytxtd(vec const& y, mat const& z, double beta, vec const& gamma, mat const& x, mat const& w, int ncomp, ivec const& indic,std::vector const& thetaStar_vector, int dimd){ // Wayne Taylor 3/14/2015 int dimx = x.n_cols; //variable type initializaion int indsize, indicsize; vec zveck, yk, mu, ytk, u, yt; mat C, wk, zk, xk, rooti, Sigma, B, L, Li, z2, zt1, zt2, xtd; uvec colAllw, colAllz(dimd), colAllx(dimx), ind, seqindk, negseqindk; //Create index vectors (uvec) for submatrix views indicsize = indic.size(); //here the uvecs are declared once, and within each loop the correctly sized vector is extracted as needed uvec seqind(indicsize);for(int i = 0;i0){ mat xtdk(2*indsize,dimd); //extract the properly sized vector section seqindk = seqind.subvec(0,indsize-1); negseqindk = negseqind.subvec(0,indsize-1); if(isw) wk = w.submat(ind,colAllw); zk = z.submat(ind,colAllz); zveck = vectorise(trans(zk)); yk = y(ind); xk = x.submat(ind,colAllx); murooti thetaStark_struct = thetaStar_vector[k]; mu = thetaStark_struct.mu; rooti = thetaStark_struct.rooti; Sigma = solve(rooti,eye(2,2)); Sigma = trans(Sigma)*Sigma; B = C*Sigma*trans(C); L = trans(chol(B)); Li = solve(trimatl(L),eye(2,2)); // L is lower triangular, trimatl interprets the matrix as lower triangular and makes solve more efficient if(isw) { u = vectorise(yk-wk*gamma-mu[1]-beta*mu[0]); } else { u = vectorise(yk-mu[1]-beta*mu[0]); } ytk = vectorise(Li * join_cols(trans(xk-mu[0]),trans(u))); z2 = trans(join_rows(zveck,beta*zveck)); //join_rows is analogous to cbind() z2 = Li*z2; zt1 = z2(0,span::all); zt2 = z2(1,span::all); zt1.reshape(dimd,indsize); zt1 = trans(zt1); zt2.reshape(dimd,indsize); zt2=trans(zt2); xtdk(seqindk,colAllz) = zt1; xtdk(negseqindk,colAllz) = zt2; yt = join_cols(yt,ytk); xtd = join_cols(xtd,xtdk); } } ytxtxtd out_struct; out_struct.yt = yt; out_struct.xtd = xtd; return(out_struct); } DPOut rthetaDP(int maxuniq, double alpha, lambda lambda_struct, priorAlpha const& priorAlpha_struct, std::vector thetaStar_vector, ivec indic, vec const& q0v, mat const& y, int gridsize, List lambda_hyper){ // Wayne Taylor 3/14/2015 // function to make one draw from DP process // P. Rossi 1/06 // added draw of alpha 2/06 // removed lambdaD,etaD and function arguments 5/06 // removed thetaStar argument to .Call and creation of newthetaStar 7/06 // removed q0 computations as eta is not drawn 7/06 // changed for new version of thetadraw and removed calculation of thetaStar before // .Call 7/07 // y(i) ~ f(y|theta[[i]],eta) // theta ~ DP(alpha,G(lambda)) //output: // list with components: // thetaDraws: list, [[i]] is a list of the ith draw of the n theta's // where n is the length of the input theta and nrow(y) // thetaNp1Draws: list, [[i]] is ith draw of theta_{n+1} //args: // maxuniq: the maximum number of unique thetaStar values -- an error will be raised // if this is exceeded // alpha,lambda: starting values (or fixed DP prior values if not drawn). // Prioralpha: list of hyperparms of alpha prior // theta: list of starting value for theta's // thetaStar: list of unique values of theta, thetaStar[[i]] // indic: n vector of indicator for which unique theta (in thetaStar) // y: is a matrix nxk // thetaStar: list of unique values of theta, thetaStar[[i]] // q0v:a double vector with the same number of rows as y, giving \Int f(y(i)|theta,eta) dG_{lambda}(theta). int n = y.n_rows; int dimy = y.n_cols; //variable type initializaion int nunique, indsize, indp, probssize; vec probs; uvec ind; mat ydenmat; uvec spanall(dimy); for(int i = 0; i new_utheta(1), thetaNp1_vector(1); murooti thetaNp10_struct, outGD; vec p(n); p[n-1] = alpha/(alpha+(n-1)); for(int i = 0; i<(n-1); i++){ p[i] = 1/(alpha+(n-1)); } nunique = thetaStar_vector.size(); if(nunique > maxuniq) stop("maximum number of unique thetas exceeded"); //ydenmat is a length(thetaStar) x n array of density values given f(y[j,] | thetaStar[[i]] // note: due to remix step (below) we must recompute ydenmat each time! ydenmat = zeros(maxuniq,n); ydenmat(span(0,nunique-1),span::all) = yden(thetaStar_vector,y); thetaStarDrawOut_struct = thetaStarDraw(indic, thetaStar_vector, y, ydenmat, q0v, alpha, lambda_struct, maxuniq); thetaStar_vector = thetaStarDrawOut_struct.thetaStar_vector; indic = thetaStarDrawOut_struct.indic; nunique = thetaStar_vector.size(); //thetaNp1 and remix probs = zeros(nunique+1); for(int j = 0; j < nunique; j++){ ind = find(indic == (j+1)); indsize = ind.size(); probs[j] = indsize/(alpha+n+0.0); new_utheta[0] = thetaD(y(ind,spanall),lambda_struct); thetaStar_vector[j] = new_utheta[0]; } probs[nunique] = alpha/(alpha+n+0.0); indp = rmultinomF(probs); probssize = probs.size(); if(indp == probssize) { outGD = GD(lambda_struct); thetaNp10_struct.mu = outGD.mu; thetaNp10_struct.rooti = outGD.rooti; thetaNp1_vector[0] = thetaNp10_struct; } else { outGD = thetaStar_vector[indp-1]; thetaNp10_struct.mu = outGD.mu; thetaNp10_struct.rooti = outGD.rooti; thetaNp1_vector[0] = thetaNp10_struct; } //draw alpha alpha = alphaD(priorAlpha_struct,nunique,gridsize); //draw lambda lambda_struct = lambdaD(lambda_struct,thetaStar_vector,lambda_hyper["alim"],lambda_hyper["nulim"],lambda_hyper["vlim"],gridsize); DPOut out_struct; out_struct.indic = indic; out_struct.thetaStar_vector = thetaStar_vector; out_struct.thetaNp1_vector = thetaNp1_vector; out_struct.alpha = alpha; out_struct.Istar = nunique; out_struct.lambda_struct = lambda_struct; return(out_struct); } //RCPP SECTION---- //[[Rcpp::export]] List rivDP_rcpp_loop(int R, int keep, int nprint, int dimd, vec const& mbg, mat const& Abg, vec const& md, mat const& Ad, vec const& y, bool isgamma, mat const& z, vec const& x, mat const& w, vec delta, List const& PrioralphaList, int gridsize, bool SCALE, int maxuniq, double scalex, double scaley, List const& lambda_hyper,double BayesmConstantA, int BayesmConstantnu){ // Wayne Taylor 3/14/2015 int n = y.size(); int dimg = 1; if(isgamma) dimg = w.n_cols; //variable type initializaion int Istar, bgsize, mkeep; double beta; vec gammaVec, q0v, bg; mat errMat, wEmpty, V; wEmpty.reset(); //enforce 0 elements ytxtxtd out_struct; //initialize indicator vector, thetaStar, ncomp, alpha ivec indic = ones(n); std::vector thetaStar_vector(1), thetaNp1_vector(1); murooti thetaNp10_struct, thetaStar0_struct; thetaStar0_struct.mu = zeros(2); thetaStar0_struct.rooti = eye(2,2); thetaStar_vector[0] = thetaStar0_struct; //Initialize lambda lambda lambda_struct; lambda_struct.mubar = zeros(2); lambda_struct.Amu = BayesmConstantA; lambda_struct.nu = BayesmConstantnu; lambda_struct.V = lambda_struct.nu*eye(2,2); //convert Prioralpha from List to struct priorAlpha priorAlpha_struct; priorAlpha_struct.power = PrioralphaList["power"]; priorAlpha_struct.alphamin = PrioralphaList["alphamin"]; priorAlpha_struct.alphamax = PrioralphaList["alphamax"]; priorAlpha_struct.n = PrioralphaList["n"]; int ncomp = 1; double alpha = 1.0; //allocate space for draws mat deltadraw = zeros(R/keep,dimd); vec betadraw = zeros(R/keep); vec alphadraw = zeros(R/keep); vec Istardraw = zeros(R/keep); mat gammadraw = zeros(R/keep,dimg); List thetaNp1draw(R/keep); vec nudraw = zeros(R/keep); vec vdraw = zeros(R/keep); vec adraw = zeros(R/keep); if(nprint>0) startMcmcTimer(); for(int rep = 0; rep < R; rep++) { //draw beta and gamma if(isgamma){ out_struct = get_ytxt(y,z,delta,x,w,ncomp,indic,thetaStar_vector); } else { out_struct = get_ytxt(y,z,delta,x,wEmpty,ncomp,indic,thetaStar_vector); } bg = breg(out_struct.yt,out_struct.xt,mbg,Abg); beta = bg[0]; bgsize = bg.size()-1; if(isgamma) gammaVec = bg.subvec(1,bgsize); //draw delta if(isgamma){ out_struct=get_ytxtd(y,z,beta,gammaVec,x,w,ncomp,indic,thetaStar_vector,dimd); } else { out_struct=get_ytxtd(y,z,beta,gammaVec,x,wEmpty,ncomp,indic,thetaStar_vector,dimd); } delta = breg(out_struct.yt,out_struct.xtd,md,Ad); //DP process stuff- theta | lambda if(isgamma) { errMat = join_rows(x-z*delta,y-beta*x-w*gammaVec); } else { errMat = join_rows(x-z*delta,y-beta*x); } q0v = q0(errMat,lambda_struct); DPOut DPout_struct = rthetaDP(maxuniq,alpha,lambda_struct,priorAlpha_struct,thetaStar_vector,indic,q0v,errMat,gridsize,lambda_hyper); indic = DPout_struct.indic; thetaStar_vector = DPout_struct.thetaStar_vector; alpha = DPout_struct.alpha; Istar = DPout_struct.Istar; thetaNp1_vector = DPout_struct.thetaNp1_vector; thetaNp10_struct = thetaNp1_vector[0]; ncomp=thetaStar_vector.size(); lambda_struct = DPout_struct.lambda_struct; if (nprint>0) if((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; deltadraw(mkeep-1,span::all) = trans(delta); betadraw[mkeep-1] = beta; alphadraw[mkeep-1] = alpha; Istardraw[mkeep-1] = Istar; if(isgamma) gammadraw(mkeep-1,span::all) = trans(gammaVec); //We need to convert from to NumericVector so that the nmix plotting works properly (it does not work for an nx1 matrix) thetaNp1draw[mkeep-1] = List::create(List::create(Named("mu") = NumericVector(thetaNp10_struct.mu.begin(),thetaNp10_struct.mu.end()),Named("rooti") = thetaNp10_struct.rooti)); adraw[mkeep-1] = lambda_struct.Amu; nudraw[mkeep-1] = lambda_struct.nu; V = lambda_struct.V; vdraw[mkeep-1] = V(0,0)/lambda_struct.nu; } } //rescale if(SCALE){ deltadraw=deltadraw*scalex; betadraw=betadraw*scaley/scalex; if(isgamma) gammadraw=gammadraw*scaley; } if (nprint>0) endMcmcTimer(); return List::create( Named("deltadraw") = deltadraw, Named("betadraw") = betadraw, Named("alphadraw") = alphadraw, Named("Istardraw") = Istardraw, Named("gammadraw") = gammadraw, Named("thetaNp1draw") = thetaNp1draw, Named("adraw") = adraw, Named("nudraw") = nudraw, Named("vdraw") = vdraw); } bayesm/src/rwishart_rcpp.cpp0000644000176000001440000000221113134410700015731 0ustar ripleyusers#include "bayesm.h" // [[Rcpp::export]] List rwishart(double nu, mat const& V){ // Wayne Taylor 4/7/2015 // Function to draw from Wishart (nu,V) and IW // W ~ W(nu,V) // E[W]=nuV // WI=W^-1 // E[WI]=V^-1/(nu-m-1) // T has sqrt chisqs on diagonal and normals below diagonal int m = V.n_rows; mat T = zeros(m,m); for(int i = 0; i < m; i++) { T(i,i) = sqrt(rchisq(1,nu-i)[0]); //rchisq returns a vectorized object, so using [0] allows for the conversion to double } for(int j = 0; j < m; j++) { for(int i = j+1; i < m; i++) { T(i,j) = rnorm(1)[0]; //rnorm returns a NumericVector, so using [0] allows for conversion to double }} mat C = trans(T)*chol(V); mat CI = solve(trimatu(C),eye(m,m)); //trimatu interprets the matrix as upper triangular and makes solve more efficient // C is the upper triangular root of Wishart therefore, W=C'C // this is the LU decomposition Inv(W) = CICI' Note: this is // the UL decomp not LU! // W is Wishart draw, IW is W^-1 return List::create( Named("W") = trans(C) * C, Named("IW") = CI * trans(CI), Named("C") = C, Named("CI") = CI); } bayesm/src/lndIChisq_rcpp.cpp0000644000176000001440000000047313134410700015754 0ustar ripleyusers#include "bayesm.h" // [[Rcpp::export]] mat lndIChisq(double nu, double ssq, mat const& X) { // Keunwoo Kim 07/24/2014 // Purpose: evaluate log-density of scaled Inverse Chi-sq density of random variable Z=nu*ssq/chisq(nu) return(-lgamma(nu/2)+(nu/2)*log((nu*ssq)/2)-((nu/2)+1)*log(X)-(nu*ssq)/(2*X)); } bayesm/src/rnmixGibbs_rcpp_loop.cpp0000644000176000001440000000241313134410700017227 0ustar ripleyusers#include "bayesm.h" //[[Rcpp::export]] List rnmixGibbs_rcpp_loop(mat const& y, mat const& Mubar, mat const& A, double nu, mat const& V, vec const& a, vec p, vec z, int const& R, int const& keep, int const& nprint) { // Wayne Taylor 9/10/2014 int mkeep = 0; mat pdraw(R/keep,p.size()); mat zdraw(R/keep,z.size()); List compdraw(R/keep); if(nprint>0) startMcmcTimer(); // start main iteration loop for(int rep = 0; rep(out["p"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> z = as(out["z"]); // print time to completion and draw # every nprint'th draw if (nprint>0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; pdraw(mkeep-1,span::all) = trans(p); zdraw(mkeep-1,span::all) = trans(z); compdraw[mkeep-1] = compsd; } } if(nprint>0) endMcmcTimer(); return List::create( Named("probdraw") = pdraw, Named("zdraw") = zdraw, Named("compdraw") = compdraw); } bayesm/src/lndMvst_rcpp.cpp0000644000176000001440000000133413134410700015522 0ustar ripleyusers#include "bayesm.h" // [[Rcpp::export]] double lndMvst(vec const& x, double nu, vec const& mu, mat const& rooti, bool NORMC = false){ // Wayne Taylor 9/7/2014 // function to evaluate log of MVstudent t density with nu df, mean mu, // and with sigmai=rooti%*%t(rooti) note: this is the UL decomp of sigmai not LU! // rooti is in the inverse of upper triangular chol root of sigma // or Sigma=root'root root=inv(rooti) int dim = x.size(); double constant; if(NORMC){ constant = (nu/2)*log(nu)+lgamma((nu+dim)/2)-(dim/2.0)*log(M_PI)-lgamma(nu/2); } else { constant = 0.0; } vec z = vectorise(trans(rooti)*(x-mu)); return((constant-((dim+nu)/2)*log(nu+trans(z)*z)+sum(log(diagvec(rooti))))[0]); } bayesm/src/rdirichlet_rcpp.cpp0000644000176000001440000000063513134410700016227 0ustar ripleyusers#include "bayesm.h" // [[Rcpp::export]] vec rdirichlet(vec const& alpha){ // Wayne Taylor 4/7/2015 // Purpose: // draw from Dirichlet(alpha) int dim = alpha.size(); vec y = zeros(dim); for(int i = 0; i regdata_vector; moments regdatai_struct; // store vector with struct for (reg=0; reg(regdatai["y"]); regdatai_struct.X = as(regdatai["X"]); regdatai_struct.XpX = as(regdatai["XpX"]); regdatai_struct.Xpy = as(regdatai["Xpy"]); regdata_vector.push_back(regdatai_struct); } mat betas(nreg, nvar); mat Vbetadraw(R/keep, nvar*nvar); mat Deltadraw(R/keep, nz*nvar); mat taudraw(R/keep, nreg); cube betadraw(nreg, nvar, R/keep); if (nprint>0) startMcmcTimer(); //start main iteration loop for (int rep=0; rep(rmregout["Sigma"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> Delta = as(rmregout["B"]); //print time to completion and draw # every nprint'th draw if (nprint>0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; Vbetadraw(mkeep-1, span::all) = trans(vectorise(Vbeta)); Deltadraw(mkeep-1, span::all) = trans(vectorise(Delta)); taudraw(mkeep-1, span::all) = trans(tau); betadraw.slice(mkeep-1) = betas; } } if (nprint>0) endMcmcTimer(); return List::create( Named("Vbetadraw") = Vbetadraw, Named("Deltadraw") = Deltadraw, Named("betadraw") = betadraw, Named("taudraw") = taudraw); } bayesm/src/utilityFunctions.cpp0000644000176000001440000006076713134410700016462 0ustar ripleyusers#include "bayesm.h" //Used in rmvpGibbs and rmnpGibbs--------------------------------------------------------------------------------- vec condmom(vec const& x, vec const& mu, mat const& sigmai, int p, int j){ // Wayne Taylor 9/24/2014 //function to compute moments of x[j] | x[-j] //output is a vec: the first element is the conditional mean // the second element is the conditional sd vec out(2); int jm1 = j-1; int ind = p*jm1; double csigsq = 1/sigmai(ind+jm1); double m = 0.0; for(int i = 0; i .999999999) arg = .999999999; if(arg < .0000000001) arg = .0000000001; result = mu + sigma*R::qnorm(arg,0.0,1.0,1,0); return (result); } //Used in rhierLinearModel, rhierLinearMixture and rhierMnlRWMixture------------------------------------------------------ mat drawDelta(mat const& x,mat const& y,vec const& z,List const& comps,vec const& deltabar,mat const& Ad){ // Wayne Taylor 10/01/2014 // delta = vec(D) // given z and comps (z[i] gives component indicator for the ith observation, // comps is a list of mu and rooti) // y is n x p // x is n x k // y = xD' + U , rows of U are indep with covs Sigma_i given by z and comps int p = y.n_cols; int k = x.n_cols; int ncomp = comps.length(); mat xtx = zeros(k*p,k*p); mat xty = zeros(p,k); //this is the unvecced version, reshaped after the sum //Create the index vectors, the colAll vectors are equal to span::all but with uvecs (as required by .submat) uvec colAlly(p), colAllx(k); for(int i = 0; i0){ mat yi = y.submat(ind,colAlly); mat xi = x.submat(ind,colAllx); List compsi = comps[compi]; rowvec mui = as(compsi[0]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> mat rootii = trimatu(as(compsi[1])); //trimatu interprets the matrix as upper triangular yi.each_row() -= mui; //subtracts mui from each row of yi mat sigi = rootii*trans(rootii); xtx = xtx + kron(trans(xi)*xi,sigi); xty = xty + (sigi * (trans(yi)*xi)); } } xty.reshape(xty.n_rows*xty.n_cols,1); //vec(t(D)) ~ N(V^{-1}(xty + Ad*deltabar),V^{-1}) where V = (xtx+Ad) // compute the inverse of xtx+Ad mat ucholinv = solve(trimatu(chol(xtx+Ad)), eye(k*p,k*p)); //trimatu interprets the matrix as upper triangular and makes solve more efficient mat Vinv = ucholinv*trans(ucholinv); return(Vinv*(xty+Ad*deltabar) + trans(chol(Vinv))*as(rnorm(deltabar.size()))); } unireg runiregG(vec const& y, mat const& X, mat const& XpX, vec const& Xpy, double sigmasq, mat const& A, vec const& Abetabar, double nu, double ssq) { // Keunwoo Kim 09/16/2014 // Purpose: // perform one Gibbs iteration for Univ Regression Model // only does one iteration so can be used in rhierLinearModel // Model: // y = Xbeta + e e ~N(0,sigmasq) // y is n x 1 // X is n x k // beta is k x 1 vector of coefficients // Prior: // beta ~ N(betabar,A^-1) // sigmasq ~ (nu*ssq)/chisq_nu unireg out_struct; int n = y.size(); int k = XpX.n_cols; //first draw beta | sigmasq mat IR = solve(trimatu(chol(XpX/sigmasq+A)), eye(k,k)); //trimatu interprets the matrix as upper triangular and makes solve more efficient vec btilde = (IR*trans(IR)) * (Xpy/sigmasq + Abetabar); vec beta = btilde + IR*vec(rnorm(k)); //now draw sigmasq | beta double s = sum(square(y-X*beta)); sigmasq = (s + nu*ssq)/rchisq(1,nu+n)[0]; //rchisq returns a vectorized object, so using [0] allows for the conversion to double out_struct.beta = beta; out_struct.sigmasq = sigmasq; return (out_struct); } //Used in rnegbinRW and rhierNegbinRw------------------------------------------------------------------------------------- double llnegbin(vec const& y, vec const& lambda, double alpha, bool constant){ // Keunwoo Kim 11/02/2014 // Computes the log-likelihood // Arguments // y - a vector of observation // lambda - a vector of mean parameter (=exp(X*beta)) // alpha - dispersion parameter // constant - TRUE(FALSE) if it computes (un)normalized log-likeihood // PMF // pmf(y) = (y+alpha-1)Choose(y) * p^alpha * (1-p)^y // (y+alpha-1)Choose(y) = (alpha)*(alpha+1)*...*(alpha+y-1) / y! when y>=1 (0 when y=0) int i; int nobs = y.size(); vec prob = alpha/(alpha+lambda); vec logp(nobs); if (constant){ // normalized log-likelihood for (i=0; i(rnorm(X.n_cols)); double cll = llmnl(betac,y,X); double clpost = cll+lndMvn(betac,betabar,rootpi); double ldiff = clpost-oldll-lndMvn(oldbeta,betabar,rootpi); alphaminv << 1 << exp(ldiff); double alpha = min(alphaminv); if(alpha < 1) { unif = runif(1)[0]; //runif returns a NumericVector, so using [0] allows for conversion to double } else { unif=0;} if (unif <= alpha) { betadraw = betac; oldll = cll; } else { betadraw = oldbeta; stay = 1; } metropout_struct.betadraw = betadraw; metropout_struct.stay = stay; metropout_struct.oldll = oldll; return (metropout_struct); } //Used in rDPGibbs, rhierMnlDP, rivDP----------------------------------------------------------------------------- int rmultinomF(vec const& p){ // Wayne Taylor 1/28/2015 vec csp = cumsum(p); double rnd = runif(1)[0]; //runif returns a NumericVector, so using [0] allows for conversion to double int res = 0; int psize = p.size(); for(int i = 0; i < psize; i++){ if(rnd > csp[i]) res = res+1; } return(res+1); } mat yden(std::vector const& thetaStar_vector, mat const& y){ // Wayne Taylor 2/4/2015 // function to compute f(y | theta) // computes f for all values of theta in theta list of lists // arguments: // thetaStar is a list of lists. thetaStar[[i]] is a list with components, mu, rooti // y |theta[[i]] ~ N(mu,(rooti %*% t(rooti))^-1) rooti is inverse of Chol root of Sigma // output: // length(thetaStar) x n array of values of f(y[j,]|thetaStar[[i]] int nunique = thetaStar_vector.size(); int n = y.n_rows; int k = y.n_cols; mat ydenmat = zeros(nunique,n); vec mu; mat rooti, transy, quads; for(int i = 0; i < nunique; i++){ //now compute vectorized version of lndMvn //compute y_i'RIRI'y_i for all i mu = thetaStar_vector[i].mu; rooti = thetaStar_vector[i].rooti; transy = trans(y); transy.each_col() -= mu; //column-wise subtraction quads = sum(square(trans(rooti) * transy),0); //same as colSums ydenmat(i,span::all) = exp(-(k/2.0)*log(2*M_PI) + sum(log(rooti.diag())) - .5*quads); } return(ydenmat); } ivec numcomp(ivec const& indic, int k){ // Wayne Taylor 1/28/2015 //find the number of times each of k integers is in the vector indic ivec ncomp(k); for(int comp = 0; comp < k; comp++){ ncomp[comp]=sum(indic == (comp+1)); } return(ncomp); } murooti thetaD(mat const& y, lambda const& lambda_struct){ // Wayne Taylor 2/4/2015 // function to draw from posterior of theta given data y and base prior G0(lambda) // here y ~ N(mu,Sigma) // theta = list(mu=mu,rooti=chol(Sigma)^-1) // mu|Sigma ~ N(mubar,Sigma (x) Amu-1) // Sigma ~ IW(nu,V) // arguments: // y is n x k matrix of obs // lambda is list(mubar,Amu,nu,V) // output: // one draw of theta, list(mu,rooti) // Sigma=inv(rooti)%*%t(inv(rooti)) // note: we assume that y is a matrix. if there is only one obs, y is a 1 x k matrix mat X = ones(y.n_rows,1); mat A(1,1); A.fill(lambda_struct.Amu); List rout = rmultireg(y,X,trans(lambda_struct.mubar),A,lambda_struct.nu,lambda_struct.V); murooti out_struct; out_struct.mu = as(rout["B"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> out_struct.rooti = solve(chol(trimatu(as(rout["Sigma"]))),eye(y.n_cols,y.n_cols)); //trimatu interprets the matrix as upper triangular and makes solve more efficient return(out_struct); } thetaStarIndex thetaStarDraw(ivec indic, std::vector thetaStar_vector, mat const& y, mat ydenmat, vec const& q0v, double alpha, lambda const& lambda_struct, int maxuniq) { // Wayne Taylor 2/4/2015 // indic is n x 1 vector of indicator of which of thetaStar is assigned to each observation // thetaStar is list of the current components (some of which may never be used) // y is n x d matrix of observations // ydenmat is maxuniq x n matrix to store density evaluations - we assume first // length(Thetastar) rows are filled in with density evals // q0v is vector of bayes factors for new component and each observation // alpha is DP process tightness prior // lambda is list of priors for the base DP process measure // maxuniq maximum number of mixture components // yden is function to fill out an array // thetaD is function to draw theta from posterior of theta given y and G0 int n = indic.size(); ivec ncomp, indicC; int k, inc, cntNonzero; std::vector listofone_vector(1); std::vector thetaStarC_vector; //draw theta_i given theta_-i for(int i = 0; i(n-1); inc = 0; for(int j = 0; j<(n-1); j++){ if(j == i) {inc = inc + 1;} indicmi[j] = indic[inc]; inc = inc+1; } ncomp = numcomp(indicmi,k); for(int comp = 0; comp maxuniq) { stop("max number of comps exceeded"); } else { listofone_vector[0] = thetaD(y(i,span::all),lambda_struct); thetaStar_vector.push_back(listofone_vector[0]); ydenmat(k,span::all) = yden(listofone_vector,y); }} } //clean out thetaStar of any components which have zero observations associated with them //and re-write indic vector k = thetaStar_vector.size(); indicC = zeros(n); ncomp = numcomp(indic,k); cntNonzero = 0; for(int comp = 0; comp 1) { vec km1(k-1); for(int i = 0; i < (k-1); i++) km1[i] = i+1; //vector of 1:k SEE SEQ_ALONG lnk1k2 = (k/2.0)*log(2.0)+log((lambda_struct.nu-k)/2)+lgamma((lambda_struct.nu-k)/2)-lgamma(lambda_struct.nu/2)+sum(log(lambda_struct.nu/2-km1/2)); } else { lnk1k2 = (k/2.0)*log(2.0)+log((lambda_struct.nu-k)/2)+lgamma((lambda_struct.nu-k)/2)-lgamma(lambda_struct.nu/2); } constant = -(k/2.0)*log(2*M_PI)+(k/2.0)*log(lambda_struct.Amu/(1+lambda_struct.Amu)) + lnk1k2 + lambda_struct.nu*logdetR; // note: here we are using the fact that |V + S_i | = |R|^2 (1 + v_i'v_i) // where v_i = sqrt(Amu/(1+Amu))*t(R^-1)*(y_i-mubar), R is chol(V) // and S_i = Amu/(1+Amu) * (y_i-mubar)(y_i-mubar)' transy = trans(y); transy.each_col() -= lambda_struct.mubar; m = sqrt(lambda_struct.Amu/(1+lambda_struct.Amu))*trans(solve(trimatu(R),eye(y.n_cols,y.n_cols)))*transy; //trimatu interprets the matrix as upper triangular and makes solve more efficient vivi = sum(square(m),0); lnq0v = constant - ((lambda_struct.nu+1)/2)*(2*logdetR+log(1+vivi)); return(trans(exp(lnq0v))); } vec seq_rcpp(double from, double to, int len){ // Wayne Taylor 1/28/2015 // Same as R::seq() vec res(len); res[len-1] = to; res[0] = from; //note the order of these two statements is important, when gridsize = 1 res[0] will be rewritten to the correct number double increment = (res[len-1]-res[0])/(len-1); for(int i = 1; i<(len-1); i++) res[i] = res[i-1] + increment; return(res); } double alphaD(priorAlpha const& priorAlpha_struct, int Istar, int gridsize){ // Wayne Taylor 2/4/2015 // function to draw alpha using prior, p(alpha)= (1-(alpha-alphamin)/(alphamax-alphamin))**power //same as seq vec alpha = seq_rcpp(priorAlpha_struct.alphamin,priorAlpha_struct.alphamax-.000001,gridsize); vec lnprob(gridsize); for(int i = 0; i(Rout["IW"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> mat root = chol(Sigma); mat draws = rnorm(k); mat mu = lambda_struct.mubar + (1/sqrt(lambda_struct.Amu))*trans(root)*draws; murooti out_struct; out_struct.mu = mu; out_struct.rooti = solve(trimatu(root),eye(k,k)); //trimatu interprets the matrix as upper triangular and makes solve more efficient return(out_struct); } lambda lambdaD(lambda const& lambda_struct, std::vector const& thetaStar_vector, vec const& alim, vec const& nulim, vec const& vlim, int gridsize){ // Wayne Taylor 2/4/2015 // revision history // p. rossi 7/06 // vectorized 1/07 // changed 2/08 to paramaterize V matrix of IW prior to nu*v*I; then mode of Sigma=nu/(nu+2)vI // this means that we have a reparameterization to v* = nu*v // function to draw (nu, v, a) using uniform priors // theta_j=(mu_j,Sigma_j) mu_j~N(0,Sigma_j/a) Sigma_j~IW(nu,vI) // recall E[Sigma]= vI/(nu-dim-1) vec lnprob, probs, rowSumslgammaarg; int ind; //placeholder for matrix indexing murooti thetaStari_struct; mat rootii; vec mui; mat mout, rimu, arg, lgammaarg; double sumdiagriri, sumlogdiag, sumquads, adraw, nudraw, vdraw; murooti thetaStar0_struct = thetaStar_vector[0]; int d = thetaStar0_struct.mu.size(); int Istar = thetaStar_vector.size(); vec aseq = seq_rcpp(alim[0],alim[1],gridsize); vec nuseq = d-1+exp(seq_rcpp(nulim[0],nulim[1],gridsize)); //log uniform grid vec vseq = seq_rcpp(vlim[0],vlim[1],gridsize); // "brute" force approach would simply loop over the // "observations" (theta_j) and use log of the appropriate densities. To vectorize, we // notice that the "data" comes via various statistics: // 1. sum of log(diag(rooti_j) // 2. sum of tr(V%*%rooti_j%*%t(rooti_j)) where V=vI_d // 3. quadratic form t(mu_j-0)%*%rooti%*%t(rooti)%*%(mu_j-0) // thus, we will compute these first. // for documentation purposes, we leave brute force code in comment fields // extract needed info from thetastar list //mout has the rootis in form: [t(rooti_1), t(rooti_2), ...,t(rooti_Istar)] mout = zeros(d,Istar*d); ind = 0; for(int i = 0; i < Istar; i++){ thetaStari_struct = thetaStar_vector[i]; rootii = thetaStari_struct.rooti; ind = i*d; mout.submat(0, ind,d-1,ind+d-1) = trans(rootii); } sumdiagriri = sum(sum(square(mout),0)); //sum_i trace(rooti_i*trans(rooti_i)) // now get diagonals of rooti sumlogdiag = 0.0; for(int i = 0; i < Istar; i++){ ind = i*d; for(int j = 0; j < d; j++){ sumlogdiag = sumlogdiag+log(mout(j,ind+j)); } } //columns of rimu contain trans(rooti_i)*mu_i rimu = zeros(d,Istar); for(int i = 0; i < Istar; i++){ thetaStari_struct = thetaStar_vector[i]; mui = thetaStari_struct.mu; rootii = thetaStari_struct.rooti; rimu(span::all,i) = trans(rootii) * mui; } sumquads = sum(sum(square(rimu),0)); // draw a (conditionally indep of nu,v given theta_j) lnprob = zeros(aseq.size()); // for(i in seq(along=aseq)){ // for(j in seq(along=thetastar)){ // lnprob[i]=lnprob[i]+lndMvn(thetastar[[j]]$mu,c(rep(0,d)),thetastar[[j]]$rooti*sqrt(aseq[i]))} lnprob = Istar*(-(d/2.0)*log(2*M_PI))-.5*aseq*sumquads+Istar*d*log(sqrt(aseq))+sumlogdiag; lnprob = lnprob-max(lnprob) + 200; probs = exp(lnprob); probs = probs/sum(probs); adraw = aseq[rmultinomF(probs)-1]; // draw nu given v lnprob = zeros(nuseq.size()); // for(i in seq(along=nuseq)){ // for(j in seq(along=thetastar)){ // Sigma_j=crossprod(backsolve(thetastar[[j]]$rooti,diag(d))) // lnprob[i]=lnprob[i]+lndIWishart(nuseq[i],V,Sigma_j)} //same as arg = (nuseq+1-arg)/2.0; arg = zeros(gridsize,d); for(int i = 0; i < d; i++) { vec indvec(gridsize); indvec.fill(-(i+1)+1); arg(span::all,i) = indvec; } arg.each_col() += nuseq; arg = arg/2.0; lgammaarg = zeros(gridsize,d); for(int i = 0; i < gridsize; i++){ for(int j = 0; j < d; j++){ lgammaarg(i,j) = lgamma(arg(i,j)); }} rowSumslgammaarg = sum(lgammaarg,1); lnprob = zeros(gridsize); for(int i = 0; i(vseq.size()); // for(i in seq(along=vseq)){ // V=vseq[i]*diag(d) // for(j in seq(along=thetastar)){ // Sigma_j=crossprod(backsolve(thetastar[[j]]$rooti,diag(d))) // lnprob[i]=lnprob[i]+lndIWishart(nudraw,V,Sigma_j)} // lnprob=Istar*nudraw*d*log(sqrt(vseq))-.5*sumdiagriri*vseq lnprob = Istar*nudraw*d*log(sqrt(vseq*nudraw))-.5*sumdiagriri*vseq*nudraw; lnprob = lnprob-max(lnprob)+200; probs = exp(lnprob); probs = probs/sum(probs); vdraw = vseq[rmultinomF(probs)-1]; // put back into lambda lambda out_struct; out_struct.mubar = zeros(d); out_struct.Amu = adraw; out_struct.nu = nudraw; out_struct.V = nudraw*vdraw*eye(d,d); return(out_struct); } //Used in llnhlogit and simnhlogit--------------------------------------------------------------------------------- double root(double c1, double c2, double tol, int iterlim){ //function to find root of c1 - c2u = lnu int iter = 0; double uold = .1; double unew = .00001; while (iter <= iterlim && fabs(uold-unew) > tol){ uold = unew; unew=uold + (uold*(c1 -c2*uold - log(uold)))/(1. + c2*uold); if(unew < 1.0e-50) unew=1.0e-50; iter=iter+1; } return(unew); } //[[Rcpp::export]] vec callroot(vec const& c1, vec const& c2, double tol, int iterlim){ int n = c1.size(); vec u = zeros(n); for(int i = 0; i(wrap(mu)))-pnorm(gamma2-as(wrap(mu))); //pnorm takes Rcpp type NumericVector, NOT arma objects of type vec vec arg = as(temp); double epsilon = 1.0/(10^-50); for (int j=0; j1){ alpha = 1.0; } if (alpha<1){ unif = runif(1)[0]; //runif returns a NumericVector, so using [0] allows for conversion to double by extracting the first element } else{ unif = 0; } if (unif<=alpha){ dstardraw = dstarc; oldll = cll; } else{ dstardraw = olddstar; stay = 1; } return List::create( Named("dstardraw") = dstardraw, Named("oldll") = oldll, Named("stay") = stay ); } //MAIN FUNCTION--------------------------------------------------------------------------------------- // [[Rcpp::export]] List rordprobitGibbs_rcpp_loop(vec const& y, mat const& X, int k, mat const& A, vec const& betabar, mat const& Ad, double s, mat const& inc_root, vec const& dstarbar, vec const& betahat, int R, int keep, int nprint){ // Keunwoo Kim 09/09/2014 // Purpose: draw from posterior for ordered probit using Gibbs Sampler and metropolis RW // Arguments: // Data // X is nobs x nvar, y is nobs vector of 1,2,.,k (ordinal variable) // Prior // A is nvar x nvar prior preci matrix // betabar is nvar x 1 prior mean // Ad is ndstar x ndstar prior preci matrix of dstar (ncut is number of cut-offs being estimated) // dstarbar is ndstar x 1 prior mean of dstar // Mcmc // R is number of draws // keep is thinning parameter // nprint - prints the estimated time remaining for every nprint'th draw // s is scale parameter of random work Metropolis // Output: list of betadraws and cutdraws // Model: // z=Xbeta + e < 0 e ~N(0,1) // y=1,..,k, if z~c(c[k], c[k+1]) // cutoffs = c[1],..,c[k+1] // dstar = dstar[1],dstar[k-2] // set c[1]=-100, c[2]=0, ...,c[k+1]=100 // c[3]=exp(dstar[1]),c[4]=c[3]+exp(dstar[2]),..., // c[k]=c[k-1]+exp(datsr[k-2]) // Note: 1. length of dstar = length of cutoffs - 3 // 2. Be careful in assessing prior parameter, Ad. .1 is too small for many applications. // Prior: // beta ~ N(betabar,A^-1) // dstar ~ N(dstarbar, Ad^-1) int stay, i, mkeep; vec z; List metropout; int nvar = X.n_cols; int ncuts = k+1; int ncut = ncuts-3; int ndstar = k-2; int ny = y.size(); mat betadraw(R/keep, nvar); mat cutdraw(R/keep, ncuts); mat dstardraw(R/keep, ndstar); vec staydraw(R/keep); vec cutoff1(ny); vec cutoff2(ny); vec sigma(X.n_rows); sigma.ones(); // compute the inverse of trans(X)*X+A mat ucholinv = solve(trimatu(chol(trans(X)*X+A)), eye(nvar,nvar)); //trimatu interprets the matrix as upper triangular and makes solve more efficient mat XXAinv = ucholinv*trans(ucholinv); mat root = chol(XXAinv); vec Abetabar = trans(A)*betabar; // compute the inverse of Ad ucholinv = solve(trimatu(chol(Ad)), eye(ndstar,ndstar)); mat Adinv = ucholinv*trans(ucholinv); mat rootdi = chol(Adinv); // set initial values for MCMC vec olddstar(ndstar); olddstar.zeros(); vec beta = betahat; vec cutoffs = dstartoc(olddstar); double oldll = lldstar(olddstar, y, X*betahat); if (nprint>0) startMcmcTimer(); //start main iteration loop for (int rep=0; rep(metropout["dstardraw"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> oldll = as(metropout["oldll"]); cutoffs = dstartoc(olddstar); stay = as(metropout["stay"]); //print time to completion and draw # every nprint'th draw if (nprint>0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; cutdraw(mkeep-1,span::all) = trans(cutoffs); dstardraw(mkeep-1,span::all) = trans(olddstar); betadraw(mkeep-1,span::all) = trans(beta); staydraw[mkeep-1] = stay; } } double accept = 1-sum(staydraw)/(R/keep); if (nprint>0) endMcmcTimer(); return List::create( Named("cutdraw") = cutdraw, Named("dstardraw") = dstardraw, Named("betadraw") = betadraw, Named("accept") = accept ); } bayesm/src/rhierMnlRwMixture_rcpp_loop.cpp0000644000176000001440000002136713134410700020603 0ustar ripleyusers#include "bayesm.h" //FUNCTION SPECIFIC TO MAIN FUNCTION------------------------------------------------------ //[[Rcpp::export]] double llmnl_con(vec const& betastar, vec const& y, mat const& X, vec const& SignRes = NumericVector::create(0)){ // Wayne Taylor 7/8/2016 // Evaluates log-likelihood for the multinomial logit model WITH SIGN CONSTRAINTS // NOTE: this is exported only because it is used in the shell .R function, it will not be available to users //Reparameterize betastar to beta to allow for sign restrictions vec beta = betastar; //The default SignRes vector is a single element vector containing a zero //any() returns true if any elements of SignRes are non-zero if(any(SignRes)){ uvec signInd = find(SignRes != 0); beta.elem(signInd) = SignRes.elem(signInd) % exp(beta.elem(signInd)); //% performs element-wise multiplication } int n = y.size(); int j = X.n_rows/n; mat Xbeta = X*beta; vec xby = zeros(n); vec denom = zeros(n); for(int i = 0; i(rnorm(X.n_cols)); double cll = llmnl_con(betac,y,X,SignRes); double clpost = cll+lndMvn(betac,betabar,rootpi); double ldiff = clpost-oldll-lndMvn(oldbeta,betabar,rootpi); alphaminv << 1 << exp(ldiff); double alpha = min(alphaminv); if(alpha < 1) { unif = as_scalar(vec(runif(1))); } else { unif=0;} if (unif <= alpha) { betadraw = betac; oldll = cll; } else { betadraw = oldbeta; stay = 1; } out_struct.betadraw = betadraw; out_struct.stay = stay; out_struct.oldll = oldll; return (out_struct); } //MAIN FUNCTION------------------------------------------------------------------------------------- //[[Rcpp::export]] List rhierMnlRwMixture_rcpp_loop(List const& lgtdata, mat const& Z, vec const& deltabar, mat const& Ad, mat const& mubar, mat const& Amu, double nu, mat const& V, double s, int R, int keep, int nprint, bool drawdelta, mat olddelta, vec const& a, vec oldprob, mat oldbetas, vec ind, vec const& SignRes){ // Wayne Taylor 10/01/2014 int nlgt = lgtdata.size(); int nvar = V.n_cols; int nz = Z.n_cols; mat rootpi, betabar, ucholinv, incroot; int mkeep; mnlMetropOnceOut metropout_struct; List lgtdatai, nmix; // convert List to std::vector of struct std::vector lgtdata_vector; moments lgtdatai_struct; for (int lgt = 0; lgt(lgtdatai["y"]); lgtdatai_struct.X = as(lgtdatai["X"]); lgtdatai_struct.hess = as(lgtdatai["hess"]); lgtdata_vector.push_back(lgtdatai_struct); } // allocate space for draws vec oldll = zeros(nlgt); cube betadraw(nlgt, nvar, R/keep); mat probdraw(R/keep, oldprob.size()); vec loglike(R/keep); mat Deltadraw(1,1); if(drawdelta) Deltadraw.zeros(R/keep, nz*nvar);//enlarge Deltadraw only if the space is required List compdraw(R/keep); if (nprint>0) startMcmcTimer(); for (int rep = 0; rep(mgout["p"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> ind = as(mgout["z"]); //now draw delta | {beta_i}, ind, comps if(drawdelta) olddelta = drawDelta(Z,oldbetas,ind,oldcomp,deltabar,Ad); //loop over all LGT equations drawing beta_i | ind[i],z[i,],mu[ind[i]],rooti[ind[i]] for(int lgt = 0; lgt(oldcomplgt[1]); //note: beta_i = Delta*z_i + u_i Delta is nvar x nz if(drawdelta){ olddelta.reshape(nvar,nz); betabar = as(oldcomplgt[0])+olddelta*vectorise(Z(lgt,span::all)); } else { betabar = as(oldcomplgt[0]); } if (rep == 0) oldll[lgt] = llmnl_con(vectorise(oldbetas(lgt,span::all)),lgtdata_vector[lgt].y,lgtdata_vector[lgt].X,SignRes); //compute inc.root ucholinv = solve(trimatu(chol(lgtdata_vector[lgt].hess+rootpi*trans(rootpi))), eye(nvar,nvar)); //trimatu interprets the matrix as upper triangular and makes solve more efficient incroot = chol(ucholinv*trans(ucholinv)); metropout_struct = mnlMetropOnce_con(lgtdata_vector[lgt].y,lgtdata_vector[lgt].X,vectorise(oldbetas(lgt,span::all)), oldll[lgt],s,incroot,betabar,rootpi,SignRes); oldbetas(lgt,span::all) = trans(metropout_struct.betadraw); oldll[lgt] = metropout_struct.oldll; } //print time to completion and draw # every nprint'th draw if (nprint>0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; betadraw.slice(mkeep-1) = oldbetas; probdraw(mkeep-1, span::all) = trans(oldprob); loglike[mkeep-1] = sum(oldll); if(drawdelta) Deltadraw(mkeep-1, span::all) = trans(vectorise(olddelta)); compdraw[mkeep-1] = oldcomp; } } if (nprint>0) endMcmcTimer(); nmix = List::create(Named("probdraw") = probdraw, Named("zdraw") = R_NilValue, //sets the value to NULL in R Named("compdraw") = compdraw); //ADDED FOR CONSTRAINTS //If there are sign constraints, return f(betadraws) as "betadraws" //conStatus will be set to true if SignRes has any non-zero elements bool conStatus = any(SignRes); if(conStatus){ int SignResSize = SignRes.size(); //loop through each sign constraint for(int i = 0;i < SignResSize; i++){ //if there is a constraint loop through each slice of betadraw if(SignRes[i] != 0){ for(int s = 0;s < (R/keep); s++){ betadraw(span(),span(i),span(s)) = SignRes[i] * exp(betadraw(span(),span(i),span(s))); } } }//end loop through SignRes } if(drawdelta){ return(List::create( Named("Deltadraw") = Deltadraw, Named("betadraw") = betadraw, Named("nmix") = nmix, Named("loglike") = loglike, Named("SignRes") = SignRes)); } else { return(List::create( Named("betadraw") = betadraw, Named("nmix") = nmix, Named("loglike") = loglike, Named("SignRes") = SignRes)); } } bayesm/src/bayesBLP_rcpp_loop.cpp0000644000176000001440000003624313134410700016574 0ustar ripleyusers#include "bayesm.h" //SUPPORT FUNCTIONS SPECIFIC TO MAIN FUNCTION-------------------------------------------------------------------------------------- mat r2Sigma(vec const& r, int K){ // // Keunwoo Kim 10/28/2014 // // Purpose: // convert r (vector) into Sigma (matrix) // // Arguments: // r : K*(K+1)/2 length vector // K : number of parameters (=nrow(Sigma)) // // Output: // Sigma (K by K matrix) // int k, i, j; mat L = zeros(K, K); L.diag() = exp(r(span(0,K-1))); k = 0; for (i=0; i(J, J); // equivalent to struc = kron(eye(T, T), onesJJ) mat struc = zeros(J*T,J*T); for (t=0; t(T*J, T*J); mat offDiag = -choiceProb*trans(choiceProb)/H; mat Jac = struc%offDiag; Jac.diag() = sum(choiceProb%(1-choiceProb), 1)/H; double sumlogJacob = 0; for (t=0; t(J*T); vec mu1 = mu0/2; //relative increasement vec rel = (mu1 - mu0)/mu0; double max_rel = max(abs(rel)); while (max_rel > tol){ mu0 = mu1; expU = exp(u + mu0*ones(1,H)); temp1 = reshape(expU, J, T*H); expSum = 1 + sum(temp1, 0); expSum = reshape(expSum, T, H); // equivalent to expSum = kron(expSum, ones(J)); for (t=0; t(J)*expSum(t, span::all); } expSum = temp2; choiceProb = expU/expSum; share_hat = sum(choiceProb, 1)/H; mu1 = mu0 + log(share/share_hat); iter = iter + 1; rel = (mu0 - mu1)/mu0; max_rel = max(abs(rel)); } mat rtn = zeros(J*T, H+1); rtn(span::all,0) = mu1; rtn(span::all,span(1,H)) = choiceProb; return (rtn); } List rivDraw(vec const& mu, vec const& Xend, mat const& z, mat const& Xexo, vec const& theta_hat, mat const& A, vec const& deltabar, mat const& Ad, mat const& V, double nu, vec const& delta_old, mat const& Omega_old){ // // Keunwoo Kim 05/21/2015 // // Purpose: draw from posterior for linear I.V. model // // Arguments: // mu is vector of obs on lhs var in structural equation // Xend is "endogenous" var in structural eqn // Xexo is matrix of obs on "exogenous" vars in the structural eqn // z is matrix of obs on instruments // // deltabar is prior mean of delta // Ad is prior prec // theta_hat is prior mean vector for theta2,theta1 // A is prior prec of same // nu,V parms for IW on Omega // // delta_old is the starting value from the previous chain // Omega_old is the starting value from the previous chain // // Output: list of draws of delta,thetabar,Omega // // Model: // Xend=z'delta + e1 // mu=thetabar1*Xend + Xexo'thetabar2 + e2 // e1,e2 ~ N(0,Omega) // // Prior: // delta ~ N(deltabar,Ad^-1) // thetabar = vec(theta2,theta1) ~ N(theta_hat,A^-1) // Omega ~ IW(nu,V) // vec e1, ee2, bg, u, theta2; mat xt, Res, S, B, L, Li, z2, zt1, zt2, ucholinv, VSinv, mut; double sig,theta1; List out; int i; int n = mu.size(); int dimd = z.n_cols; int dimg = Xexo.n_cols; vec thetabar(dimg+1); mat C = eye(2,2); // set initial values mat Omega = Omega_old; vec delta = delta_old; mat xtd(2*n, dimd); vec zvec = vectorise(trans(z)); // // draw beta,gamma // e1 = Xend - z*delta; ee2 = (Omega(0,1)/Omega(0,0)) * e1; sig = sqrt(Omega(1,1)-((Omega(0,1)*Omega(0,1))/Omega(0,0))); mut = (mu-ee2)/sig; xt = join_rows(Xend,Xexo)/sig; bg = breg(mut,xt,theta_hat,A); theta1 = bg[0]; theta2 = bg(span(1,bg.size()-1)); // // draw delta // C(1,0) = theta1; B = C*Omega*trans(C); L = trans(chol(B)); Li = solve(trimatl(L),eye(2,2)); u = mu - Xexo*theta2; mut = vectorise(Li * trans(join_rows(Xend,u))); z2 = trans(join_rows(zvec, theta1*zvec)); z2 = Li*z2; zt1 = z2(0,span::all); zt2 = z2(1,span::all); zt1.reshape(dimd,n); zt1 = trans(zt1); zt2.reshape(dimd,n); zt2 = trans(zt2); for (i=0; i(out["IW"]); thetabar(span(0,dimg-1)) = theta2; thetabar[dimg] = theta1; return List::create( Named("deltadraw") = delta, Named("thetabardraw") = thetabar, Named("Omegadraw") = Omega ); } //MAIN FUNCTION--------------------------------------------------------------------------------------- // [[Rcpp::export]] List bayesBLP_rcpp_loop(bool IV, mat const& X, mat const& Z, vec const& share, int J, int T, mat const& v, int R, vec const& sigmasqR, mat const& A, vec const& theta_hat, vec const& deltabar, mat const& Ad, double nu0, double s0_sq, mat const& VOmega, double ssq, mat const& cand_cov, vec const& theta_bar_initial, vec const& r_initial, double tau_sq_initial, mat const& Omega_initial, vec const& delta_initial, double tol, int keep, int nprint){ // // Keunwoo Kim 05/21/2015 // // Purpose: // draw theta_bar and Sigma via hybrid Gibbs sampler (Jiang, Manchanda, and Rossi, 2009) // // Arguments: // Observation // IV: whether to use instrumental variable (TRUE or FALSE) // X: J*T by H (If IV is TRUE, the last column is endogenous variable.) // z: instrumental variables (If IV is FALSE, it is not used.) // share: vector of length J*T // // Dimension // J: number of alternatives // T: number of time // R: number of Gibbs sampling // // Prior // sigmasqR // theta_hat // A // deltabar (used when IV is TRUE) // Ad (used when IV is TRUE) // nu0 // s0_sq (used when IV is FALSE) // VOmega (used when IV is TRUE) // // Metropolis-Hastings // ssq: scaling parameter // cand_cov: var-cov matrix of random walk // // Initial values // theta_bar_initial // r_initial // tau_sq_initial (used when IV is FALSE) // Omega_initial (used when IV is TRUE) // delta_initial (used when IV is TRUE) // // Contraction mapping // tol: convergence tolerance for the contraction mapping // v: draws used for Monte-Carlo integration // // Output: // a List of theta_bar, r (Sigma), tau_sq, Omega, and delta draws // number of acceptance and loglikelihood // // Model & Prior: // shown in the below comments. int mkeep, I, jt; mat prob_t, Sigma_new, b, S, Sigma, Sigma_inv, rel, expU, share_hat, choiceProb, expSum, L, ucholinv, XXAinv, out_cont, Xexo, Xend, Omega_all, delta_all, zetaeta_old, zetaeta_new, rootiOmega; vec r_new, mu_new, theta_tilde, z, mu, err, mu0, mu1, eta_new, eta_old, tau_sq_all, zeta; double nu1, alpha, ll_new, ll_old, sumLogJaco_new, prior_new, prior_old, s1_sq, acceptrate; List ivout; double pi = M_PI; int K = theta_hat.size(); if (IV==TRUE){ Xexo = X(span::all, span(0,K-2)); Xend = X(span::all, K-1); I = Z.n_cols; } // number of MC integration draws int H = v.n_cols; // Allocate matrix for draws to be stored during MCMC if (IV==TRUE){ Omega_all = zeros(4,R/keep); delta_all = zeros(I,R/keep); }else{ tau_sq_all = zeros(R/keep); } mat theta_bar_all = zeros(K,R/keep); mat r_all = zeros(K*(K+1)/2,R/keep); mat Sigma_all = zeros(K*K,R/keep); vec ll_all = zeros(R/keep); // list to be returned to R List rtn; // initial values vec theta_bar = theta_bar_initial; mat Omega = Omega_initial; vec delta = delta_initial; vec r_old = r_initial; double tau_sq = tau_sq_initial; mat Sigma_old = r2Sigma(r_old, K); //=================================================================== // get initial mu and sumLogJaco: Contraction Mapping //=================================================================== // convert shares into mu out_cont = share2mu(Sigma_old, X, v, share, J, tol); mu = out_cont(span::all,0); choiceProb = out_cont(span::all,span(1,H)); // Jacobian double sumLogJaco_old = logJacob(choiceProb, J); vec mu_old = mu; //=================================================================== // Start MCMC //=================================================================== if (nprint>0) startMcmcTimer(); double n_accept = 0.0; for (int rep=0; rep(K*(K+1)/2); Sigma_new = r2Sigma(r_new, K); // convert share into mu_new out_cont = share2mu(Sigma_new, X, v, share, J, tol); mu_new = out_cont(span::all,0); choiceProb = out_cont(span::all,span(1,H)); // get eta_new eta_new = mu_new - X*theta_bar; // get eta_old eta_old = mu_old - X*theta_bar; if (IV==TRUE){ // get zeta zeta = Xend - Z*delta; // get ll_old zetaeta_old = join_rows(zeta, eta_old); rootiOmega = solve(trimatu(chol(Omega)), eye(2,2)); ll_old = 0; for (jt=0; jt(2), rootiOmega); } ll_old = ll_old + sumLogJaco_old; // get ll_new zetaeta_new = join_rows(zeta, eta_new); sumLogJaco_new = logJacob(choiceProb, J); ll_new = 0; for (jt=0; jt(2), rootiOmega); } ll_new = ll_new + sumLogJaco_new; }else{ // get ll_old ll_old = sum(log((1/sqrt(2*pi*tau_sq)) * exp(-(eta_old%eta_old)/(2*tau_sq)))) + sumLogJaco_old; // get ll_new sumLogJaco_new = logJacob(choiceProb, J); ll_new = sum(log((1/sqrt(2*pi*tau_sq)) * exp(-(eta_new%eta_new)/(2*tau_sq)))) + sumLogJaco_new; } // priors prior_new = sum(log((1/sqrt(2*pi*sigmasqR)) % exp(-(r_new%r_new)/(2*sigmasqR)))); prior_old = sum(log((1/sqrt(2*pi*sigmasqR)) % exp(-(r_old%r_old)/(2*sigmasqR)))); alpha = exp(ll_new + prior_new - ll_old - prior_old); if (alpha>1) {alpha = 1;} if (runif(1)[0]<=alpha) { r_old = r_new; Sigma_old = Sigma_new; mu_old = mu_new; sumLogJaco_old = sumLogJaco_new; n_accept = n_accept + 1; } //======================================================================== // STEP 2 // Draw theta_bar & tau^2 (or Omega & delta): Gibbs Sampler // mu = X*theta_bar + eta, eta~N(0,tau_sq) // (For IV case, see the comments in rivDraw above.) // Prior: // 1. theta_bar ~ N(theta_hat, A^-1) // 2. tau_sq ~ nu0*s0_sq/chisq(nu0) // Posterior: // 1. theta_bar | tau_sq ~ N(theta_tilde, (X^t X/tau_sq + A)^-1) // theta_tilde = (X^t X/tau_sq + A)^-1 * (tau_sq^-1*X^t mu + A*theta_hat) // 2. tau_sq | theta_bar ~ nu1*s1_sq/chisq(nu1) // nu1 = nu0 + n (n=J*T) // s1_sq = [nu0*s0_sq + (mu-X^t theta_bar)^t (mu-X^t theta_bar)]/[nu0 + n] //======================================================================== if (IV==TRUE){ ivout = rivDraw(mu_old, Xend, Z, Xexo, theta_hat, A, deltabar, Ad, VOmega, nu0, delta, Omega); delta = as(ivout["deltadraw"]); theta_bar = as(ivout["thetabardraw"]); Omega = as(ivout["Omegadraw"]); }else{ // compute the inverse of (trans(X)*X)/tau_sq + A ucholinv = solve(trimatu(chol((trans(X)*X)/tau_sq + A)), eye(K,K)); XXAinv = ucholinv*trans(ucholinv); theta_tilde = XXAinv * (trans(X)*mu_old/tau_sq + A*theta_hat); theta_bar = theta_tilde + ucholinv*vec(rnorm(K)); nu1 = nu0 + J*T; err = mu_old - X*theta_bar; s1_sq = (nu0*s0_sq + sum(err%err))/nu1; z = vec(rnorm(nu1)); tau_sq = nu1*s1_sq/sum(z%z); } // // print time to completion and draw # every nprint'th draw // if (nprint>0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); //======================================================================== // STEP 3 // Store Draws //======================================================================== if((rep+1)%keep==0){ mkeep = (rep+1)/keep; if (IV==TRUE){ Omega_all(span::all,mkeep-1) = vectorise(Omega); delta_all(span::all,mkeep-1) = delta; }else{ tau_sq_all[mkeep-1] = tau_sq; } theta_bar_all(span::all,mkeep-1) = theta_bar; r_all(span::all,mkeep-1) = r_old; Sigma_all(span::all,mkeep-1) = vectorise(r2Sigma(r_old, K)); ll_all[mkeep-1] = ll_old; } } acceptrate = n_accept/R; rtn["tausqdraw"] = tau_sq_all; rtn["Omegadraw"] = Omega_all; rtn["deltadraw"] = delta_all; rtn["thetabardraw"] = theta_bar_all; rtn["rdraw"] = r_all; rtn["Sigmadraw"] = Sigma_all; rtn["ll"] = ll_all; rtn["acceptrate"] = acceptrate; if (nprint>0) endMcmcTimer(); return (rtn); } bayesm/src/ghkvec_rcpp.cpp0000644000176000001440000001175613134410700015353 0ustar ripleyusers#include "bayesm.h" //SUPPORT FUNCTIONS SPECIFIC TO MAIN FUNCTION-------------------------------------------------------------------------------------- vec HaltonSeq(int pn, int r, int burnin, bool rand){ // Keunwoo Kim 10/28/2014 // Purpose: // create a random Halton sequence // Arguments: // pn: prime number // r: number of draws // burnin: number of initial burn // rand: if TRUE, add a random scalor to sequence // Output: // a vector of Halton sequence, size r int t; vec add; // start at 0 vec seq = zeros(r+burnin+1); // how many numbers I have drawn so far. // I have 1 draw (0) now. int index = 1; // if done==1, it is done. int done = 0; int factor = pn; do{ for (t=0; t(index)*(t+1)/factor; if ((t+2)*index-1>r+burnin){ seq(span((t+1)*index, r+burnin)) = add(span(0, r+burnin-(t+1)*index)); done = 1; }else{ seq(span((t+1)*index, (t+2)*index-1)) = add; if ((t+2)*index==r+burnin+1){ done = 1; } } } } factor = factor*pn; index = index*pn; }while (done==0); // exclude the first 0 and some initial draws seq = seq(span(burnin+1,burnin+r)); if (rand==TRUE){ // make it random seq = seq + runif(1)[0]; for (int i=0; i=1) seq[i] = seq[i]-1; } } return (seq); } bool IsPrime(int number){ // Keunwoo Kim 5/14/2015 // This function is to check whether a number is prime or not. // This is used for setting default prime numbers. for (int f=2; f(dim); double res = 0; // choose R::runif vs. Halton draws vec udraw(r*dim); mat udrawHalton(dim, r); if (HALTON){ for (j=0; j0){ pa = 0.0; pb = R::pnorm(tpz,0,1,1,0); }else{ pb = 1.0; pa = R::pnorm(tpz,0,1,1,0); } prod = prod * (pb-pa); u = udraw[i*dim+j]; arg = u*pb + (1.0-u)*pa; if (arg > .999999999) arg=.999999999; if (arg < .0000000001) arg=.0000000001; z[j] = R::qnorm(arg,0,1,1,0); } res = res + prod; } res = res / r; return (res); } //MAIN FUNCTION--------------------------------------------------------------------------------------- // [[Rcpp::export]] vec ghkvec(mat const& L, vec const& trunpt, vec const& above, int r, bool HALTON=true, vec pn=IntegerVector::create(0)){ // Keunwoo Kim 5/14/2015 // Purpose: // routine to call ghk_oneside for n different truncation points stacked in to the // vector trunpt -- puts n results in vector res // Arguments: // L: lower Cholesky root of cov. matrix // trunpt: vector of truncation points // above: truncation above(1) or below(0) // r: number of draws // HALTON: TRUE or FALSE. If FALSE, use R::runif random number generator. // pn: prime number used in Halton sequence. // burnin: number of initial burnin of draws. Only applied when HALTON is TRUE. (not used any more) // Output: // a vector of integration values int dim = above.size(); int n = trunpt.size()/dim; // // handling default arguments // // generate prime numbers if (HALTON==true && pn[0]==0){ Rcout << "Halton sequence is generated by the smallest prime numbers: \n"; Rcout << " "; pn = zeros(dim); int cand = 2; int which = 0; while (pn[dim-1]==0){ if (IsPrime(cand)){ pn[which] = cand; which = which + 1; Rprintf("%d ", cand); } cand = cand + 1; } Rcout << "\n"; } // burn-in //if (HALTON==true && burnin==NA_INTEGER){ // burnin = max(pn); // Rprintf("Initial %d (= max of prime numbers) draws are burned. \n", burnin); //} int burnin = 0; vec res(n); for (int i=0; i(dimd); if (nprint>0) startMcmcTimer(); mat xtd(2*n, dimd); vec zvec = vectorise(trans(z)); // start main iteration loop for (int rep=0; rep(out["IW"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> // print time to completion and draw # every nprint'th draw if (nprint>0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; deltadraw(mkeep-1, span::all) = trans(delta); betadraw[mkeep-1] = beta; gammadraw(mkeep-1, span::all) = trans(gamma); Sigmadraw(mkeep-1, span::all) = trans(vectorise(Sigma)); } } if (nprint>0) endMcmcTimer(); return List::create( Named("deltadraw") = deltadraw, Named("betadraw") = NumericVector(betadraw.begin(),betadraw.end()), Named("gammadraw") = gammadraw, Named("Sigmadraw") = Sigmadraw); } bayesm/src/rmultireg_rcpp.cpp0000644000176000001440000000427613134410700016115 0ustar ripleyusers#include "bayesm.h" // [[Rcpp::export]] List rmultireg(mat const& Y, mat const& X, mat const& Bbar, mat const& A, double nu, mat const& V) { // Keunwoo Kim 09/09/2014 // Purpose: draw from posterior for Multivariate Regression Model with natural conjugate prior // Arguments: // Y is n x m matrix // X is n x k // Bbar is the prior mean of regression coefficients (k x m) // A is prior precision matrix // nu, V are parameters for prior on Sigma // Output: list of B, Sigma draws of matrix of coefficients and Sigma matrix // Model: // Y=XB+U cov(u_i) = Sigma // B is k x m matrix of coefficients // Prior: // beta|Sigma ~ N(betabar,Sigma (x) A^-1) // betabar=vec(Bbar) // beta = vec(B) // Sigma ~ IW(nu,V) or Sigma^-1 ~ W(nu, V^-1) int n = Y.n_rows; int m = Y.n_cols; int k = X.n_cols; //first draw Sigma mat RA = chol(A); mat W = join_cols(X, RA); //analogous to rbind() in R mat Z = join_cols(Y, RA*Bbar); // note: Y,X,A,Bbar must be matrices! mat IR = solve(trimatu(chol(trans(W)*W)), eye(k,k)); //trimatu interprets the matrix as upper triangular and makes solve more efficient // W'W = R'R & (W'W)^-1 = IRIR' -- this is the UL decomp! mat Btilde = (IR*trans(IR)) * (trans(W)*Z); // IRIR'(W'Z) = (X'X+A)^-1(X'Y + ABbar) mat E = Z-W*Btilde; mat S = trans(E)*E; // E'E // compute the inverse of V+S mat ucholinv = solve(trimatu(chol(V+S)), eye(m,m)); mat VSinv = ucholinv*trans(ucholinv); List rwout = rwishart(nu+n, VSinv); // now draw B given Sigma // note beta ~ N(vec(Btilde),Sigma (x) Covxxa) // Cov=(X'X + A)^-1 = IR t(IR) // Sigma=CICI' // therefore, cov(beta)= Omega = CICI' (x) IR IR' = (CI (x) IR) (CI (x) IR)' // so to draw beta we do beta= vec(Btilde) +(CI (x) IR)vec(Z_mk) // Z_mk is m x k matrix of N(0,1) // since vec(ABC) = (C' (x) A)vec(B), we have // B = Btilde + IR Z_mk CI' mat CI = rwout["CI"]; //there is no need to use as(rwout["CI"]) since CI is being initiated as a mat in the same line mat draw = mat(rnorm(k*m)); draw.reshape(k,m); mat B = Btilde + IR*draw*trans(CI); return List::create( Named("B") = B, Named("Sigma") = rwout["IW"]); } bayesm/src/rsurGibbs_rcpp_loop.cpp0000644000176000001440000001031713134410700017067 0ustar ripleyusers#include "bayesm.h" // [[Rcpp::export]] List rsurGibbs_rcpp_loop(List const& regdata, vec const& indreg, vec const& cumnk, vec const& nk, mat const& XspXs, mat Sigmainv, mat const& A, vec const& Abetabar, double nu, mat const& V, int nvar, mat E, mat const& Y, int R, int keep, int nprint){ // Keunwoo Kim 09/19/2014 // Purpose: implement Gibbs Sampler for SUR // Arguments: // Data -- regdata // regdata is a list of lists of data for each regression // regdata[[i]] contains data for regression equation i // regdata[[i]]$y is y, regdata[[i]]$X is X // note: each regression can have differing numbers of X vars // but you must have same no of obs in each equation. // Prior -- list of prior hyperparameters // betabar,A prior mean, prior precision // nu, V prior on Sigma // Mcmc -- list of MCMC parms // R number of draws // keep -- thinning parameter // nprint - print estimated time remaining on every nprint'th draw // Output: list of betadraw,Sigmadraw // Model: // y_i = X_ibeta + e_i // y is nobs x 1 // X is nobs x k_i // beta is k_i x 1 vector of coefficients // i=1,nreg total regressions // (e_1,k,...,e_nreg,k) ~ N(0,Sigma) k=1,...,nobs // we can also write as stacked regression // y = Xbeta+e // y is nobs*nreg x 1,X is nobs*nreg x (sum(k_i)) // routine draws beta -- the stacked vector of all coefficients // Prior: // beta ~ N(betabar,A^-1) // Sigma ~ IW(nu,V) int reg, mkeep, i, j; vec beta, btilde, yti; mat IR, ucholinv, EEVinv, Sigma, Xtipyti, Ydti; List regdatai, rwout; int nreg = regdata.size(); // convert List to std::vector of struct std::vector regdata_vector; moments regdatai_struct; // store vector with struct for (reg=0; reg(regdatai["y"]); regdatai_struct.X = as(regdatai["X"]); regdata_vector.push_back(regdatai_struct); } int nobs = (regdatai_struct.y).size(); mat XtipXti = zeros(sum(nk), sum(nk)); mat Sigmadraw(R/keep, nreg*nreg); mat betadraw(R/keep, nvar); if (nprint>0) startMcmcTimer(); for (int rep=0; rep(rwout["IW"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> Sigmainv = as(rwout["W"]); //print time to completion and draw # every nprint'th draw if (nprint>0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; betadraw(mkeep-1, span::all) = trans(beta); Sigmadraw(mkeep-1, span::all) = trans(vectorise(Sigma)); } } if (nprint>0) endMcmcTimer(); return List::create( Named("betadraw") = betadraw, Named("Sigmadraw") = Sigmadraw); } bayesm/src/rnegbinRw_rcpp_loop.cpp0000644000176000001440000000650113134410700017062 0ustar ripleyusers#include "bayesm.h" // [[Rcpp::export]] List rnegbinRw_rcpp_loop(vec const& y, mat const& X, vec const& betabar, mat const& rootA, double a, double b, vec beta, double alpha, bool fixalpha, mat const& betaroot, double alphacroot, int R, int keep, int nprint){ // Keunwoo Kim 11/02/2014 // Arguments: // Data // X is nobs X nvar matrix // y is nobs vector // Prior - list containing the prior parameters // betabar, rootA - mean of beta prior, chol-root of inverse of variance covariance of beta prior // a, b - parameters of alpha prior // Mcmc - list containing // R is number of draws // keep is thinning parameter (def = 1) // nprint - print estimated time remaining on every nprint'th draw (def = 100) // betaroot - step size for beta RW // alphacroot - step size for alpha RW // beta - initial guesses for beta // alpha - initial guess for alpha // fixalpha - if TRUE, fix alpha and draw only beta // // Output: // // Model: // (y|lambda,alpha) ~ Negative Binomial(Mean = lambda, Overdispersion par = alpha) // ln(lambda) = X * beta // // Prior: // beta ~ N(betabar, A^-1) // alpha ~ Gamma(a,b) where mean = a/b and variance = a/(b^2) // vec betac; double ldiff, acc, unif, logalphac, oldlpostalpha, oldlpostbeta, clpostbeta, clpostalpha; int mkeep, rep; int nvar = X.n_cols; int nacceptbeta = 0; int nacceptalpha = 0; vec alphadraw(R/keep); mat betadraw(R/keep, nvar); if (nprint>0) startMcmcTimer(); //start main iteration loop for (rep=0; rep 1) acc = 1; if(acc < 1) {unif=runif(1)[0];} else {unif=0;} //runif returns a NumericVector, so using [0] allows for conversion to double by extracting the first element if (unif <= acc){ beta = betac; nacceptbeta = nacceptbeta + 1; } // Draw alpha if (!fixalpha){ logalphac = log(alpha) + alphacroot*rnorm(1)[0]; //rnorm returns a NumericVector, so using [0] allows for conversion to double oldlpostalpha = lpostalpha(alpha, beta, X, y, a, b); clpostalpha = lpostalpha(exp(logalphac), beta, X, y, a, b); ldiff = clpostalpha - oldlpostalpha; acc = exp(ldiff); if (acc > 1) acc = 1; if(acc < 1) {unif=runif(1)[0];} else {unif=0;} //runif returns a NumericVector, so using [0] allows for conversion to double by extracting the first element if (unif <= acc){ alpha = exp(logalphac); nacceptalpha = nacceptalpha + 1; } } if (nprint>0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; betadraw(mkeep-1, span::all) = trans(beta); alphadraw[mkeep-1] = alpha; } } if (nprint>0) endMcmcTimer(); return List::create( Named("betadraw") = betadraw, Named("alphadraw") = alphadraw, Named("nacceptbeta") = nacceptbeta, Named("nacceptalpha") = nacceptalpha); } bayesm/src/rscaleUsage_rcpp_loop.cpp0000644000176000001440000003060713134410700017367 0ustar ripleyusers#include "bayesm.h" #include //used for "sample" function //SUPPORT FUNCTIONS SPECIFIC TO MAIN FUNCTION-------------------------------------------------------------------------------------- double ghk(mat const& L, vec const& a, vec const& b, int const& n, int const& dim){ // Wayne Taylor 4/29/15 //routine to implement ghk with a region : a[i-1] <= x_i <= b[i-1] //r mcculloch 8/04 //L is lower triangular root of Sigma random vector is assumed to have zero mean //n is number of draws to use in GHK //dim is the dimension of L //modified 6/05 by rossi to check arg into qnorm //converted to rcpp 5/15 int i,j; NumericVector aa(1),bb(1),pa(1),pb(1),arg(1); double u,prod,mu; vec z(dim); double res=0.0; for(i=0;i0) mu = as_scalar(L(j,span(0,j-1))*z(span(0,j-1))); //previously done via a loop for(k=0;k .999999999) arg[0]=.999999999; if(arg[0] < .0000000001) arg[0]=.0000000001; z[j] = qnorm(arg,0.0,1.0)[0]; } res += prod; } res /= n; return (res); } mat dy(mat y, mat const& x, vec const& c, vec const& mu, mat const& beta, vec const& s, vec const& tau, vec const& sigma){ // Wayne Taylor 4/29/15 //Variable declaration double sigman,taun; rowvec yn; vec xn; int p = y.n_cols; int nobs = y.n_rows; //cm = conditional mean, cs = condtional standard deviation //u =uniform for truncated normal draw double cm,cs,u; // standardized truncation points (a,b) // cdf at truncation points (pa,pb) NumericVector a(1),b(1),pa(1),pb(1); double qout; //loop over coordinates of y - first by rows, then by columns for(int n = 0; n(n); double offset = p*log((double)k); vec a,b; double ghkres,lghkres; uvec xia(p),xib(p); mat Li; for(int i = 0; i(cbetarows,p); uvec ui(1),ind(p-1); int counter; uvec cbetaAllRow(cbetarows); for(int i = 0; i(2,2); S(0,0) = (n-1)*moms[2] + n*pow(moms[0],2.0); S(0,1) = (n-1)*moms[3] + n*moms[0]*(moms[1]-Lam(1,1)); S(1,0) = S(0,1); S(1,1) = (n-1)*moms[4] + n*pow(moms[1]-Lam(1,1),2.0); return(S); } double llL(mat const& Lam, int n, mat const& S, mat const& V,double nu){ //Wayne Taylor 4/29/15 int d = Lam.n_cols; double dlam = Lam(0,0)*Lam(1,1)-pow(Lam(0,1),2.0); mat M = (S+V) * solve(Lam,eye(d,d)); double ll = -.5*(n+nu+3)*log(dlam) -.5*sum(M.diag()); return(ll); } //MAIN FUNCTION------------------------------------------------------------------------------------ //[[Rcpp::export]] List rscaleUsage_rcpp_loop(int k, mat const& x, int p, int n, int R, int keep, int ndghk, int nprint, mat y, vec mu, mat Sigma, vec tau, vec sigma, mat Lambda, double e, bool domu, bool doSigma, bool dosigma, bool dotau, bool doLambda, bool doe, double nu, mat const& V, mat const& mubar, mat const& Am, vec const& gsigma, vec const& gl11,vec const& gl22, vec const& gl12, int nuL, mat const& VL, vec const& ge){ // R.McCulloch, 12/04 code for scale usage R function (rScaleUsage) // changed to R error function, P. Rossi 05/12 // converted to rcpp W. Taylor 04/15 //variable declaration int mkeep, ng, ei, pi; double eprop, eold; double Ai, A, xtx, beta, s2, m, a, b, s, qr, llold, llprop, lrat, paccept; vec cc, xty, ete, pv, h, moms(5),rgl11, rgl12a, rgl12, rgl22, absege, minvec; uvec eiu; mat Res, S, yd, Si, Vmi, Rm, Ri, Vm, mm, onev, xx, ytemp, yy, eps, dat, temp, SS; List bs, rwout; rowvec onesp = ones(p); int nk = R/keep; int ndpost = nk*keep; mat drSigma = zeros(nk,pow(p,2.0)); mat drmu = zeros(nk,p); mat drtau = zeros(nk,n); mat drsigma = zeros(nk,n); mat drLambda = zeros(nk,4); vec dre = zeros(nk); if(nprint>0) startMcmcTimer(); for(int rep = 0; rep < ndpost; rep++) { cc = cgetC(e,k); bs = condd(Sigma); y = dy(y,x,cc,mu,as(bs["beta"]),as(bs["s"]),tau,sigma); //draw Sigma if(doSigma) { Res = y; Res.each_row() -= trans(mu); Res.each_col() -= tau; Res.each_col() /= sigma; S = trans(Res)*Res; rwout = rwishart(nu+n,solve(V+S,eye(p,p))); Sigma = as(rwout["IW"]); } //draw mu if(domu) { yd = y; yd.each_col() -= tau; Si = solve(Sigma,eye(p,p)); Vmi = as_scalar(sum(1/pow(sigma,2.0)))*Si + Am; Rm = chol(Vmi); Ri = solve(trimatu(Rm),eye(p,p)); Vm = solve(Vmi,eye(p,p)); mm = Vm * (Si * (trans(yd) * (1/pow(sigma,2.0))) + Am * mubar); mu = vectorise(mm + Ri * as(rnorm(p))); } //draw tau if(dotau) { Ai = Lambda(0,0) - pow(Lambda(0,1),2.0)/Lambda(1,1); A = 1.0/Ai; onev = ones(p,1); Rm = chol(Sigma); xx = trans(solve(trans(Rm),onev)); ytemp = trans(y); ytemp.each_col() -= mu; yy = trans(solve(trans(Rm),ytemp)); xtx = accu(pow(xx,2.0)); //To get a sum of all the elements regardless of the argument type (ie. matrix or vector), use accu() xty = vectorise(xx*trans(yy)); beta = A*Lambda(0,1)/Lambda(1,1); for(int j = 0; j(p); ete = vectorise(onesp * pow(eps,2.0)); a = Lambda(1,1); b = Lambda(0,1)/Lambda(0,0); s = sqrt(Lambda(1,1)-pow(Lambda(0,1),2.0)/Lambda(0,0)); for(int j = 0; j pow(Lambda(0,1),2.0)/Lambda(1,1))); ng = rgl11.size(); pv = zeros(ng); for(int j = 0; j -sqrt(Lambda(0,0)*Lambda(1,1)))); ng = rgl12.size(); pv = zeros(ng); for(int j = 0; j pow(Lambda(0,1),2.0)/Lambda(0,0))); ng = rgl22.size(); pv = zeros(ng); for(int j = 0;j0) { e = eprop; } else { minvec << 1 << exp(lrat); paccept = min(minvec); if(rbinom(1,1,paccept)[0]==1){ e = eprop; } else { e = eold; } } } if (nprint>0) if((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; drSigma(mkeep-1,span::all) = trans(vectorise(Sigma)); drmu(mkeep-1,span::all) = trans(mu); drtau(mkeep-1,span::all) = trans(tau); drsigma(mkeep-1,span::all) = trans(sigma); drLambda(mkeep-1,span::all) = trans(vectorise(Lambda)); dre[mkeep-1] = e; } } if (nprint>0) endMcmcTimer(); return List::create( Named("ndpost") = ndpost, Named("drmu") = drmu, Named("drtau") = drtau, Named("drsigma") = drsigma, Named("drLambda") = drLambda, Named("dre") = dre, Named("drSigma") = drSigma); } bayesm/src/trunNorm.cpp0000644000176000001440000000566013134410700014701 0ustar ripleyusers// [[Rcpp::depends("RcppArmadillo")]] #include #include #include #include #include "bayesm.h" using namespace Rcpp; using namespace arma; double dexpr(double const& a) { // rossi 10/2016 // routine to draw use rejection sampling to draw from a truncated normal // truncated to the tail. Use exponential distribution as the acceptance function // a is the rejection point (usually, (a-mu)/sigma)) double x,e,e1; int success; success=0; while(success == 0){ e = -log(runif(1)[0]); e1 = -log(runif(1)[0]); if(pow(e,2) <= 2.0*e1*pow(a,2)){ x = a + e/a; success = 1; } } return(x); } double invCdfNorm(double const& a) { // rossi 10/2016 // draw from truncated normal truncated from below by a using inverse CDF method double Phia,unif,arg,z; Phia = R::pnorm(a,0.0,1.0,1,0); unif = runif(1)[0]; arg = unif*(1.0-Phia)+Phia; z = R::qnorm(arg,0.0,1.0,1,0); return(z); } double dnr(double const& a) { // rossi 10/2016 // draw from standard normal truncated below by a using rejection sampling double candz,z; int success; success=0; while(success == 0){ candz=rnorm(1)[0]; if(candz >= a){ z=candz; success =1; } } return(z); } double trunNormBelow(double const& a){ // rossi 10/2016 // draw from standard normal truncated below by a // we divide into three regions (regions given for trun below) // let a = (trunpt-mu)/sig // 1: a > 4, use exponential rejection sampling // 2: -4 < a <=4, use inverse CDF // 3: a <= -4, normal rejection sampling double z; if (a > 4){ // do tail sampling using exponential rejection z=dexpr(a); } else { if (a <= -4){ // normal rejection sampling z=dnr(a); } // -4 < a <=4 z=invCdfNorm(a); } return(z); } double trunNorm(double mu,double sig, double trunpt, int above){ // rossi 10/2016 // function to draw from N(mu,sig) truncated by trunpt // if above=0, truncate from below at trunpt // if above=1, truncate from above at trunpt double a,z,draw; if(above == 0){ a=(trunpt-mu)/sig; z= trunNormBelow(a); draw = sig*z + mu; } else { a=(mu-trunpt)/sig; z= trunNormBelow(a); draw = -sig*z + mu; } return(draw); } // vec trunNorm_multi(double mu, double sig, double trunpt, int above, int nd){ // // Dan Yavorsky 10/16 // // Just loops over trunNorm, multiple draws from single truncated distribution // vec rtn_vec(nd); // for (int i = 0; i0) startMcmcTimer(); for (int rep=0; rep0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; betadraw(mkeep-1, span::all) = trans(beta); sigmasqdraw[mkeep-1] = sigmasq; } } if (nprint>0) endMcmcTimer(); return List::create( Named("betadraw") = betadraw, Named("sigmasqdraw") = NumericVector(sigmasqdraw.begin(),sigmasqdraw.end())); } bayesm/src/clusterMix_rcpp_loop.cpp0000644000176000001440000001014213134410700017260 0ustar ripleyusers#include "bayesm.h" //EXTRA FUNCTIONS SPECIFIC TO THE MAIN FUNCTION-------------------------------------------- mat ztoSim(vec const& z){ // function to convert indicator vector to Similarity matrix // Sim is n x n matrix, Sim[i,j]=1 if pair(i,j) are in same group // z is n x 1 vector of indicators (1,...,p) int n = z.size(); vec onevec = ones(n); // equivalent to zvec=c(rep(z,n)) in R vec zvec = kron(onevec, z); vec zcomp = kron(z, onevec);// equivalent to as.numeric((zvec==zcomp)) in R mat Sim = zeros(n*n,1); for (int i=0; i(n); int groupn = 1; for (i=0; i0){ groupn = groupn + 1; } } return (z); } //MAIN FUNCTION--------------------------------------------------------------------------------------- // [[Rcpp::export]] List clusterMix_rcpp_loop(mat const& zdraw, double cutoff, bool SILENT, int nprint){ // Keunwoo Kim 10/06/2014 // Purpose: // cluster observations based on draws of indicators of // normal mixture components // Arguments: // zdraw is a R x nobs matrix of draws of indicators (typically output from rnmixGibbs) // the rth row of zdraw contains rth draw of indicators for each observations // each element of zdraw takes on up to p values for up to p groups. The maximum // number of groups is nobs. Typically, however, the number of groups will be small // and equal to the number of components used in the normal mixture fit. // cutoff is a cutoff used in determining one clustering scheme it must be // a number between .5 and 1. // nprint - print every nprint'th draw // Output: // two clustering schemes each with a vector of length nobs which gives the assignment // of each observation to a cluster // clustera (finds zdraw with similarity matrix closest to posterior mean of similarity) // clusterb (finds clustering scheme by assigning ones if posterior mean of similarity matrix cutoff and computing associated z ) int rep, i; uword index; // type uword means unsigned integer. Necessary for finding the index of min. int nobs = zdraw.n_cols; char buf[32]; // compute posterior mean of Similarity matrix if (!SILENT){ Rcout << "Computing Posterior Expectation of Similarity Matrix\n"; Rcout << "processing draws ...\n"; } mat Pmean = zeros(nobs, nobs); int R = zdraw.n_rows; for (rep=0; rep(R); for (rep=0; rep cutoff vec Pmeanvec = vectorise(Pmean); mat Sim = zeros(nobs*nobs,1); for (i=0; i=cutoff) Sim(i,0) = 1; } Sim.reshape(nobs,nobs); vec clusterb = Simtoz(Sim); return List::create( Named("clustera") = clustera, Named("clusterb") = clusterb); } bayesm/src/rtrun_rcpp.cpp0000644000176000001440000000102413134410700015241 0ustar ripleyusers#include "bayesm.h" // [[Rcpp::export]] NumericVector rtrun(NumericVector const& mu, NumericVector const& sigma, NumericVector const& a, NumericVector const& b){ // Wayne Taylor 9/7/2014 // function to draw from univariate truncated norm // a is vector of lower bounds for truncation // b is vector of upper bounds for truncation NumericVector FA = pnorm((a-mu)/sigma); NumericVector FB = pnorm((b-mu)/sigma); return(mu+sigma*qnorm(runif(mu.size())*(FB-FA)+FA)); } bayesm/src/Makevars.win0000644000176000001440000000012213134410700014625 0ustar ripleyusersPKG_LIBS = $(LAPACK_LIBS) $(BLAS_LIBS) $(FLIBS) PKG_CPPFLAGS = -I../inst/include/ bayesm/src/rhierNegbinRw_rcpp_loop.cpp0000644000176000001440000001514713134410700017700 0ustar ripleyusers#include "bayesm.h" //EXTRA FUNCTIONS SPECIFIC TO THE MAIN FUNCTION-------------------------------------------- double llnegbinpooled(std::vector regdata_vector, mat Beta, double alpha){ // Wayne Taylor 12/01/2014 // "Unlists" the regdata and calculates the negative binomial loglikelihood using individual-level betas int nreg = regdata_vector.size(); double ll = 0.0; for(int reg = 0; reg(nreg); vec clpostbeta = zeros(nreg); cube Betadraw = zeros(nreg, nvar, R/keep); vec alphadraw = zeros(R/keep); vec llike = zeros(R/keep); mat Vbetadraw = zeros(R/keep,nvar*nvar); mat Deltadraw = zeros(R/keep,nvar*nz); // convert regdata and hessdata Lists to std::vector of struct std::vector regdata_vector; moments regdatai_struct; List regdatai,hessi; // store vector with struct for (int reg = 0; reg(regdatai["y"]); regdatai_struct.X = as(regdatai["X"]); regdatai_struct.hess = as(hessi["hess"]); regdata_vector.push_back(regdatai_struct); } if (nprint>0) startMcmcTimer(); // start main iteration loop for (rep = 0; rep < R; rep++){ mat betabar = Z*Delta; // Draw betai for(int reg = 0; reg 1) acc = 1; if(acc < 1) {unif=runif(1)[0];} else {unif=0;} //runif returns a NumericVector, so using [0] allows for conversion to double by extracting the first element if (unif <= acc){ Beta(reg,span::all) = trans(betac); nacceptbeta = nacceptbeta + 1; } } // Draw alpha if (!fixalpha){ logalphac = log(alpha) + alphacroot*rnorm(1)[0]; //rnorm returns a NumericVector, so using [0] allows for conversion to double oldlpostalpha = llnegbinpooled(regdata_vector,Beta,alpha)+(a-1)*log(alpha) - b*alpha; clpostalpha = llnegbinpooled(regdata_vector,Beta,exp(logalphac))+(a-1)*logalphac - b*exp(logalphac); ldiff = clpostalpha - oldlpostalpha; acc = exp(ldiff); if (acc > 1) acc = 1; if(acc < 1) {unif=runif(1)[0];} else {unif=0;} //runif returns a NumericVector, so using [0] allows for conversion to double by extracting the first element if (unif <= acc){ alpha = exp(logalphac); nacceptalpha = nacceptalpha + 1; } } // Draw Vbeta and Delta using rmultireg List temp = rmultireg(Beta,Z,Deltabar,Adelta,nu,V); mat Vbeta = as(temp["Sigma"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> Vbetainv = solve(Vbeta,eye(nvar,nvar)); rootA = chol(Vbetainv); Delta = as(temp["B"]); if (nprint>0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; Betadraw.slice(mkeep-1) = Beta; alphadraw[mkeep-1] = alpha; Vbetadraw(mkeep-1,span::all) = trans(vectorise(Vbeta)); Deltadraw(mkeep-1,span::all) = trans(vectorise(Delta)); llike[mkeep-1] = llnegbinpooled(regdata_vector,Beta,alpha); } } if (nprint>0) endMcmcTimer(); return List::create( Named("llike") = llike, Named("Betadraw") = Betadraw, Named("alphadraw") = alphadraw, Named("Vbetadraw") = Vbetadraw, Named("Deltadraw") = Deltadraw, Named("acceptrbeta") = nacceptbeta/(R*nreg*1.0)*100, Named("acceptralpha") = nacceptalpha/(R*1.0)*100); } bayesm/src/rmixture_rcpp.cpp0000644000176000001440000000373413134410700015760 0ustar ripleyusers#include "bayesm.h" //FUNCTION SPECIFIC TO MAIN FUNCTION-------------------------------- vec rcomp(List comp) { // Wayne Taylor 9/10/14 //purpose: draw multivariate normal with mean and variance given by comp // arguments: // comp is a list of length 2, // comp[[1]] is the mean and comp[[2]] is R^{-1} = comp[[2]], Sigma = t(R)%*%R vec mu = comp[0]; mat rooti = comp[1]; int dim = rooti.n_cols; mat root = solve(trimatu(rooti),eye(dim,dim)); //trimatu interprets the matrix as upper triangular and makes solve more efficient return(vectorise(mu+trans(root)*as(rnorm(mu.size())))); } //[[Rcpp::export]] List rmixture(int n, vec pvec, List comps) { // Wayne Taylor 9/10/2014 // revision history: // commented by rossi 3/05 // // purpose: iid draws from mixture of multivariate normals // arguments: // n: number of draws // pvec: prior probabilities of normal components // comps: list, each member is a list comp with ith normal component // ~N(comp[[1]],Sigma), Sigma = t(R)%*%R, R^{-1} = comp[[2]] // output: // list of x (n by length(comp[[1]]) matrix of draws) and z latent indicators of // component //Draw vector of indices using base R 'sample' function mat prob(n,pvec.size()); for(int i = 0; i(runif(n)) % prob.col(pvec.size()-1); // Evaluative each column of "prob" until the uniform draw is less than the cumulative value vec z = zeros(n); for(int i = 0; i prob(i, z[i]++)); List comp0 = comps[0]; vec mu0 = comp0[0]; mat x(n,mu0.size()); //Draw from MVN from comp determined from z index //Note z starts at 1, not 0 for(int i = 0; i do not edit by hand // Generator token: 10BE3573-1514-4C36-9D1C-5A225CD40393 #include "../inst/include/bayesm.h" #include #include using namespace Rcpp; // bayesBLP_rcpp_loop List bayesBLP_rcpp_loop(bool IV, mat const& X, mat const& Z, vec const& share, int J, int T, mat const& v, int R, vec const& sigmasqR, mat const& A, vec const& theta_hat, vec const& deltabar, mat const& Ad, double nu0, double s0_sq, mat const& VOmega, double ssq, mat const& cand_cov, vec const& theta_bar_initial, vec const& r_initial, double tau_sq_initial, mat const& Omega_initial, vec const& delta_initial, double tol, int keep, int nprint); RcppExport SEXP bayesm_bayesBLP_rcpp_loop(SEXP IVSEXP, SEXP XSEXP, SEXP ZSEXP, SEXP shareSEXP, SEXP JSEXP, SEXP TSEXP, SEXP vSEXP, SEXP RSEXP, SEXP sigmasqRSEXP, SEXP ASEXP, SEXP theta_hatSEXP, SEXP deltabarSEXP, SEXP AdSEXP, SEXP nu0SEXP, SEXP s0_sqSEXP, SEXP VOmegaSEXP, SEXP ssqSEXP, SEXP cand_covSEXP, SEXP theta_bar_initialSEXP, SEXP r_initialSEXP, SEXP tau_sq_initialSEXP, SEXP Omega_initialSEXP, SEXP delta_initialSEXP, SEXP tolSEXP, SEXP keepSEXP, SEXP nprintSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< bool >::type IV(IVSEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); Rcpp::traits::input_parameter< mat const& >::type Z(ZSEXP); Rcpp::traits::input_parameter< vec const& >::type share(shareSEXP); Rcpp::traits::input_parameter< int >::type J(JSEXP); Rcpp::traits::input_parameter< int >::type T(TSEXP); Rcpp::traits::input_parameter< mat const& >::type v(vSEXP); Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< vec const& >::type sigmasqR(sigmasqRSEXP); Rcpp::traits::input_parameter< mat const& >::type A(ASEXP); Rcpp::traits::input_parameter< vec const& >::type theta_hat(theta_hatSEXP); Rcpp::traits::input_parameter< vec const& >::type deltabar(deltabarSEXP); Rcpp::traits::input_parameter< mat const& >::type Ad(AdSEXP); Rcpp::traits::input_parameter< double >::type nu0(nu0SEXP); Rcpp::traits::input_parameter< double >::type s0_sq(s0_sqSEXP); Rcpp::traits::input_parameter< mat const& >::type VOmega(VOmegaSEXP); Rcpp::traits::input_parameter< double >::type ssq(ssqSEXP); Rcpp::traits::input_parameter< mat const& >::type cand_cov(cand_covSEXP); Rcpp::traits::input_parameter< vec const& >::type theta_bar_initial(theta_bar_initialSEXP); Rcpp::traits::input_parameter< vec const& >::type r_initial(r_initialSEXP); Rcpp::traits::input_parameter< double >::type tau_sq_initial(tau_sq_initialSEXP); Rcpp::traits::input_parameter< mat const& >::type Omega_initial(Omega_initialSEXP); Rcpp::traits::input_parameter< vec const& >::type delta_initial(delta_initialSEXP); Rcpp::traits::input_parameter< double >::type tol(tolSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); rcpp_result_gen = Rcpp::wrap(bayesBLP_rcpp_loop(IV, X, Z, share, J, T, v, R, sigmasqR, A, theta_hat, deltabar, Ad, nu0, s0_sq, VOmega, ssq, cand_cov, theta_bar_initial, r_initial, tau_sq_initial, Omega_initial, delta_initial, tol, keep, nprint)); return rcpp_result_gen; END_RCPP } // breg vec breg(vec const& y, mat const& X, vec const& betabar, mat const& A); RcppExport SEXP bayesm_breg(SEXP ySEXP, SEXP XSEXP, SEXP betabarSEXP, SEXP ASEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< vec const& >::type y(ySEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); Rcpp::traits::input_parameter< vec const& >::type betabar(betabarSEXP); Rcpp::traits::input_parameter< mat const& >::type A(ASEXP); rcpp_result_gen = Rcpp::wrap(breg(y, X, betabar, A)); return rcpp_result_gen; END_RCPP } // cgetC vec cgetC(double e, int k); RcppExport SEXP bayesm_cgetC(SEXP eSEXP, SEXP kSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< double >::type e(eSEXP); Rcpp::traits::input_parameter< int >::type k(kSEXP); rcpp_result_gen = Rcpp::wrap(cgetC(e, k)); return rcpp_result_gen; END_RCPP } // clusterMix_rcpp_loop List clusterMix_rcpp_loop(mat const& zdraw, double cutoff, bool SILENT, int nprint); RcppExport SEXP bayesm_clusterMix_rcpp_loop(SEXP zdrawSEXP, SEXP cutoffSEXP, SEXP SILENTSEXP, SEXP nprintSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< mat const& >::type zdraw(zdrawSEXP); Rcpp::traits::input_parameter< double >::type cutoff(cutoffSEXP); Rcpp::traits::input_parameter< bool >::type SILENT(SILENTSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); rcpp_result_gen = Rcpp::wrap(clusterMix_rcpp_loop(zdraw, cutoff, SILENT, nprint)); return rcpp_result_gen; END_RCPP } // ghkvec vec ghkvec(mat const& L, vec const& trunpt, vec const& above, int r, bool HALTON, vec pn); RcppExport SEXP bayesm_ghkvec(SEXP LSEXP, SEXP trunptSEXP, SEXP aboveSEXP, SEXP rSEXP, SEXP HALTONSEXP, SEXP pnSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< mat const& >::type L(LSEXP); Rcpp::traits::input_parameter< vec const& >::type trunpt(trunptSEXP); Rcpp::traits::input_parameter< vec const& >::type above(aboveSEXP); Rcpp::traits::input_parameter< int >::type r(rSEXP); Rcpp::traits::input_parameter< bool >::type HALTON(HALTONSEXP); Rcpp::traits::input_parameter< vec >::type pn(pnSEXP); rcpp_result_gen = Rcpp::wrap(ghkvec(L, trunpt, above, r, HALTON, pn)); return rcpp_result_gen; END_RCPP } // llmnl double llmnl(vec const& beta, vec const& y, mat const& X); RcppExport SEXP bayesm_llmnl(SEXP betaSEXP, SEXP ySEXP, SEXP XSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< vec const& >::type beta(betaSEXP); Rcpp::traits::input_parameter< vec const& >::type y(ySEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); rcpp_result_gen = Rcpp::wrap(llmnl(beta, y, X)); return rcpp_result_gen; END_RCPP } // lndIChisq mat lndIChisq(double nu, double ssq, mat const& X); RcppExport SEXP bayesm_lndIChisq(SEXP nuSEXP, SEXP ssqSEXP, SEXP XSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< double >::type ssq(ssqSEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); rcpp_result_gen = Rcpp::wrap(lndIChisq(nu, ssq, X)); return rcpp_result_gen; END_RCPP } // lndIWishart double lndIWishart(double nu, mat const& V, mat const& IW); RcppExport SEXP bayesm_lndIWishart(SEXP nuSEXP, SEXP VSEXP, SEXP IWSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); Rcpp::traits::input_parameter< mat const& >::type IW(IWSEXP); rcpp_result_gen = Rcpp::wrap(lndIWishart(nu, V, IW)); return rcpp_result_gen; END_RCPP } // lndMvn double lndMvn(vec const& x, vec const& mu, mat const& rooti); RcppExport SEXP bayesm_lndMvn(SEXP xSEXP, SEXP muSEXP, SEXP rootiSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< vec const& >::type x(xSEXP); Rcpp::traits::input_parameter< vec const& >::type mu(muSEXP); Rcpp::traits::input_parameter< mat const& >::type rooti(rootiSEXP); rcpp_result_gen = Rcpp::wrap(lndMvn(x, mu, rooti)); return rcpp_result_gen; END_RCPP } // lndMvst double lndMvst(vec const& x, double nu, vec const& mu, mat const& rooti, bool NORMC); RcppExport SEXP bayesm_lndMvst(SEXP xSEXP, SEXP nuSEXP, SEXP muSEXP, SEXP rootiSEXP, SEXP NORMCSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< vec const& >::type x(xSEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< vec const& >::type mu(muSEXP); Rcpp::traits::input_parameter< mat const& >::type rooti(rootiSEXP); Rcpp::traits::input_parameter< bool >::type NORMC(NORMCSEXP); rcpp_result_gen = Rcpp::wrap(lndMvst(x, nu, mu, rooti, NORMC)); return rcpp_result_gen; END_RCPP } // rbprobitGibbs_rcpp_loop List rbprobitGibbs_rcpp_loop(vec const& y, mat const& X, vec const& Abetabar, mat const& root, vec beta, vec const& sigma, vec const& trunpt, vec const& above, int R, int keep, int nprint); RcppExport SEXP bayesm_rbprobitGibbs_rcpp_loop(SEXP ySEXP, SEXP XSEXP, SEXP AbetabarSEXP, SEXP rootSEXP, SEXP betaSEXP, SEXP sigmaSEXP, SEXP trunptSEXP, SEXP aboveSEXP, SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< vec const& >::type y(ySEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); Rcpp::traits::input_parameter< vec const& >::type Abetabar(AbetabarSEXP); Rcpp::traits::input_parameter< mat const& >::type root(rootSEXP); Rcpp::traits::input_parameter< vec >::type beta(betaSEXP); Rcpp::traits::input_parameter< vec const& >::type sigma(sigmaSEXP); Rcpp::traits::input_parameter< vec const& >::type trunpt(trunptSEXP); Rcpp::traits::input_parameter< vec const& >::type above(aboveSEXP); Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); rcpp_result_gen = Rcpp::wrap(rbprobitGibbs_rcpp_loop(y, X, Abetabar, root, beta, sigma, trunpt, above, R, keep, nprint)); return rcpp_result_gen; END_RCPP } // rdirichlet vec rdirichlet(vec const& alpha); RcppExport SEXP bayesm_rdirichlet(SEXP alphaSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< vec const& >::type alpha(alphaSEXP); rcpp_result_gen = Rcpp::wrap(rdirichlet(alpha)); return rcpp_result_gen; END_RCPP } // rDPGibbs_rcpp_loop List rDPGibbs_rcpp_loop(int R, int keep, int nprint, mat y, List const& lambda_hyper, bool SCALE, int maxuniq, List const& PrioralphaList, int gridsize, double BayesmConstantA, int BayesmConstantnuInc, double BayesmConstantDPalpha); RcppExport SEXP bayesm_rDPGibbs_rcpp_loop(SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP, SEXP ySEXP, SEXP lambda_hyperSEXP, SEXP SCALESEXP, SEXP maxuniqSEXP, SEXP PrioralphaListSEXP, SEXP gridsizeSEXP, SEXP BayesmConstantASEXP, SEXP BayesmConstantnuIncSEXP, SEXP BayesmConstantDPalphaSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); Rcpp::traits::input_parameter< mat >::type y(ySEXP); Rcpp::traits::input_parameter< List const& >::type lambda_hyper(lambda_hyperSEXP); Rcpp::traits::input_parameter< bool >::type SCALE(SCALESEXP); Rcpp::traits::input_parameter< int >::type maxuniq(maxuniqSEXP); Rcpp::traits::input_parameter< List const& >::type PrioralphaList(PrioralphaListSEXP); Rcpp::traits::input_parameter< int >::type gridsize(gridsizeSEXP); Rcpp::traits::input_parameter< double >::type BayesmConstantA(BayesmConstantASEXP); Rcpp::traits::input_parameter< int >::type BayesmConstantnuInc(BayesmConstantnuIncSEXP); Rcpp::traits::input_parameter< double >::type BayesmConstantDPalpha(BayesmConstantDPalphaSEXP); rcpp_result_gen = Rcpp::wrap(rDPGibbs_rcpp_loop(R, keep, nprint, y, lambda_hyper, SCALE, maxuniq, PrioralphaList, gridsize, BayesmConstantA, BayesmConstantnuInc, BayesmConstantDPalpha)); return rcpp_result_gen; END_RCPP } // rhierLinearMixture_rcpp_loop List rhierLinearMixture_rcpp_loop(List const& regdata, mat const& Z, vec const& deltabar, mat const& Ad, mat const& mubar, mat const& Amu, double nu, mat const& V, double nu_e, vec const& ssq, int R, int keep, int nprint, bool drawdelta, mat olddelta, vec const& a, vec oldprob, vec ind, vec tau); RcppExport SEXP bayesm_rhierLinearMixture_rcpp_loop(SEXP regdataSEXP, SEXP ZSEXP, SEXP deltabarSEXP, SEXP AdSEXP, SEXP mubarSEXP, SEXP AmuSEXP, SEXP nuSEXP, SEXP VSEXP, SEXP nu_eSEXP, SEXP ssqSEXP, SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP, SEXP drawdeltaSEXP, SEXP olddeltaSEXP, SEXP aSEXP, SEXP oldprobSEXP, SEXP indSEXP, SEXP tauSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< List const& >::type regdata(regdataSEXP); Rcpp::traits::input_parameter< mat const& >::type Z(ZSEXP); Rcpp::traits::input_parameter< vec const& >::type deltabar(deltabarSEXP); Rcpp::traits::input_parameter< mat const& >::type Ad(AdSEXP); Rcpp::traits::input_parameter< mat const& >::type mubar(mubarSEXP); Rcpp::traits::input_parameter< mat const& >::type Amu(AmuSEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); Rcpp::traits::input_parameter< double >::type nu_e(nu_eSEXP); Rcpp::traits::input_parameter< vec const& >::type ssq(ssqSEXP); Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); Rcpp::traits::input_parameter< bool >::type drawdelta(drawdeltaSEXP); Rcpp::traits::input_parameter< mat >::type olddelta(olddeltaSEXP); Rcpp::traits::input_parameter< vec const& >::type a(aSEXP); Rcpp::traits::input_parameter< vec >::type oldprob(oldprobSEXP); Rcpp::traits::input_parameter< vec >::type ind(indSEXP); Rcpp::traits::input_parameter< vec >::type tau(tauSEXP); rcpp_result_gen = Rcpp::wrap(rhierLinearMixture_rcpp_loop(regdata, Z, deltabar, Ad, mubar, Amu, nu, V, nu_e, ssq, R, keep, nprint, drawdelta, olddelta, a, oldprob, ind, tau)); return rcpp_result_gen; END_RCPP } // rhierLinearModel_rcpp_loop List rhierLinearModel_rcpp_loop(List const& regdata, mat const& Z, mat const& Deltabar, mat const& A, double nu, mat const& V, double nu_e, vec const& ssq, vec tau, mat Delta, mat Vbeta, int R, int keep, int nprint); RcppExport SEXP bayesm_rhierLinearModel_rcpp_loop(SEXP regdataSEXP, SEXP ZSEXP, SEXP DeltabarSEXP, SEXP ASEXP, SEXP nuSEXP, SEXP VSEXP, SEXP nu_eSEXP, SEXP ssqSEXP, SEXP tauSEXP, SEXP DeltaSEXP, SEXP VbetaSEXP, SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< List const& >::type regdata(regdataSEXP); Rcpp::traits::input_parameter< mat const& >::type Z(ZSEXP); Rcpp::traits::input_parameter< mat const& >::type Deltabar(DeltabarSEXP); Rcpp::traits::input_parameter< mat const& >::type A(ASEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); Rcpp::traits::input_parameter< double >::type nu_e(nu_eSEXP); Rcpp::traits::input_parameter< vec const& >::type ssq(ssqSEXP); Rcpp::traits::input_parameter< vec >::type tau(tauSEXP); Rcpp::traits::input_parameter< mat >::type Delta(DeltaSEXP); Rcpp::traits::input_parameter< mat >::type Vbeta(VbetaSEXP); Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); rcpp_result_gen = Rcpp::wrap(rhierLinearModel_rcpp_loop(regdata, Z, Deltabar, A, nu, V, nu_e, ssq, tau, Delta, Vbeta, R, keep, nprint)); return rcpp_result_gen; END_RCPP } // rhierMnlDP_rcpp_loop List rhierMnlDP_rcpp_loop(int R, int keep, int nprint, List const& lgtdata, mat const& Z, vec const& deltabar, mat const& Ad, List const& PrioralphaList, List const& lambda_hyper, bool drawdelta, int nvar, mat oldbetas, double s, int maxuniq, int gridsize, double BayesmConstantA, int BayesmConstantnuInc, double BayesmConstantDPalpha); RcppExport SEXP bayesm_rhierMnlDP_rcpp_loop(SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP, SEXP lgtdataSEXP, SEXP ZSEXP, SEXP deltabarSEXP, SEXP AdSEXP, SEXP PrioralphaListSEXP, SEXP lambda_hyperSEXP, SEXP drawdeltaSEXP, SEXP nvarSEXP, SEXP oldbetasSEXP, SEXP sSEXP, SEXP maxuniqSEXP, SEXP gridsizeSEXP, SEXP BayesmConstantASEXP, SEXP BayesmConstantnuIncSEXP, SEXP BayesmConstantDPalphaSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); Rcpp::traits::input_parameter< List const& >::type lgtdata(lgtdataSEXP); Rcpp::traits::input_parameter< mat const& >::type Z(ZSEXP); Rcpp::traits::input_parameter< vec const& >::type deltabar(deltabarSEXP); Rcpp::traits::input_parameter< mat const& >::type Ad(AdSEXP); Rcpp::traits::input_parameter< List const& >::type PrioralphaList(PrioralphaListSEXP); Rcpp::traits::input_parameter< List const& >::type lambda_hyper(lambda_hyperSEXP); Rcpp::traits::input_parameter< bool >::type drawdelta(drawdeltaSEXP); Rcpp::traits::input_parameter< int >::type nvar(nvarSEXP); Rcpp::traits::input_parameter< mat >::type oldbetas(oldbetasSEXP); Rcpp::traits::input_parameter< double >::type s(sSEXP); Rcpp::traits::input_parameter< int >::type maxuniq(maxuniqSEXP); Rcpp::traits::input_parameter< int >::type gridsize(gridsizeSEXP); Rcpp::traits::input_parameter< double >::type BayesmConstantA(BayesmConstantASEXP); Rcpp::traits::input_parameter< int >::type BayesmConstantnuInc(BayesmConstantnuIncSEXP); Rcpp::traits::input_parameter< double >::type BayesmConstantDPalpha(BayesmConstantDPalphaSEXP); rcpp_result_gen = Rcpp::wrap(rhierMnlDP_rcpp_loop(R, keep, nprint, lgtdata, Z, deltabar, Ad, PrioralphaList, lambda_hyper, drawdelta, nvar, oldbetas, s, maxuniq, gridsize, BayesmConstantA, BayesmConstantnuInc, BayesmConstantDPalpha)); return rcpp_result_gen; END_RCPP } // llmnl_con double llmnl_con(vec const& betastar, vec const& y, mat const& X, vec const& SignRes); RcppExport SEXP bayesm_llmnl_con(SEXP betastarSEXP, SEXP ySEXP, SEXP XSEXP, SEXP SignResSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< vec const& >::type betastar(betastarSEXP); Rcpp::traits::input_parameter< vec const& >::type y(ySEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); Rcpp::traits::input_parameter< vec const& >::type SignRes(SignResSEXP); rcpp_result_gen = Rcpp::wrap(llmnl_con(betastar, y, X, SignRes)); return rcpp_result_gen; END_RCPP } // rhierMnlRwMixture_rcpp_loop List rhierMnlRwMixture_rcpp_loop(List const& lgtdata, mat const& Z, vec const& deltabar, mat const& Ad, mat const& mubar, mat const& Amu, double nu, mat const& V, double s, int R, int keep, int nprint, bool drawdelta, mat olddelta, vec const& a, vec oldprob, mat oldbetas, vec ind, vec const& SignRes); RcppExport SEXP bayesm_rhierMnlRwMixture_rcpp_loop(SEXP lgtdataSEXP, SEXP ZSEXP, SEXP deltabarSEXP, SEXP AdSEXP, SEXP mubarSEXP, SEXP AmuSEXP, SEXP nuSEXP, SEXP VSEXP, SEXP sSEXP, SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP, SEXP drawdeltaSEXP, SEXP olddeltaSEXP, SEXP aSEXP, SEXP oldprobSEXP, SEXP oldbetasSEXP, SEXP indSEXP, SEXP SignResSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< List const& >::type lgtdata(lgtdataSEXP); Rcpp::traits::input_parameter< mat const& >::type Z(ZSEXP); Rcpp::traits::input_parameter< vec const& >::type deltabar(deltabarSEXP); Rcpp::traits::input_parameter< mat const& >::type Ad(AdSEXP); Rcpp::traits::input_parameter< mat const& >::type mubar(mubarSEXP); Rcpp::traits::input_parameter< mat const& >::type Amu(AmuSEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); Rcpp::traits::input_parameter< double >::type s(sSEXP); Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); Rcpp::traits::input_parameter< bool >::type drawdelta(drawdeltaSEXP); Rcpp::traits::input_parameter< mat >::type olddelta(olddeltaSEXP); Rcpp::traits::input_parameter< vec const& >::type a(aSEXP); Rcpp::traits::input_parameter< vec >::type oldprob(oldprobSEXP); Rcpp::traits::input_parameter< mat >::type oldbetas(oldbetasSEXP); Rcpp::traits::input_parameter< vec >::type ind(indSEXP); Rcpp::traits::input_parameter< vec const& >::type SignRes(SignResSEXP); rcpp_result_gen = Rcpp::wrap(rhierMnlRwMixture_rcpp_loop(lgtdata, Z, deltabar, Ad, mubar, Amu, nu, V, s, R, keep, nprint, drawdelta, olddelta, a, oldprob, oldbetas, ind, SignRes)); return rcpp_result_gen; END_RCPP } // rhierNegbinRw_rcpp_loop List rhierNegbinRw_rcpp_loop(List const& regdata, List const& hessdata, mat const& Z, mat Beta, mat Delta, mat const& Deltabar, mat const& Adelta, double nu, mat const& V, double a, double b, int R, int keep, double sbeta, double alphacroot, int nprint, mat rootA, double alpha, bool fixalpha); RcppExport SEXP bayesm_rhierNegbinRw_rcpp_loop(SEXP regdataSEXP, SEXP hessdataSEXP, SEXP ZSEXP, SEXP BetaSEXP, SEXP DeltaSEXP, SEXP DeltabarSEXP, SEXP AdeltaSEXP, SEXP nuSEXP, SEXP VSEXP, SEXP aSEXP, SEXP bSEXP, SEXP RSEXP, SEXP keepSEXP, SEXP sbetaSEXP, SEXP alphacrootSEXP, SEXP nprintSEXP, SEXP rootASEXP, SEXP alphaSEXP, SEXP fixalphaSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< List const& >::type regdata(regdataSEXP); Rcpp::traits::input_parameter< List const& >::type hessdata(hessdataSEXP); Rcpp::traits::input_parameter< mat const& >::type Z(ZSEXP); Rcpp::traits::input_parameter< mat >::type Beta(BetaSEXP); Rcpp::traits::input_parameter< mat >::type Delta(DeltaSEXP); Rcpp::traits::input_parameter< mat const& >::type Deltabar(DeltabarSEXP); Rcpp::traits::input_parameter< mat const& >::type Adelta(AdeltaSEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); Rcpp::traits::input_parameter< double >::type a(aSEXP); Rcpp::traits::input_parameter< double >::type b(bSEXP); Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< double >::type sbeta(sbetaSEXP); Rcpp::traits::input_parameter< double >::type alphacroot(alphacrootSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); Rcpp::traits::input_parameter< mat >::type rootA(rootASEXP); Rcpp::traits::input_parameter< double >::type alpha(alphaSEXP); Rcpp::traits::input_parameter< bool >::type fixalpha(fixalphaSEXP); rcpp_result_gen = Rcpp::wrap(rhierNegbinRw_rcpp_loop(regdata, hessdata, Z, Beta, Delta, Deltabar, Adelta, nu, V, a, b, R, keep, sbeta, alphacroot, nprint, rootA, alpha, fixalpha)); return rcpp_result_gen; END_RCPP } // rivDP_rcpp_loop List rivDP_rcpp_loop(int R, int keep, int nprint, int dimd, vec const& mbg, mat const& Abg, vec const& md, mat const& Ad, vec const& y, bool isgamma, mat const& z, vec const& x, mat const& w, vec delta, List const& PrioralphaList, int gridsize, bool SCALE, int maxuniq, double scalex, double scaley, List const& lambda_hyper, double BayesmConstantA, int BayesmConstantnu); RcppExport SEXP bayesm_rivDP_rcpp_loop(SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP, SEXP dimdSEXP, SEXP mbgSEXP, SEXP AbgSEXP, SEXP mdSEXP, SEXP AdSEXP, SEXP ySEXP, SEXP isgammaSEXP, SEXP zSEXP, SEXP xSEXP, SEXP wSEXP, SEXP deltaSEXP, SEXP PrioralphaListSEXP, SEXP gridsizeSEXP, SEXP SCALESEXP, SEXP maxuniqSEXP, SEXP scalexSEXP, SEXP scaleySEXP, SEXP lambda_hyperSEXP, SEXP BayesmConstantASEXP, SEXP BayesmConstantnuSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); Rcpp::traits::input_parameter< int >::type dimd(dimdSEXP); Rcpp::traits::input_parameter< vec const& >::type mbg(mbgSEXP); Rcpp::traits::input_parameter< mat const& >::type Abg(AbgSEXP); Rcpp::traits::input_parameter< vec const& >::type md(mdSEXP); Rcpp::traits::input_parameter< mat const& >::type Ad(AdSEXP); Rcpp::traits::input_parameter< vec const& >::type y(ySEXP); Rcpp::traits::input_parameter< bool >::type isgamma(isgammaSEXP); Rcpp::traits::input_parameter< mat const& >::type z(zSEXP); Rcpp::traits::input_parameter< vec const& >::type x(xSEXP); Rcpp::traits::input_parameter< mat const& >::type w(wSEXP); Rcpp::traits::input_parameter< vec >::type delta(deltaSEXP); Rcpp::traits::input_parameter< List const& >::type PrioralphaList(PrioralphaListSEXP); Rcpp::traits::input_parameter< int >::type gridsize(gridsizeSEXP); Rcpp::traits::input_parameter< bool >::type SCALE(SCALESEXP); Rcpp::traits::input_parameter< int >::type maxuniq(maxuniqSEXP); Rcpp::traits::input_parameter< double >::type scalex(scalexSEXP); Rcpp::traits::input_parameter< double >::type scaley(scaleySEXP); Rcpp::traits::input_parameter< List const& >::type lambda_hyper(lambda_hyperSEXP); Rcpp::traits::input_parameter< double >::type BayesmConstantA(BayesmConstantASEXP); Rcpp::traits::input_parameter< int >::type BayesmConstantnu(BayesmConstantnuSEXP); rcpp_result_gen = Rcpp::wrap(rivDP_rcpp_loop(R, keep, nprint, dimd, mbg, Abg, md, Ad, y, isgamma, z, x, w, delta, PrioralphaList, gridsize, SCALE, maxuniq, scalex, scaley, lambda_hyper, BayesmConstantA, BayesmConstantnu)); return rcpp_result_gen; END_RCPP } // rivGibbs_rcpp_loop List rivGibbs_rcpp_loop(vec const& y, vec const& x, mat const& z, mat const& w, vec const& mbg, mat const& Abg, vec const& md, mat const& Ad, mat const& V, double nu, int R, int keep, int nprint); RcppExport SEXP bayesm_rivGibbs_rcpp_loop(SEXP ySEXP, SEXP xSEXP, SEXP zSEXP, SEXP wSEXP, SEXP mbgSEXP, SEXP AbgSEXP, SEXP mdSEXP, SEXP AdSEXP, SEXP VSEXP, SEXP nuSEXP, SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< vec const& >::type y(ySEXP); Rcpp::traits::input_parameter< vec const& >::type x(xSEXP); Rcpp::traits::input_parameter< mat const& >::type z(zSEXP); Rcpp::traits::input_parameter< mat const& >::type w(wSEXP); Rcpp::traits::input_parameter< vec const& >::type mbg(mbgSEXP); Rcpp::traits::input_parameter< mat const& >::type Abg(AbgSEXP); Rcpp::traits::input_parameter< vec const& >::type md(mdSEXP); Rcpp::traits::input_parameter< mat const& >::type Ad(AdSEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); rcpp_result_gen = Rcpp::wrap(rivGibbs_rcpp_loop(y, x, z, w, mbg, Abg, md, Ad, V, nu, R, keep, nprint)); return rcpp_result_gen; END_RCPP } // rmixGibbs List rmixGibbs(mat const& y, mat const& Bbar, mat const& A, double nu, mat const& V, vec const& a, vec const& p, vec const& z); RcppExport SEXP bayesm_rmixGibbs(SEXP ySEXP, SEXP BbarSEXP, SEXP ASEXP, SEXP nuSEXP, SEXP VSEXP, SEXP aSEXP, SEXP pSEXP, SEXP zSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< mat const& >::type y(ySEXP); Rcpp::traits::input_parameter< mat const& >::type Bbar(BbarSEXP); Rcpp::traits::input_parameter< mat const& >::type A(ASEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); Rcpp::traits::input_parameter< vec const& >::type a(aSEXP); Rcpp::traits::input_parameter< vec const& >::type p(pSEXP); Rcpp::traits::input_parameter< vec const& >::type z(zSEXP); rcpp_result_gen = Rcpp::wrap(rmixGibbs(y, Bbar, A, nu, V, a, p, z)); return rcpp_result_gen; END_RCPP } // rmixture List rmixture(int n, vec pvec, List comps); RcppExport SEXP bayesm_rmixture(SEXP nSEXP, SEXP pvecSEXP, SEXP compsSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< int >::type n(nSEXP); Rcpp::traits::input_parameter< vec >::type pvec(pvecSEXP); Rcpp::traits::input_parameter< List >::type comps(compsSEXP); rcpp_result_gen = Rcpp::wrap(rmixture(n, pvec, comps)); return rcpp_result_gen; END_RCPP } // rmnlIndepMetrop_rcpp_loop List rmnlIndepMetrop_rcpp_loop(int R, int keep, double nu, vec const& betastar, mat const& root, vec const& y, mat const& X, vec const& betabar, mat const& rootpi, mat const& rooti, double oldlimp, double oldlpost, int nprint); RcppExport SEXP bayesm_rmnlIndepMetrop_rcpp_loop(SEXP RSEXP, SEXP keepSEXP, SEXP nuSEXP, SEXP betastarSEXP, SEXP rootSEXP, SEXP ySEXP, SEXP XSEXP, SEXP betabarSEXP, SEXP rootpiSEXP, SEXP rootiSEXP, SEXP oldlimpSEXP, SEXP oldlpostSEXP, SEXP nprintSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< vec const& >::type betastar(betastarSEXP); Rcpp::traits::input_parameter< mat const& >::type root(rootSEXP); Rcpp::traits::input_parameter< vec const& >::type y(ySEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); Rcpp::traits::input_parameter< vec const& >::type betabar(betabarSEXP); Rcpp::traits::input_parameter< mat const& >::type rootpi(rootpiSEXP); Rcpp::traits::input_parameter< mat const& >::type rooti(rootiSEXP); Rcpp::traits::input_parameter< double >::type oldlimp(oldlimpSEXP); Rcpp::traits::input_parameter< double >::type oldlpost(oldlpostSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); rcpp_result_gen = Rcpp::wrap(rmnlIndepMetrop_rcpp_loop(R, keep, nu, betastar, root, y, X, betabar, rootpi, rooti, oldlimp, oldlpost, nprint)); return rcpp_result_gen; END_RCPP } // rmnpGibbs_rcpp_loop List rmnpGibbs_rcpp_loop(int R, int keep, int nprint, int pm1, ivec const& y, mat const& X, vec const& beta0, mat const& sigma0, mat const& V, double nu, vec const& betabar, mat const& A); RcppExport SEXP bayesm_rmnpGibbs_rcpp_loop(SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP, SEXP pm1SEXP, SEXP ySEXP, SEXP XSEXP, SEXP beta0SEXP, SEXP sigma0SEXP, SEXP VSEXP, SEXP nuSEXP, SEXP betabarSEXP, SEXP ASEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); Rcpp::traits::input_parameter< int >::type pm1(pm1SEXP); Rcpp::traits::input_parameter< ivec const& >::type y(ySEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); Rcpp::traits::input_parameter< vec const& >::type beta0(beta0SEXP); Rcpp::traits::input_parameter< mat const& >::type sigma0(sigma0SEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< vec const& >::type betabar(betabarSEXP); Rcpp::traits::input_parameter< mat const& >::type A(ASEXP); rcpp_result_gen = Rcpp::wrap(rmnpGibbs_rcpp_loop(R, keep, nprint, pm1, y, X, beta0, sigma0, V, nu, betabar, A)); return rcpp_result_gen; END_RCPP } // rmultireg List rmultireg(mat const& Y, mat const& X, mat const& Bbar, mat const& A, double nu, mat const& V); RcppExport SEXP bayesm_rmultireg(SEXP YSEXP, SEXP XSEXP, SEXP BbarSEXP, SEXP ASEXP, SEXP nuSEXP, SEXP VSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< mat const& >::type Y(YSEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); Rcpp::traits::input_parameter< mat const& >::type Bbar(BbarSEXP); Rcpp::traits::input_parameter< mat const& >::type A(ASEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); rcpp_result_gen = Rcpp::wrap(rmultireg(Y, X, Bbar, A, nu, V)); return rcpp_result_gen; END_RCPP } // rmvpGibbs_rcpp_loop List rmvpGibbs_rcpp_loop(int R, int keep, int nprint, int p, ivec const& y, mat const& X, vec const& beta0, mat const& sigma0, mat const& V, double nu, vec const& betabar, mat const& A); RcppExport SEXP bayesm_rmvpGibbs_rcpp_loop(SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP, SEXP pSEXP, SEXP ySEXP, SEXP XSEXP, SEXP beta0SEXP, SEXP sigma0SEXP, SEXP VSEXP, SEXP nuSEXP, SEXP betabarSEXP, SEXP ASEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); Rcpp::traits::input_parameter< int >::type p(pSEXP); Rcpp::traits::input_parameter< ivec const& >::type y(ySEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); Rcpp::traits::input_parameter< vec const& >::type beta0(beta0SEXP); Rcpp::traits::input_parameter< mat const& >::type sigma0(sigma0SEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< vec const& >::type betabar(betabarSEXP); Rcpp::traits::input_parameter< mat const& >::type A(ASEXP); rcpp_result_gen = Rcpp::wrap(rmvpGibbs_rcpp_loop(R, keep, nprint, p, y, X, beta0, sigma0, V, nu, betabar, A)); return rcpp_result_gen; END_RCPP } // rmvst vec rmvst(double nu, vec const& mu, mat const& root); RcppExport SEXP bayesm_rmvst(SEXP nuSEXP, SEXP muSEXP, SEXP rootSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< vec const& >::type mu(muSEXP); Rcpp::traits::input_parameter< mat const& >::type root(rootSEXP); rcpp_result_gen = Rcpp::wrap(rmvst(nu, mu, root)); return rcpp_result_gen; END_RCPP } // rnegbinRw_rcpp_loop List rnegbinRw_rcpp_loop(vec const& y, mat const& X, vec const& betabar, mat const& rootA, double a, double b, vec beta, double alpha, bool fixalpha, mat const& betaroot, double alphacroot, int R, int keep, int nprint); RcppExport SEXP bayesm_rnegbinRw_rcpp_loop(SEXP ySEXP, SEXP XSEXP, SEXP betabarSEXP, SEXP rootASEXP, SEXP aSEXP, SEXP bSEXP, SEXP betaSEXP, SEXP alphaSEXP, SEXP fixalphaSEXP, SEXP betarootSEXP, SEXP alphacrootSEXP, SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< vec const& >::type y(ySEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); Rcpp::traits::input_parameter< vec const& >::type betabar(betabarSEXP); Rcpp::traits::input_parameter< mat const& >::type rootA(rootASEXP); Rcpp::traits::input_parameter< double >::type a(aSEXP); Rcpp::traits::input_parameter< double >::type b(bSEXP); Rcpp::traits::input_parameter< vec >::type beta(betaSEXP); Rcpp::traits::input_parameter< double >::type alpha(alphaSEXP); Rcpp::traits::input_parameter< bool >::type fixalpha(fixalphaSEXP); Rcpp::traits::input_parameter< mat const& >::type betaroot(betarootSEXP); Rcpp::traits::input_parameter< double >::type alphacroot(alphacrootSEXP); Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); rcpp_result_gen = Rcpp::wrap(rnegbinRw_rcpp_loop(y, X, betabar, rootA, a, b, beta, alpha, fixalpha, betaroot, alphacroot, R, keep, nprint)); return rcpp_result_gen; END_RCPP } // rnmixGibbs_rcpp_loop List rnmixGibbs_rcpp_loop(mat const& y, mat const& Mubar, mat const& A, double nu, mat const& V, vec const& a, vec p, vec z, int const& R, int const& keep, int const& nprint); RcppExport SEXP bayesm_rnmixGibbs_rcpp_loop(SEXP ySEXP, SEXP MubarSEXP, SEXP ASEXP, SEXP nuSEXP, SEXP VSEXP, SEXP aSEXP, SEXP pSEXP, SEXP zSEXP, SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< mat const& >::type y(ySEXP); Rcpp::traits::input_parameter< mat const& >::type Mubar(MubarSEXP); Rcpp::traits::input_parameter< mat const& >::type A(ASEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); Rcpp::traits::input_parameter< vec const& >::type a(aSEXP); Rcpp::traits::input_parameter< vec >::type p(pSEXP); Rcpp::traits::input_parameter< vec >::type z(zSEXP); Rcpp::traits::input_parameter< int const& >::type R(RSEXP); Rcpp::traits::input_parameter< int const& >::type keep(keepSEXP); Rcpp::traits::input_parameter< int const& >::type nprint(nprintSEXP); rcpp_result_gen = Rcpp::wrap(rnmixGibbs_rcpp_loop(y, Mubar, A, nu, V, a, p, z, R, keep, nprint)); return rcpp_result_gen; END_RCPP } // rordprobitGibbs_rcpp_loop List rordprobitGibbs_rcpp_loop(vec const& y, mat const& X, int k, mat const& A, vec const& betabar, mat const& Ad, double s, mat const& inc_root, vec const& dstarbar, vec const& betahat, int R, int keep, int nprint); RcppExport SEXP bayesm_rordprobitGibbs_rcpp_loop(SEXP ySEXP, SEXP XSEXP, SEXP kSEXP, SEXP ASEXP, SEXP betabarSEXP, SEXP AdSEXP, SEXP sSEXP, SEXP inc_rootSEXP, SEXP dstarbarSEXP, SEXP betahatSEXP, SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< vec const& >::type y(ySEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); Rcpp::traits::input_parameter< int >::type k(kSEXP); Rcpp::traits::input_parameter< mat const& >::type A(ASEXP); Rcpp::traits::input_parameter< vec const& >::type betabar(betabarSEXP); Rcpp::traits::input_parameter< mat const& >::type Ad(AdSEXP); Rcpp::traits::input_parameter< double >::type s(sSEXP); Rcpp::traits::input_parameter< mat const& >::type inc_root(inc_rootSEXP); Rcpp::traits::input_parameter< vec const& >::type dstarbar(dstarbarSEXP); Rcpp::traits::input_parameter< vec const& >::type betahat(betahatSEXP); Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); rcpp_result_gen = Rcpp::wrap(rordprobitGibbs_rcpp_loop(y, X, k, A, betabar, Ad, s, inc_root, dstarbar, betahat, R, keep, nprint)); return rcpp_result_gen; END_RCPP } // rscaleUsage_rcpp_loop List rscaleUsage_rcpp_loop(int k, mat const& x, int p, int n, int R, int keep, int ndghk, int nprint, mat y, vec mu, mat Sigma, vec tau, vec sigma, mat Lambda, double e, bool domu, bool doSigma, bool dosigma, bool dotau, bool doLambda, bool doe, double nu, mat const& V, mat const& mubar, mat const& Am, vec const& gsigma, vec const& gl11, vec const& gl22, vec const& gl12, int nuL, mat const& VL, vec const& ge); RcppExport SEXP bayesm_rscaleUsage_rcpp_loop(SEXP kSEXP, SEXP xSEXP, SEXP pSEXP, SEXP nSEXP, SEXP RSEXP, SEXP keepSEXP, SEXP ndghkSEXP, SEXP nprintSEXP, SEXP ySEXP, SEXP muSEXP, SEXP SigmaSEXP, SEXP tauSEXP, SEXP sigmaSEXP, SEXP LambdaSEXP, SEXP eSEXP, SEXP domuSEXP, SEXP doSigmaSEXP, SEXP dosigmaSEXP, SEXP dotauSEXP, SEXP doLambdaSEXP, SEXP doeSEXP, SEXP nuSEXP, SEXP VSEXP, SEXP mubarSEXP, SEXP AmSEXP, SEXP gsigmaSEXP, SEXP gl11SEXP, SEXP gl22SEXP, SEXP gl12SEXP, SEXP nuLSEXP, SEXP VLSEXP, SEXP geSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< int >::type k(kSEXP); Rcpp::traits::input_parameter< mat const& >::type x(xSEXP); Rcpp::traits::input_parameter< int >::type p(pSEXP); Rcpp::traits::input_parameter< int >::type n(nSEXP); Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type ndghk(ndghkSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); Rcpp::traits::input_parameter< mat >::type y(ySEXP); Rcpp::traits::input_parameter< vec >::type mu(muSEXP); Rcpp::traits::input_parameter< mat >::type Sigma(SigmaSEXP); Rcpp::traits::input_parameter< vec >::type tau(tauSEXP); Rcpp::traits::input_parameter< vec >::type sigma(sigmaSEXP); Rcpp::traits::input_parameter< mat >::type Lambda(LambdaSEXP); Rcpp::traits::input_parameter< double >::type e(eSEXP); Rcpp::traits::input_parameter< bool >::type domu(domuSEXP); Rcpp::traits::input_parameter< bool >::type doSigma(doSigmaSEXP); Rcpp::traits::input_parameter< bool >::type dosigma(dosigmaSEXP); Rcpp::traits::input_parameter< bool >::type dotau(dotauSEXP); Rcpp::traits::input_parameter< bool >::type doLambda(doLambdaSEXP); Rcpp::traits::input_parameter< bool >::type doe(doeSEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); Rcpp::traits::input_parameter< mat const& >::type mubar(mubarSEXP); Rcpp::traits::input_parameter< mat const& >::type Am(AmSEXP); Rcpp::traits::input_parameter< vec const& >::type gsigma(gsigmaSEXP); Rcpp::traits::input_parameter< vec const& >::type gl11(gl11SEXP); Rcpp::traits::input_parameter< vec const& >::type gl22(gl22SEXP); Rcpp::traits::input_parameter< vec const& >::type gl12(gl12SEXP); Rcpp::traits::input_parameter< int >::type nuL(nuLSEXP); Rcpp::traits::input_parameter< mat const& >::type VL(VLSEXP); Rcpp::traits::input_parameter< vec const& >::type ge(geSEXP); rcpp_result_gen = Rcpp::wrap(rscaleUsage_rcpp_loop(k, x, p, n, R, keep, ndghk, nprint, y, mu, Sigma, tau, sigma, Lambda, e, domu, doSigma, dosigma, dotau, doLambda, doe, nu, V, mubar, Am, gsigma, gl11, gl22, gl12, nuL, VL, ge)); return rcpp_result_gen; END_RCPP } // rsurGibbs_rcpp_loop List rsurGibbs_rcpp_loop(List const& regdata, vec const& indreg, vec const& cumnk, vec const& nk, mat const& XspXs, mat Sigmainv, mat const& A, vec const& Abetabar, double nu, mat const& V, int nvar, mat E, mat const& Y, int R, int keep, int nprint); RcppExport SEXP bayesm_rsurGibbs_rcpp_loop(SEXP regdataSEXP, SEXP indregSEXP, SEXP cumnkSEXP, SEXP nkSEXP, SEXP XspXsSEXP, SEXP SigmainvSEXP, SEXP ASEXP, SEXP AbetabarSEXP, SEXP nuSEXP, SEXP VSEXP, SEXP nvarSEXP, SEXP ESEXP, SEXP YSEXP, SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< List const& >::type regdata(regdataSEXP); Rcpp::traits::input_parameter< vec const& >::type indreg(indregSEXP); Rcpp::traits::input_parameter< vec const& >::type cumnk(cumnkSEXP); Rcpp::traits::input_parameter< vec const& >::type nk(nkSEXP); Rcpp::traits::input_parameter< mat const& >::type XspXs(XspXsSEXP); Rcpp::traits::input_parameter< mat >::type Sigmainv(SigmainvSEXP); Rcpp::traits::input_parameter< mat const& >::type A(ASEXP); Rcpp::traits::input_parameter< vec const& >::type Abetabar(AbetabarSEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); Rcpp::traits::input_parameter< int >::type nvar(nvarSEXP); Rcpp::traits::input_parameter< mat >::type E(ESEXP); Rcpp::traits::input_parameter< mat const& >::type Y(YSEXP); Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); rcpp_result_gen = Rcpp::wrap(rsurGibbs_rcpp_loop(regdata, indreg, cumnk, nk, XspXs, Sigmainv, A, Abetabar, nu, V, nvar, E, Y, R, keep, nprint)); return rcpp_result_gen; END_RCPP } // rtrun NumericVector rtrun(NumericVector const& mu, NumericVector const& sigma, NumericVector const& a, NumericVector const& b); RcppExport SEXP bayesm_rtrun(SEXP muSEXP, SEXP sigmaSEXP, SEXP aSEXP, SEXP bSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< NumericVector const& >::type mu(muSEXP); Rcpp::traits::input_parameter< NumericVector const& >::type sigma(sigmaSEXP); Rcpp::traits::input_parameter< NumericVector const& >::type a(aSEXP); Rcpp::traits::input_parameter< NumericVector const& >::type b(bSEXP); rcpp_result_gen = Rcpp::wrap(rtrun(mu, sigma, a, b)); return rcpp_result_gen; END_RCPP } // runireg_rcpp_loop List runireg_rcpp_loop(vec const& y, mat const& X, vec const& betabar, mat const& A, double nu, double ssq, int R, int keep, int nprint); RcppExport SEXP bayesm_runireg_rcpp_loop(SEXP ySEXP, SEXP XSEXP, SEXP betabarSEXP, SEXP ASEXP, SEXP nuSEXP, SEXP ssqSEXP, SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< vec const& >::type y(ySEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); Rcpp::traits::input_parameter< vec const& >::type betabar(betabarSEXP); Rcpp::traits::input_parameter< mat const& >::type A(ASEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< double >::type ssq(ssqSEXP); Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); rcpp_result_gen = Rcpp::wrap(runireg_rcpp_loop(y, X, betabar, A, nu, ssq, R, keep, nprint)); return rcpp_result_gen; END_RCPP } // runiregGibbs_rcpp_loop List runiregGibbs_rcpp_loop(vec const& y, mat const& X, vec const& betabar, mat const& A, double nu, double ssq, double sigmasq, int R, int keep, int nprint); RcppExport SEXP bayesm_runiregGibbs_rcpp_loop(SEXP ySEXP, SEXP XSEXP, SEXP betabarSEXP, SEXP ASEXP, SEXP nuSEXP, SEXP ssqSEXP, SEXP sigmasqSEXP, SEXP RSEXP, SEXP keepSEXP, SEXP nprintSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< vec const& >::type y(ySEXP); Rcpp::traits::input_parameter< mat const& >::type X(XSEXP); Rcpp::traits::input_parameter< vec const& >::type betabar(betabarSEXP); Rcpp::traits::input_parameter< mat const& >::type A(ASEXP); Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< double >::type ssq(ssqSEXP); Rcpp::traits::input_parameter< double >::type sigmasq(sigmasqSEXP); Rcpp::traits::input_parameter< int >::type R(RSEXP); Rcpp::traits::input_parameter< int >::type keep(keepSEXP); Rcpp::traits::input_parameter< int >::type nprint(nprintSEXP); rcpp_result_gen = Rcpp::wrap(runiregGibbs_rcpp_loop(y, X, betabar, A, nu, ssq, sigmasq, R, keep, nprint)); return rcpp_result_gen; END_RCPP } // rwishart List rwishart(double nu, mat const& V); RcppExport SEXP bayesm_rwishart(SEXP nuSEXP, SEXP VSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< double >::type nu(nuSEXP); Rcpp::traits::input_parameter< mat const& >::type V(VSEXP); rcpp_result_gen = Rcpp::wrap(rwishart(nu, V)); return rcpp_result_gen; END_RCPP } // callroot vec callroot(vec const& c1, vec const& c2, double tol, int iterlim); RcppExport SEXP bayesm_callroot(SEXP c1SEXP, SEXP c2SEXP, SEXP tolSEXP, SEXP iterlimSEXP) { BEGIN_RCPP Rcpp::RObject rcpp_result_gen; Rcpp::RNGScope rcpp_rngScope_gen; Rcpp::traits::input_parameter< vec const& >::type c1(c1SEXP); Rcpp::traits::input_parameter< vec const& >::type c2(c2SEXP); Rcpp::traits::input_parameter< double >::type tol(tolSEXP); Rcpp::traits::input_parameter< int >::type iterlim(iterlimSEXP); rcpp_result_gen = Rcpp::wrap(callroot(c1, c2, tol, iterlim)); return rcpp_result_gen; END_RCPP } static const R_CallMethodDef CallEntries[] = { {"bayesm_bayesBLP_rcpp_loop", (DL_FUNC) &bayesm_bayesBLP_rcpp_loop, 26}, {"bayesm_breg", (DL_FUNC) &bayesm_breg, 4}, {"bayesm_cgetC", (DL_FUNC) &bayesm_cgetC, 2}, {"bayesm_clusterMix_rcpp_loop", (DL_FUNC) &bayesm_clusterMix_rcpp_loop, 4}, {"bayesm_ghkvec", (DL_FUNC) &bayesm_ghkvec, 6}, {"bayesm_llmnl", (DL_FUNC) &bayesm_llmnl, 3}, {"bayesm_lndIChisq", (DL_FUNC) &bayesm_lndIChisq, 3}, {"bayesm_lndIWishart", (DL_FUNC) &bayesm_lndIWishart, 3}, {"bayesm_lndMvn", (DL_FUNC) &bayesm_lndMvn, 3}, {"bayesm_lndMvst", (DL_FUNC) &bayesm_lndMvst, 5}, {"bayesm_rbprobitGibbs_rcpp_loop", (DL_FUNC) &bayesm_rbprobitGibbs_rcpp_loop, 11}, {"bayesm_rdirichlet", (DL_FUNC) &bayesm_rdirichlet, 1}, {"bayesm_rDPGibbs_rcpp_loop", (DL_FUNC) &bayesm_rDPGibbs_rcpp_loop, 12}, {"bayesm_rhierLinearMixture_rcpp_loop", (DL_FUNC) &bayesm_rhierLinearMixture_rcpp_loop, 19}, {"bayesm_rhierLinearModel_rcpp_loop", (DL_FUNC) &bayesm_rhierLinearModel_rcpp_loop, 14}, {"bayesm_rhierMnlDP_rcpp_loop", (DL_FUNC) &bayesm_rhierMnlDP_rcpp_loop, 18}, {"bayesm_llmnl_con", (DL_FUNC) &bayesm_llmnl_con, 4}, {"bayesm_rhierMnlRwMixture_rcpp_loop", (DL_FUNC) &bayesm_rhierMnlRwMixture_rcpp_loop, 19}, {"bayesm_rhierNegbinRw_rcpp_loop", (DL_FUNC) &bayesm_rhierNegbinRw_rcpp_loop, 19}, {"bayesm_rivDP_rcpp_loop", (DL_FUNC) &bayesm_rivDP_rcpp_loop, 23}, {"bayesm_rivGibbs_rcpp_loop", (DL_FUNC) &bayesm_rivGibbs_rcpp_loop, 13}, {"bayesm_rmixGibbs", (DL_FUNC) &bayesm_rmixGibbs, 8}, {"bayesm_rmixture", (DL_FUNC) &bayesm_rmixture, 3}, {"bayesm_rmnlIndepMetrop_rcpp_loop", (DL_FUNC) &bayesm_rmnlIndepMetrop_rcpp_loop, 13}, {"bayesm_rmnpGibbs_rcpp_loop", (DL_FUNC) &bayesm_rmnpGibbs_rcpp_loop, 12}, {"bayesm_rmultireg", (DL_FUNC) &bayesm_rmultireg, 6}, {"bayesm_rmvpGibbs_rcpp_loop", (DL_FUNC) &bayesm_rmvpGibbs_rcpp_loop, 12}, {"bayesm_rmvst", (DL_FUNC) &bayesm_rmvst, 3}, {"bayesm_rnegbinRw_rcpp_loop", (DL_FUNC) &bayesm_rnegbinRw_rcpp_loop, 14}, {"bayesm_rnmixGibbs_rcpp_loop", (DL_FUNC) &bayesm_rnmixGibbs_rcpp_loop, 11}, {"bayesm_rordprobitGibbs_rcpp_loop", (DL_FUNC) &bayesm_rordprobitGibbs_rcpp_loop, 13}, {"bayesm_rscaleUsage_rcpp_loop", (DL_FUNC) &bayesm_rscaleUsage_rcpp_loop, 32}, {"bayesm_rsurGibbs_rcpp_loop", (DL_FUNC) &bayesm_rsurGibbs_rcpp_loop, 16}, {"bayesm_rtrun", (DL_FUNC) &bayesm_rtrun, 4}, {"bayesm_runireg_rcpp_loop", (DL_FUNC) &bayesm_runireg_rcpp_loop, 9}, {"bayesm_runiregGibbs_rcpp_loop", (DL_FUNC) &bayesm_runiregGibbs_rcpp_loop, 10}, {"bayesm_rwishart", (DL_FUNC) &bayesm_rwishart, 2}, {"bayesm_callroot", (DL_FUNC) &bayesm_callroot, 4}, {NULL, NULL, 0} }; RcppExport void R_init_bayesm(DllInfo *dll) { R_registerRoutines(dll, NULL, CallEntries, NULL, NULL); R_useDynamicSymbols(dll, FALSE); } bayesm/src/rmvpGibbs_rcpp_loop.cpp0000644000176000001440000000764713134410700017074 0ustar ripleyusers#include "bayesm.h" //EXTRA FUNCTIONS SPECIFIC TO THE MAIN FUNCTION-------------------------------------------- vec drawwi_mvp(vec const& w, vec const& mu, mat const& sigmai, int p, ivec y){ //Wayne Taylor 9/8/2014 //function to draw w_i by Gibbing thru p vector int above; vec outwi = w; for(int i = 0; i(w.size()); for(int i = 0; i(R/keep, p*p); mat betadraw = zeros(R/keep,k); vec wnew = zeros(X.n_rows); //set initial values of w,beta, sigma (or root of inv) vec wold = wnew; vec betaold = beta0; mat C = chol(solve(trimatu(sigma0),eye(sigma0.n_cols,sigma0.n_cols))); //C is upper triangular root of sigma^-1 (G) = C'C //trimatu interprets the matrix as upper triangular and makes solve more efficient mat sigmai, zmat, epsilon, S, IW, ucholinv, VSinv; vec betanew; List W; // start main iteration loop int mkeep = 0; if(nprint>0) startMcmcTimer(); for(int rep = 0; rep(W["C"]); //conversion from Rcpp to Armadillo requires explict declaration of variable type using as<> //print time to completion if (nprint>0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); //save every keepth draw if((rep+1)%keep==0){ mkeep = (rep+1)/keep; betadraw(mkeep-1,span::all) = trans(betanew); IW = as(W["IW"]); sigmadraw(mkeep-1,span::all) = trans(vectorise(IW)); } wold = wnew; betaold = betanew; } if(nprint>0) endMcmcTimer(); return List::create( Named("betadraw") = betadraw, Named("sigmadraw") = sigmadraw); } bayesm/src/cgetC_rcpp.cpp0000644000176000001440000000233313134410700015120 0ustar ripleyusers#include "bayesm.h" // [[Rcpp::export]] vec cgetC(double e, int k){ //Wayne Taylor 4/29/15 //purpose: get a list of cutoffs for use with scale usage problems //arguments: // e: the "e" parameter from the paper // k: the point scale, eg. items are rated from 1,2,...k // output: // vector of grid points vec temp = zeros(k-1); for(int i = 0; i<(k-1); i++) temp[i] = i + 1.5; double m1 = sum(temp); temp = pow(temp,2.0); double m2 = sum(temp); vec c = zeros(k+1); //first sum to get s's, this is a waste since it should be done //once but I don't want to see this things anywhere else and it should take no time double s0 = k-1; double s1=0.0,s2=0.0,s3=0.0,s4=0.0; for(int i=1;i(ncolX); rowvec beta = zeros(ncolX); double cloglike, clpost, climp, ldiff, alpha, unif, oldloglike; vec alphaminv; if(nprint>0) startMcmcTimer(); // start main iteration loop for(int rep = 0; rep0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; betadraw(mkeep-1,span::all) = beta; loglike[mkeep-1] = oldloglike; } } if(nprint>0) endMcmcTimer(); return List::create( Named("betadraw") = betadraw, Named("loglike") = loglike, Named("naccept") = naccept); } bayesm/src/lndIWishart_rcpp.cpp0000644000176000001440000000260713134410700016327 0ustar ripleyusers#include "bayesm.h" // [[Rcpp::export]] double lndIWishart(double nu, mat const& V, mat const& IW){ // Keunwoo Kim 07/24/2014 // Wayne Taylor 7/19/2016 corrected bug: replaced: // return (...*sum((V*IWi.diag()))); // with // mat VIWi = V*IWi; // return (...*sum((VIWi.diag()))); // Purpose: evaluate log-density of inverted Wishart with normalizing constant // Arguments: // nu is d. f. parm // V is location matrix // IW is the value at which the density should be evaluated // Note: in this parameterization, E[IW]=V/(nu-k-1) int k = V.n_cols; mat Uiw = chol(IW); mat Uiwi = solve(trimatu(Uiw), eye(k,k)); //trimatu interprets the matrix as upper triangular and makes solve more efficient mat IWi = Uiwi*trans(Uiwi); mat cholV = chol(V); double lndetVd2 = sum(log(cholV.diag())); double lndetIWd2 = sum(log(Uiw.diag())); // first evaluate constant double cnst = ((nu*k)/2)*log(2.0)+((k*(k-1))/4.0)*log(M_PI); // (k*(k-1))/4 is recognized as integer. "4.0" allows it to be recognized as a double. vec seq_1_k = cumsum(ones(k)); // build c(1:k) through cumsum function vec arg = (nu+1-seq_1_k)/2.0; // lgamma cannot receive arma::vec input. Compute cnst+sum(lgamma(arg)). for (int i=0; i0 e~N(0,1) // Prior: beta ~ N(betabar,A^-1) int mkeep; vec mu; vec z; int nvar = X.n_cols; mat betadraw(R/keep, nvar); if (nprint>0) startMcmcTimer(); //start main iteration loop for (int rep=0; rep0) if ((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; betadraw(mkeep-1, span::all) = trans(beta); } } if (nprint>0) endMcmcTimer(); return List::create(Named("betadraw") = betadraw); } bayesm/src/rhierMnlDP_rcpp_loop.cpp0000644000176000001440000003071313134410700017133 0ustar ripleyusers#include "bayesm.h" //FUNCTIONS SPECIFIC TO MAIN FUNCTION------------------------------------------------------ mat drawDelta(mat const& x,mat const& y,ivec const& z,std::vector const& comps_vector,vec const& deltabar,mat const& Ad){ // Wayne Taylor 2/21/2015 // delta = vec(D) // given z and comps (z[i] gives component indicator for the ith observation, // comps is a list of mu and rooti) // y is n x p // x is n x k // y = xD' + U , rows of U are indep with covs Sigma_i given by z and comps int p = y.n_cols; int k = x.n_cols; int ncomp = comps_vector.size(); mat xtx = zeros(k*p,k*p); mat xty = zeros(p,k); //this is the unvecced version, reshaped after the sum //Create the index vectors, the colAll vectors are equal to span::all but with uvecs (as required by .submat) uvec colAlly(p), colAllx(k); for(int i = 0; i0){ mat yi = y.submat(ind,colAlly); mat xi = x.submat(ind,colAllx); murooti compsi_struct = comps_vector[compi]; yi.each_row() -= trans(compsi_struct.mu); //the subtraction operation is repeated on each row of yi mat sigi = compsi_struct.rooti*trans(compsi_struct.rooti); xtx = xtx + kron(trans(xi)*xi,sigi); xty = xty + (sigi * (trans(yi)*xi)); } } xty.reshape(xty.n_rows*xty.n_cols,1); //vec(t(D)) ~ N(V^{-1}(xty + Ad*deltabar),V^{-1}) where V = (xtx+Ad) // compute the inverse of xtx+Ad mat ucholinv = solve(trimatu(chol(xtx+Ad)), eye(k*p,k*p)); //trimatu interprets the matrix as upper triangular and makes solve more efficient mat Vinv = ucholinv*trans(ucholinv); return(Vinv*(xty+Ad*deltabar) + trans(chol(Vinv))*as(rnorm(deltabar.size()))); } DPOut rDPGibbs1(mat y, lambda lambda_struct, std::vector thetaStar_vector, int maxuniq, ivec indic, vec q0v, double alpha, priorAlpha const& priorAlpha_struct, int gridsize, List const& lambda_hyper){ // Wayne Taylor 2/21/2015 //revision history: //created from rDPGibbs by Rossi 3/08 //do one draw of DP Gibbs sampler with normal base //Model: // y_i ~ N(y|thetai) // thetai|G ~ G // G|lambda,alpha ~ DP(G|G0(lambda),alpha) //Priors: // alpha: starting value // lambda: // G0 ~ N(mubar,Sigma (x) Amu^-1) // mubar=vec(mubar) // Sigma ~ IW(nu,nu*V) V=v*I note: mode(Sigma)=nu/(nu+2)*v*I // mubar=0 // amu is uniform on grid specified by alim // nu is log uniform, nu=d-1+exp(Z) z is uniform on seq defined bvy nulim // v is uniform on sequence specificd by vlim // priorAlpha_struct: // alpha ~ (1-(alpha-alphamin)/(alphamax-alphamin))^power // alphamin=exp(digamma(Istarmin)-log(gamma+log(N))) // alphamax=exp(digamma(Istarmax)-log(gamma+log(N))) // gamma= .5772156649015328606 //output: // ind - vector of indicators for which observations are associated with which comp in thetaStar // thetaStar - list of unique normal component parms // lambda - list of of (a,nu,V) // alpha // thetaNp1 - one draw from predictive given thetaStar, lambda,alphama int n = y.n_rows; int dimy = y.n_cols; int nunique, indsize, indp, probssize; vec probs; uvec ind; mat ydenmat; uvec spanall(dimy); for(int i = 0; i new_utheta_vector(1), thetaNp1_vector(1); murooti thetaNp10_struct, outGD_struct; for(int rep = 0; rep<1; rep++) { //note we only do one loop! q0v = q0(y,lambda_struct); nunique = thetaStar_vector.size(); if(nunique > maxuniq) stop("maximum number of unique thetas exceeded"); //ydenmat is a length(thetaStar) x n array of density values given f(y[j,] | thetaStar[[i]] // note: due to remix step (below) we must recompute ydenmat each time! ydenmat = zeros(maxuniq,n); ydenmat(span(0,nunique-1),span::all) = yden(thetaStar_vector,y); thetaStarDrawOut_struct = thetaStarDraw(indic, thetaStar_vector, y, ydenmat, q0v, alpha, lambda_struct, maxuniq); thetaStar_vector = thetaStarDrawOut_struct.thetaStar_vector; indic = thetaStarDrawOut_struct.indic; nunique = thetaStar_vector.size(); //thetaNp1 and remix probs = zeros(nunique+1); for(int j = 0; j < nunique; j++){ ind = find(indic == (j+1)); indsize = ind.size(); probs[j] = indsize/(alpha+n+0.0); new_utheta_vector[0] = thetaD(y(ind,spanall),lambda_struct); thetaStar_vector[j] = new_utheta_vector[0]; } probs[nunique] = alpha/(alpha+n+0.0); indp = rmultinomF(probs); probssize = probs.size(); if(indp == probssize) { outGD_struct = GD(lambda_struct); thetaNp10_struct.mu = outGD_struct.mu; thetaNp10_struct.rooti = outGD_struct.rooti; thetaNp1_vector[0] = thetaNp10_struct; } else { outGD_struct = thetaStar_vector[indp-1]; thetaNp10_struct.mu = outGD_struct.mu; thetaNp10_struct.rooti = outGD_struct.rooti; thetaNp1_vector[0] = thetaNp10_struct; } //draw alpha alpha = alphaD(priorAlpha_struct,nunique,gridsize); //draw lambda lambda_struct = lambdaD(lambda_struct,thetaStar_vector,lambda_hyper["alim"],lambda_hyper["nulim"],lambda_hyper["vlim"],gridsize); } //note indic is the vector of indicators for each obs correspond to which thetaStar DPOut out_struct; out_struct.thetaStar_vector = thetaStar_vector; out_struct.thetaNp1_vector = thetaNp1_vector; out_struct.alpha = alpha; out_struct.lambda_struct = lambda_struct; out_struct.indic = indic; return(out_struct); } //MAIN FUNCTION------------------------------------------------------------------------------------- //[[Rcpp::export]] List rhierMnlDP_rcpp_loop(int R, int keep, int nprint, List const& lgtdata, mat const& Z, vec const& deltabar, mat const& Ad, List const& PrioralphaList, List const& lambda_hyper, bool drawdelta, int nvar, mat oldbetas, double s, int maxuniq, int gridsize, double BayesmConstantA, int BayesmConstantnuInc, double BayesmConstantDPalpha){ // Wayne Taylor 2/21/2015 //Initialize variable placeholders int mkeep, Istar; vec betabar, q0v; mat rootpi, ucholinv, incroot, V; List compdraw(R/keep), nmix; DPOut mgout_struct; mnlMetropOnceOut metropout_struct; murooti thetaStarLgt_struct; int nz = Z.n_cols; int nlgt = lgtdata.size(); // convert List to std::vector of struct List lgtdatai; std::vector lgtdata_vector; moments lgtdatai_struct; for (int lgt = 0; lgt(lgtdatai["y"]); lgtdatai_struct.X = as(lgtdatai["X"]); lgtdatai_struct.hess = as(lgtdatai["hess"]); lgtdata_vector.push_back(lgtdatai_struct); } //initialize indicator vector, delta, thetaStar, thetaNp10, alpha, oldprob ivec indic = ones(nlgt); mat olddelta; if (drawdelta) olddelta = zeros(nz*nvar); std::vector thetaStar_vector(1); murooti thetaNp10_struct, thetaStar0_struct; thetaStar0_struct.mu = zeros(nvar); thetaStar0_struct.rooti = eye(nvar,nvar); thetaStar_vector[0] = thetaStar0_struct; double alpha = BayesmConstantDPalpha; //fix oldprob (only one comp) double oldprob = 1.0; //convert Prioralpha from List to struct priorAlpha priorAlpha_struct; priorAlpha_struct.power = PrioralphaList["power"]; priorAlpha_struct.alphamin = PrioralphaList["alphamin"]; priorAlpha_struct.alphamax = PrioralphaList["alphamax"]; priorAlpha_struct.n = PrioralphaList["n"]; //initialize lambda lambda lambda_struct; lambda_struct.mubar = zeros(nvar); lambda_struct.Amu = BayesmConstantA; lambda_struct.nu = nvar+BayesmConstantnuInc; lambda_struct.V = lambda_struct.nu*eye(nvar,nvar); //allocate space for draws mat Deltadraw(1,1); if(drawdelta) Deltadraw.zeros(R/keep, nz*nvar);//enlarge Deltadraw only if the space is required cube betadraw(nlgt, nvar, R/keep); vec probdraw = zeros(R/keep); vec oldll = zeros(nlgt); vec loglike = zeros(R/keep); vec Istardraw = zeros(R/keep); vec alphadraw = zeros(R/keep); vec nudraw = zeros(R/keep); vec vdraw = zeros(R/keep); vec adraw = zeros(R/keep); if (nprint>0) startMcmcTimer(); //start main iteration loop for(int rep = 0; rep0) if((rep+1)%nprint==0) infoMcmcTimer(rep, R); if((rep+1)%keep==0){ mkeep = (rep+1)/keep; betadraw.slice(mkeep-1) = oldbetas; probdraw[mkeep-1] = oldprob; alphadraw[mkeep-1] = alpha; Istardraw[mkeep-1] = Istar; adraw[mkeep-1] = lambda_struct.Amu; nudraw[mkeep-1] = lambda_struct.nu; V = lambda_struct.V; vdraw[mkeep-1] = V(0,0)/lambda_struct.nu; loglike[mkeep-1] = sum(oldll); if(drawdelta) Deltadraw(mkeep-1, span::all) = trans(vectorise(olddelta)); thetaNp10_struct = mgout_struct.thetaNp1_vector[0]; //we have to convert to a NumericVector for the plotting functions to work compdraw[mkeep-1] = List::create(List::create(Named("mu") = NumericVector(thetaNp10_struct.mu.begin(),thetaNp10_struct.mu.end()),Named("rooti") = thetaNp10_struct.rooti)); } } if (nprint>0) endMcmcTimer(); nmix = List::create(Named("probdraw") = probdraw, Named("zdraw") = R_NilValue, //sets the value to NULL in R Named("compdraw") = compdraw); if(drawdelta){ return(List::create( Named("Deltadraw") = Deltadraw, Named("betadraw") = betadraw, Named("nmix") = nmix, Named("alphadraw") = alphadraw, Named("Istardraw") = Istardraw, Named("adraw") = adraw, Named("nudraw") = nudraw, Named("vdraw") = vdraw, Named("loglike") = loglike)); } else { return(List::create( Named("betadraw") = betadraw, Named("nmix") = nmix, Named("alphadraw") = alphadraw, Named("Istardraw") = Istardraw, Named("adraw") = adraw, Named("nudraw") = nudraw, Named("vdraw") = vdraw, Named("loglike") = loglike)); } } bayesm/NAMESPACE0000644000176000001440000000273413114117322013002 0ustar ripleyusersuseDynLib(bayesm) importFrom(Rcpp, evalCpp) importFrom(utils, flush.console) importFrom(stats, acf, cov, dnbinom, dnorm, lm, median, optim, pnorm, qchisq, quantile, rmultinom, rnorm, runif, var) importFrom(graphics, abline, boxplot, bxp, contour, hist, image, lines, par, plot, plot.default, points, polygon, text, title) importFrom(grDevices, dev.interactive, devAskNewPage, terrain.colors) ## exportPattern("^[[:alpha:]]+") this line is automatically created when using package.skeleton but should be removed to prevent the _loop functions from exporting. Instead use the export() function (as is done here) export(breg,createX,eMixMargDen,mixDen,llmnl,llmnp,llnhlogit, lndIChisq,lndIWishart,lndMvn,lndMvst,mnlHess,momMix,nmat,numEff,rdirichlet, rmixture,rmultireg, rwishart,rmvst,rtrun,rbprobitGibbs,runireg, runiregGibbs,simnhlogit,rmnpGibbs,rmixGibbs,rnmixGibbs, rmvpGibbs,rhierLinearModel,rhierMnlRwMixture,rivGibbs, rmnlIndepMetrop,rscaleUsage,ghkvec,condMom,logMargDenNR, rhierBinLogit,rnegbinRw,rhierNegbinRw,rbiNormGibbs,clusterMix,rsurGibbs, mixDenBi,mnpProb,rhierLinearMixture, summary.bayesm.mat,summary.bayesm.nmix,summary.bayesm.var, plot.bayesm.mat,plot.bayesm.hcoef,plot.bayesm.nmix, rordprobitGibbs,rivGibbs,rivDP,rDPGibbs, rhierMnlDP,cgetC,rbayesBLP) ## register S3 methods S3method(plot, bayesm.mat) S3method(plot, bayesm.nmix) S3method(plot, bayesm.hcoef) S3method(summary, bayesm.mat) S3method(summary, bayesm.var) S3method(summary, bayesm.nmix) bayesm/data/0000755000176000001440000000000013114117322012466 5ustar ripleyusersbayesm/data/detailing.rda0000644000176000001440000010076412516003354015132 0ustar ripleyusersý7zXZi"Þ6!ÏXÌê|²¶])TW"änRÊŸ’Øáà[áß^ ·ÖnŒÍV6$iú«eË'ª‰d8Xïš«/8U£BS!Ì¥ ‚ªÞ› {/„/Þã‚VÄ^¶²¾@æ< ö¼CkpšJÚ.˜/RÀÃ̆„Ñ@s,«4<úwŸˆ èŽf:8ÜÇôˆºY‹‡•{'ó˜Åà¨î‹ **ä£2Ïq%_¯¨—¤!„3Êa5E5·Ö´ß×D7žnužïÿsÁ{uYØ kAÒ»åNœ©5E‚áÅ[Å[ꜹƒߢÜp/5&¬UPD•ã¯S·õæ„Ò|&,ê±+x÷ˆ°r‘ÓÀqª±û‚_ºSná->%YX[¢ ‚]»’Òž²™!uÓŠÑ‹,áp_•V ´ŸÔ§À!ò#¡áØ£œˆƒ@rÏÉ—a.f>c›Éߟ ÖýÊÍË ]¡º¹_ ñöA™{ørnE®}šÂŒÞ˜Ga7;ŽÿMY—C w]Eæø×)ÿo¹¶ûE¿éYžòÔÐ:DPb¦.¸ Y¤@›‰‚r¯A˜L½v‹FØvn ½ï™éƸá4×%Æ~Íž´ó ÿ_Û0˜f’#-¶‚rf¢ŽWô´3àÙõÖNG dü.î ûËCJ*M€¦ÀÎX½õä±R«Hv=OÑw’”@oK=í$2ð8¢¬zÃ[„Ý&R=,­8uáœo×0Òý&‰ÿ» ;ú®á£–Ó!†³G8¥öë–-8´Û%H ¨òˆ>„µ+ }–m'6—›>â!¸Ö¡£ÁûGv8E©ÿª‘Uð¨ÿÎè‚nÔÈvcC%¥þתœñ‰Â+ìiulìÀy€ú=ì!Eä” î¾(ðeßp~_âÐæÒ —âx²ÙjrËúÁ_›øw¨ûÑ×”‡ׇь=|X/À‘vp:˜,ª¿êï–;Œ^–k¥± ñŸ‹ÑSgX¯,¡Úí¸¡7‡ÝZ›_Ò½žÏv|RâQ+°ÃÄ#ØÌT¶?ékçAå­Ö3c×g²¬ÝFõ åkq{ë …6ehó’Ò1’Ù<Ý…?Zs;Çè“ÔC^Ö–$¬Ј@Åýn´¬N Ÿ̘«õÖ WÏÙ‰ßÅ&¨7ðч!œ~. <¬ï :‹B²/ß¶~Ç Š¢Àt ßéGÍÌñˆ¤ÕA<‚3HVI¬Õ•öKKÚÎ׉f’š½_!~cMRÍPðÆ•Ýí÷ôÕŒj] •pGöjK\Ž…‰z¬Ž“±ºÜÂJCºeƒ,|_ô='”YáoN2&ÆÀ± ñЦÅï&’xß$ù€o¹FË_[ðþä‰Ó,áxh½–és°”Scqת¶Ž [âmF pÆD½Îú1.!jã+œQ+ܰÁ­üNðUã‹ôíly`zΕ8æ;cZÒíK2®4»afô5¢Ü7Ü)cþT`!©I^@òŒÓbŸOÓ}êÚõ' úN@7<™7áRÔ¼:¯pÚ²Ø*´¯˜EýÎ?Q'•Ä^žxFÓ RcA:ÄóÐñQ¡‰¹c%¨f¨cÈ1¨KϸÏó†$…ÔÄtpU””°Ì^O]¼ƒ«m‚4ù@2ªCÍùoßÓb$™»²N›P"Ë´†“æÊÍEA*o œÛá¥Å®´ù€™’oó¦„êÐå¥Ë­›1¶t~DRRìüèFœSîyU—{Á«TtC5aP†¯®sÉri¦¸Ì]ZL(©þÇ[ÊQ)é¬1Pp êÞjÂÑÐ2ž«mæ` L\ñX´Gj#pyŠToòsKÇ:¨k¯!9Œ¡YUR®{ÁªÕ4ýííÔóñ«G{™a¹Ô¨ÖüÍNŸò5@™c“Y9·|JIv²7ÓX)£fÇ)dNN@Íy„ÛüM¼ ƒ1²{>sǤ!œûv;TŒ:¼²éÂp»w€ÿ•Ä‹ž5–@hU¾1~kqaÞºÀ{˜¬¿ïsÌ?x=vA½žj»Wtª\%üðu˜7¼ðòxÝ¿Žö?€îók:¾öWŒ¸Ã'0ïÕdžÜ…¤î÷q9t›yÐäüj9­2P!{Ùz¤þEa¥‹Emí ¸&õ«±ô+õãZ±:†™à[œ|¹æLlP1»ÿB¯â(Éc³évL_ì·Œ_tR¾ŸuyHаÆ(„µ}ìASÐñvXvl<ÙÜ$¤'ŒÓp¢;mMüwí;åxIòÏM-kçn/ãÙâ]úÑ'ƒÏ§â­É`þÅJ³˜íJè¡ÞÉØwx®ˆžMÆòùD¸G¹ ”oòн•…µÁײàÏ¡ñ¹ÀÇ À¨ƒ/óØ Æ–v·*68.D‚aà¶ß<6òIî_~ŸÙÙAh]´œ—K* ‘æz4ˆ¡ÝÚûNÇQ5¥”¸HA·“„ƒÃy4Ï9jðè¼iƒ)!N|öðÉ.¼fÁ>O`ñU­¹…D´#𢣫© Ùòîž°L.¶Ì›¡ jŒ£:UÌ6âŒáYôÁ<ÒÊ?Z))K q|(ãÒúD÷š"ÔHÆ € Êi78ßÚUkGõ$ÿ}}A£zo NZI鄚ˆ# W ôÞù ”KeR•3oOY•ûÌ”µ·Ïn ¼Ù'=§ÌnE~7®wÇ…p´ùûœðA3ã…èþÿ-C;`TÊù IÓ5E^¢— f}.‰Î…¤4æ œE´}Ò@ñϛߡ„Q?³uÕå{—Ã’õñégÌL·²|¿ûrcøçHƒÊ›ÊªðÏë|dKrϨ3G”ƒD„ڕꔫ:4*@ºfœÇob<°7ëRŽÈâ—flFÌé-7–¿q¶*)V£ù8ÁttÞ¦âY4ŸÅô8ü­'/¥…ÀŸrvycAV¿¼²o—¹Zÿ ÄmŸ¦ÏOÏŽmˆUíÊe"P›1mUžL*Vá\GwžYû,á„. tX¶9Pbì@Ë’€wžpk”m×çhi3ÑspüHŠÅLô^:{µÃÆŸâøfu•ÓcšU|aId A…Üç±¥iin6¨…Ÿ :yöaË]ȳ§‰681H»¬ÛØ«J} DCˆ.FëË/¸$ðéðtÞ>›ˆ€¨Ñ JëªÿԀηÙwøÄäÕç5·oÅó"žGÚ³[˜b€§¼|÷{î 8n¿¤è‚«bl…ø YBÖ4GÓÁ1Hpmr:2£€æ+ ÞûÉ}¾A[àå@°I«½]Ø\Ü0 £1®™åG}3=Xƻɭ™0zl‰½øvÍèò¼¼©÷¤Õô§+Ì¢`Þ^ 7?ò}• ×±H12Öñ<×>e­IéŽùqǶýýÒ/ÆgeäN*›7Žkp/Ý ñ‹D æGý‰ëÓ…Ñ Òç„L¨úÓ¸`g]‚81¤‘G[﹌ýŽLænÿâ°Õª Ù)FY¸‚ì 1,·Ô€ÙzVV¾MÛ€““£B˸³ÇVÄÈJ÷…a4K¶L”2³d§&¾§û[k BI¼L²í¸3#í“’@ÀEŒÉÒÅ]j¶ß=/£ÞœÓÏñ§”»§¹Êã±Ýµœ|5 ê p=¼¸¡Äæd«çý»Ý@G™DÀ‹k´/<ă"øÞ dÚõëp*P¡GÀ&ÅZ†ðãOñZ ÿ ®tâ ¢ f,ÝwG(T䛯eÝAlÁ%¬Ø¾#œÄ½IßB»>xAOjØ'ç)Ì>9¿€Ž÷ÁnèL:©Ì®²½z‹Û£‰ïDv®æY•*Lò|7ú;àl>ç»Õ³’Ø-k°}#£a$û½G&¯ÃovÈ2xû9=&zJãî|Ü>C¸7¾¨÷¬?,ã—ZÝÜ»EšÕµØg>|b ¾éášÒ»—z À½'S@wœ¹=Žî ªÓ§®wyjÜI\-„µB¢á±öc YɸuTFç7–ÊDqðÉ…ã3èÆÍíú*ATC•IÖ6~#õ¦\O ¸Çì‚ëÛˆï—Ög°^Ÿ©uŽhÐ÷zÑ„=I±ê߆ÙTv¸BÈXû­-!}ˆJTÙí[»ûk_ÅÒB¡F½¥‡¸qQ\»F_<—¸&å¾´‚ö:ü¤y1Ozr†Ëx¶Åø2ß®÷LÝB¸_—-òµ„8 *l¡ 01¹‚€¨ùÛDu·]Åé=ÍŽPmÍeñ%Î ri@Ÿt×ßßílJ P;}0uQ ¼¢•Ìãæ øJ>JsSðsiÞvO,x• @Èœ+t ¡7hnª 4ŸŠûýH)¿ù‰™¿{Þ@C/”ùDìó öÔ°9EwÎt¼rÏŘíÈ.èÍ_ÊÒ ½9Oàö?6B†žeÝÕ', U‚¤z`€o>Z¬•–€\,4U? 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Rossi 1/17/05 # 3/07 added classes # W. Taylor 4/15 - added nprint option to MCMC argument # Purpose: # perform Gibbs iterations for Univ Regression Model using # prior with beta, sigma-sq indep # # Arguments: # Data -- list of data # y,X # Prior -- list of prior hyperparameters # betabar,A prior mean, prior precision # nu, ssq prior on sigmasq # Mcmc -- list of MCMC parms # sigmasq=initial value for sigmasq # R number of draws # keep -- thinning parameter # nprint - print estimated time remaining on every nprint'th draw # # Output: # list of beta, sigmasq # # Model: # y = Xbeta + e e ~N(0,sigmasq) # y is n x 1 # X is n x k # beta is k x 1 vector of coefficients # # Priors: beta ~ N(betabar,A^-1) # sigmasq ~ (nu*ssq)/chisq_nu # # # check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of y and X")} if(is.null(Data$X)) {pandterm("Requires Data element X")} X=Data$X if(is.null(Data$y)) {pandterm("Requires Data element y")} y=Data$y nvar=ncol(X) nobs=length(y) # # check data for validity # if(nobs != nrow(X) ) {pandterm("length(y) ne nrow(X)")} # # check for Prior # if(missing(Prior)) { betabar=c(rep(0,nvar)); A=.01*diag(nvar); nu=3; ssq=var(y)} else { if(is.null(Prior$betabar)) {betabar=c(rep(0,nvar))} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=.01*diag(nvar)} else {A=Prior$A} if(is.null(Prior$nu)) {nu=3} else {nu=Prior$nu} if(is.null(Prior$ssq)) {ssq=var(y)} else {ssq=Prior$ssq} } # # check dimensions of Priors # if(ncol(A) != nrow(A) || ncol(A) != nvar || nrow(A) != nvar) {pandterm(paste("bad dimensions for A",dim(A)))} if(length(betabar) != nvar) {pandterm(paste("betabar wrong length, length= ",length(betabar)))} # # check MCMC argument # if(missing(Mcmc)) {pandterm("requires Mcmc argument")} else { if(is.null(Mcmc$R)) {pandterm("requires Mcmc element R")} else {R=Mcmc$R} if(is.null(Mcmc$keep)) {keep=1} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=100} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} if(is.null(Mcmc$sigmasq)) {sigmasq=var(y)} else {sigmasq=Mcmc$sigmasq} } # # print out problem # cat(" ", fill=TRUE) cat("Starting Gibbs Sampler for Univariate Regression Model",fill=TRUE) cat(" with ",nobs," observations",fill=TRUE) cat(" ", fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat("A",fill=TRUE) print(A) cat("nu = ",nu," ssq= ",ssq,fill=TRUE) cat(" ", fill=TRUE) cat("MCMC parms: ",fill=TRUE) cat("R= ",R," keep= ",keep," nprint= ",nprint,fill=TRUE) cat(" ",fill=TRUE) ################################################################### # Keunwoo Kim # 08/05/2014 ################################################################### draws = runiregGibbs_rcpp_loop(y, X, betabar, A, nu, ssq, sigmasq, R, keep, nprint) ################################################################### attributes(draws$betadraw)$class=c("bayesm.mat","mcmc") attributes(draws$betadraw)$mcpar=c(1,R,keep) attributes(draws$sigmasqdraw)$class=c("bayesm.mat","mcmc") attributes(draws$sigmasqdraw)$mcpar=c(1,R,keep) return(draws) } bayesm/R/nmat.R0000755000176000001440000000042710225356251013054 0ustar ripleyusersnmat=function(vec) { # # function to take var-cov matrix in vector form and create correlation matrix # and store in vector form # p=as.integer(sqrt(length(vec))) sigma=matrix(vec,ncol=p) nsig=1/sqrt(diag(sigma)) return(as.vector(nsig*(t(nsig*sigma)))) } bayesm/R/condMom.R0000755000176000001440000000117610227517711013515 0ustar ripleyuserscondMom= function(x,mu,sigi,i) { # # revision history: # rossi modified allenby code 4/05 # # purpose:compute moments of conditional distribution of ith element of normal given # all others # # arguments: # x: vector of values to condition on # mu: mean vector of length(x)-dim MVN # sigi: inverse of covariance matrix # i: element to condition on # # output: # list with conditional mean and variance # # Model: x ~MVN(mu,Sigma) # computes moments of x_i given x_{-1} # sig=1./sigi[i,i] m=mu[i] - as.vector(x[-i]-mu[-i])%*%as.vector(sigi[-i,i])*sig return(list(cmean=as.vector(m),cvar=sig)) } bayesm/R/runireg_rcpp.r0000644000176000001440000000673712566706215014674 0ustar ripleyusersrunireg= function(Data,Prior,Mcmc) { # # revision history: # P. Rossi 1/17/05 # revised 9/05 to put in Data,Prior,Mcmc calling convention # 3/07 added classes # W. Taylor 4/15 - added nprint option to MCMC argument # Purpose: # perform iid draws from posterior of regression model using # conjugate prior # # Arguments: # Data -- list of data # y,X # Prior -- list of prior hyperparameters # betabar,A prior mean, prior precision # nu, ssq prior on sigmasq # Mcmc -- list of MCMC parms # R number of draws # keep -- thinning parameter # nprint - print estimated time remaining on every nprint'th draw # # Output: # list of beta, sigmasq # # Model: # y = Xbeta + e e ~N(0,sigmasq) # y is n x 1 # X is n x k # beta is k x 1 vector of coefficients # # Priors: beta ~ N(betabar,sigmasq*A^-1) # sigmasq ~ (nu*ssq)/chisq_nu # # # check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of y and X")} if(is.null(Data$X)) {pandterm("Requires Data element X")} X=Data$X if(is.null(Data$y)) {pandterm("Requires Data element y")} y=Data$y nvar=ncol(X) nobs=length(y) # # check data for validity # if(nobs != nrow(X) ) {pandterm("length(y) ne nrow(X)")} # # check for Prior # if(missing(Prior)) { betabar=c(rep(0,nvar)); A=BayesmConstant.A*diag(nvar); nu=BayesmConstant.nu; ssq=var(y)} else { if(is.null(Prior$betabar)) {betabar=c(rep(0,nvar))} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=BayesmConstant.A*diag(nvar)} else {A=Prior$A} if(is.null(Prior$nu)) {nu=BayesmConstant.nu} else {nu=Prior$nu} if(is.null(Prior$ssq)) {ssq=var(y)} else {ssq=Prior$ssq} } # # check dimensions of Priors # if(ncol(A) != nrow(A) || ncol(A) != nvar || nrow(A) != nvar) {pandterm(paste("bad dimensions for A",dim(A)))} if(length(betabar) != nvar) {pandterm(paste("betabar wrong length, length= ",length(betabar)))} # # check MCMC argument # if(missing(Mcmc)) {pandterm("requires Mcmc argument")} else { if(is.null(Mcmc$R)) {pandterm("requires Mcmc element R")} else {R=Mcmc$R} if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} } # # print out problem # cat(" ", fill=TRUE) cat("Starting IID Sampler for Univariate Regression Model",fill=TRUE) cat(" with ",nobs," observations",fill=TRUE) cat(" ", fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat("A",fill=TRUE) print(A) cat("nu = ",nu," ssq= ",ssq,fill=TRUE) cat(" ", fill=TRUE) cat("MCMC parms: ",fill=TRUE) cat("R= ",R," keep= ",keep," nprint= ",nprint,fill=TRUE) cat(" ",fill=TRUE) ################################################################### # Keunwoo Kim # 08/05/2014 ################################################################### draws = runireg_rcpp_loop(y, X, betabar, A, nu, ssq, R, keep, nprint) ################################################################### attributes(draws$betadraw)$class=c("bayesm.mat","mcmc") attributes(draws$betadraw)$mcpar=c(1,R,keep) attributes(draws$sigmasqdraw)$class=c("bayesm.mat","mcmc") attributes(draws$sigmasqdraw)$mcpar=c(1,R,keep) return(draws) } bayesm/R/momMix.R0000755000176000001440000000413110307453451013360 0ustar ripleyusersmomMix= function(probdraw,compdraw) { # # Revision History: # R. McCulloch 11/04 # P. Rossi 3/05 put in backsolve fixed documentation # P. Rossi 9/05 fixed error in mom -- return var not sigma # # purpose: compute moments of normal mixture averaged over MCMC draws # # arguments: # probdraw -- ith row is ith draw of probabilities of mixture comp # compdraw -- list of lists of draws of mixture comp moments (each sublist is from mixgibbs) # # output: # a list with the mean vector, covar matrix, vector of std deve, and corr matrix # # ---------------------------------------------------------------------------------- # define function needed mom=function(prob,comps){ # purpose: obtain mu and cov from list of normal components # # arguments: # prob: vector of mixture probs # comps: list, each member is a list comp with ith normal component ~N(comp[[1]],Sigma), # Sigma = t(R)%*%R, R^{-1} = comp[[2]] # returns: # a list with [[1]]=$mu a vector # [[2]]=$sigma a matrix # nc = length(comps) dim = length(comps[[1]][[1]]) mu = double(dim) sigma = matrix(0.0,dim,dim) for(i in 1:nc) { mu = mu+ prob[i]*comps[[i]][[1]] } var=matrix(double(dim*dim),ncol=dim) for(i in 1:nc) { mui=comps[[i]][[1]] # root = solve(comps[[i]][[2]]) root=backsolve(comps[[i]][[2]],diag(rep(1,dim))) sigma=t(root)%*%root var=var+prob[i]*sigma+prob[i]*(mui-mu)%o%(mui-mu) } list(mu=mu,sigma=var) } #--------------------------------------------------------------------------------------- dim=length(compdraw[[1]][[1]][[1]]) nc=length(compdraw[[1]]) dim(probdraw)=c(length(compdraw),nc) mu=double(dim) sigma=matrix(double(dim*dim),ncol=dim) sd=double(dim) corr=matrix(double(dim*dim),ncol=dim) for(i in 1:length(compdraw)) { out=mom(probdraw[i,],compdraw[[i]]) sd=sd+sqrt(diag(out$sigma)) corr=corr+matrix(nmat(out$sigma),ncol=dim) mu=mu+out$mu sigma=sigma+out$sigma } mu=mu/length(compdraw) sigma=sigma/length(compdraw) sd=sd/length(compdraw) corr=corr/length(compdraw) return(list(mu=mu,sigma=sigma,sd=sd,corr=corr)) } bayesm/R/rnegbinrw_rcpp.r0000755000176000001440000001413713114117322015173 0ustar ripleyusersrnegbinRw=function(Data, Prior, Mcmc){ # Revision History # Sridhar Narayanan - 05/2005 # P. Rossi 6/05 # 3/07 added classes # Keunwoo Kim 11/2014 # 1. added "alphafix" argument # 2. corrected code in more clear way (in Cpp) # W. Taylor 4/15 - added nprint option to MCMC argument # # Model # (y|lambda,alpha) ~ Negative Binomial(Mean = lambda, Overdispersion par = alpha) # # ln(lambda) = X * beta # # Priors # beta ~ N(betabar, A^-1) # alpha ~ Gamma(a,b) where mean = a/b and variance = a/(b^2) # # Arguments # Data = list of y, X # e.g. regdata[[i]]=list(y=y,X=X) # X has nvar columns including a first column of ones # # Prior - list containing the prior parameters # betabar, A - mean of beta prior, inverse of variance covariance of beta prior # a, b - parameters of alpha prior # # Mcmc - list containing # R is number of draws # keep is thinning parameter (def = 1) # nprint - print estimated time remaining on every nprint'th draw (def = 100) # s_beta - scaling parameter for beta RW (def = 2.93/sqrt(nvar)) # s_alpha - scaling parameter for alpha RW (def = 2.93) # beta0 - initial guesses for parameters, if not supplied default values are used # alpha - value of alpha fixed. If it is given, draw only beta # # # Definitions of functions used within rhierNegbinRw # llnegbin = function(par,X,y, nvar) { # Computes the log-likelihood beta = par[1:nvar] alpha = exp(par[nvar+1])+1.0e-50 mean=exp(X%*%beta) prob=alpha/(alpha+mean) prob=ifelse(prob<1.0e-100,1.0e-100,prob) out=dnbinom(y,size=alpha,prob=prob,log=TRUE) return(sum(out)) } # # Error Checking # if(missing(Data)) {pandterm("Requires Data argument -- list of X and y")} if(is.null(Data$X)) {pandterm("Requires Data element X")} else {X=Data$X} if(is.null(Data$y)) {pandterm("Requires Data element y")} else {y=Data$y} nvar = ncol(X) if (length(y) != nrow(X)) {pandterm("Mismatch in the number of observations in X and y")} nobs=length(y) # # check for prior elements # if(missing(Prior)) { betabar=rep(0,nvar); A=BayesmConstant.A*diag(nvar) ; a=BayesmConstant.agammaprior; b=BayesmConstant.bgammaprior; } else { if(is.null(Prior$betabar)) {betabar=rep(0,nvar)} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=BayesmConstant.A*diag(nvar)} else {A=Prior$A} if(is.null(Prior$a)) {a=BayesmConstant.agammaprior} else {a=Prior$a} if(is.null(Prior$b)) {b=BayesmConstant.bgammaprior} else {b=Prior$b} } if(length(betabar) != nvar) pandterm("betabar is of incorrect dimension") if(sum(dim(A)==c(nvar,nvar)) != 2) pandterm("A is of incorrect dimension") if((length(a) != 1) | (a <=0)) pandterm("a should be a positive number") if((length(b) != 1) | (b <=0)) pandterm("b should be a positive number") # # check for Mcmc # if(missing(Mcmc)) pandterm("Requires Mcmc argument -- at least R") if(is.null(Mcmc$R)) {pandterm("Requires element R of Mcmc")} else {R=Mcmc$R} if(is.null(Mcmc$beta0)) {beta0=rep(0,nvar)} else {beta0=Mcmc$beta0} if(length(beta0) !=nvar) pandterm("beta0 is not of dimension nvar") if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} if(is.null(Mcmc$s_alpha)) {cat("Using default s_alpha = 2.93",fill=TRUE); s_alpha=BayesmConstant.RRScaling} else {s_alpha = Mcmc$s_alpha} if(is.null(Mcmc$s_beta)) {cat("Using default s_beta = 2.93/sqrt(nvar)",fill=TRUE); s_beta=BayesmConstant.RRScaling/sqrt(nvar)} else {s_beta = Mcmc$s_beta} # Keunwoo Kim 11/2014 ############################################# if(is.null(Mcmc$alpha)) {fixalpha=FALSE} else {fixalpha=TRUE; alpha=Mcmc$alpha} if(fixalpha & alpha<=0) pandterm("alpha is not positive") ################################################################### # # print out problem # cat(" ",fill=TRUE) cat("Starting Random Walk Metropolis Sampler for Negative Binomial Regression",fill=TRUE) cat(" ",nobs," obs; ",nvar," covariates (including intercept); ",fill=TRUE) cat("Prior Parameters:",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat("A",fill=TRUE) print(A) if (!fixalpha) { cat("a",fill=TRUE) print(a) cat("b",fill=TRUE) print(b) } cat(" ",fill=TRUE) cat("MCMC Parms: ",fill=TRUE) cat("R= ",R," keep= ",keep," nprint= ",nprint,fill=TRUE) cat("s_alpha = ",s_alpha,fill=TRUE) cat("s_beta = ",s_beta,fill=TRUE) if (fixalpha) { cat("alpha",fill=TRUE) print(alpha) } cat(" ",fill=TRUE) par = rep(0,(nvar+1)) cat(" Initializing RW Increment Covariance Matrix...",fill=TRUE) fsh() mle = optim(par,llnegbin, X=X, y=y, nvar=nvar, method="L-BFGS-B", upper=c(Inf,Inf,Inf,log(100000000)), hessian=TRUE, control=list(fnscale=-1)) fsh() beta_mle=mle$par[1:nvar] alpha_mle = exp(mle$par[nvar+1]) varcovinv = -mle$hessian beta = beta0 betacvar = s_beta*solve(varcovinv[1:nvar,1:nvar]) betaroot = t(chol(betacvar)) if(!fixalpha) {alpha = alpha_mle} alphacvar = s_alpha/varcovinv[nvar+1,nvar+1] alphacroot = sqrt(alphacvar) cat("beta_mle = ",beta_mle,fill=TRUE) cat("alpha_mle = ",alpha_mle, fill = TRUE) fsh() ################################################################### # Keunwoo Kim # 09/03/2014 ################################################################### if (fixalpha) {alpha=Mcmc$alpha} draws=rnegbinRw_rcpp_loop(y, X, betabar, chol(A), a, b, beta, alpha, fixalpha, betaroot, alphacroot, R, keep, nprint) ################################################################### attributes(draws$betadraw)$class=c("bayesm.mat","mcmc") attributes(draws$betadraw)$mcpar=c(1,R,keep) attributes(draws$alphadraw)$class=c("bayesm.mat","mcmc") attributes(draws$alphadraw)$mcpar=c(1,R,keep) return(list(betadraw=draws$betadraw,alphadraw=draws$alphadraw, acceptrbeta=draws$nacceptbeta/R*keep,acceptralpha=draws$nacceptalpha/R*keep)) } bayesm/R/simnhlogit.R0000755000176000001440000000241612524673031014274 0ustar ripleyuserssimnhlogit=function(theta,lnprices,Xexpend) { # function to simulate non-homothetic logit model # creates y a n x 1 vector with indicator of choice (1,...,m) # lnprices is n x m array of log-prices faced # Xexpend is n x d array of variables predicting expenditure # # non-homothetic model specifies ln(psi_i(u))= alpha_i - exp(k_i)u # # structure of theta vector: # alpha (m x 1) # k (m x1 ) # gamma (k x 1) expenditure function coefficients # tau -- scaling of v # m=ncol(lnprices) n=nrow(lnprices) d=ncol(Xexpend) alpha=theta[1:m] k=theta[(m+1):(2*m)] gamma=theta[(2*m+1):(2*m+d)] tau=theta[length(theta)] iotam=c(rep(1,m)) c1=as.vector(Xexpend%*%gamma)%x%iotam-as.vector(t(lnprices))+alpha c2=c(rep(exp(k),n)) u=callroot(c1,c2,.0000001,20) v=alpha - u*exp(k)-as.vector(t(lnprices)) vmat=matrix(v,ncol=m,byrow=TRUE) vmat=tau*vmat Prob=exp(vmat) denom=Prob%*%iotam Prob=Prob/as.vector(denom) # draw y y=vector("double",n) ind=1:m for (i in 1:n) { yvec=rmultinom(1,1,Prob[i,]) y[i]=ind%*%yvec } return(list(y=y,Xexpend=Xexpend,lnprices=lnprices,theta=theta,prob=Prob)) }bayesm/R/llmnp.R0000755000176000001440000000541713114117322013235 0ustar ripleyusersllmnp= function(beta,Sigma,X,y,r) { # # revision history: # edited by rossi 2/8/05 # adde 1.0e-50 before taking log to avoid -Inf 6/05 # changed order of arguments to put beta first 9/05 # # purpose: # function to evaluate MNP likelihood using GHK # # arguments: # X is n*(p-1) x k array of covariates (including intercepts) # note: X is from the "differenced" system # y is vector of n indicators of multinomial response # beta is k x 1 with k = ncol(X) # Sigma is p-1 x p-1 # r is the number of random draws to use in GHK # # output -- value of log-likelihood # for each observation w = Xbeta + e e ~N(0,Sigma) # if y=j (j max(w_-j) and w_j >0 # if y=p, w < 0 # # to use GHK we must transform so that these are rectangular regions # e.g. if y=1, w_1 > 0 and w_1 - w_-1 > 0 # # define Aj such that if j=1,..,p-1, Ajw = Ajmu + Aje > 0 is equivalent to y=j # implies Aje > -Ajmu # lower truncation is -Ajmu and cov = AjSigma t(Aj) # # for p, e < - mu # #################################################################################### # 08/2016 # Keunwoo Kim # We do not use this anymore, do call directly from rcpp ghkvec function. # # # # define functions needed # # # ghkvec = function(L,trunpt,above,r){ # dim=length(above) # n=length(trunpt)/dim # .C('ghk_vec',as.integer(n),as.double(L),as.double(trunpt),as.integer(above),as.integer(dim), # as.integer(r),res=double(n))$res} #################################################################################### # # compute means for each observation # pm1=ncol(Sigma) k=length(beta) mu=matrix(X%*%beta,nrow=pm1) logl=0.0 above=rep(0,pm1) for (j in 1:pm1) { muj=mu[,y==j] Aj=-diag(pm1) Aj[,j]=rep(1,pm1) trunpt=as.vector(-Aj%*%muj) Lj=t(chol(Aj%*%Sigma%*%t(Aj))) # note: rob's routine expects lower triangular root #################################################################################### # 08/2016 # Keunwoo Kim # now refers rcpp version directly. #logl=logl + sum(log(ghkvec(Lj,trunpt,above,r)+1.0e-50)) logl=logl + sum(log(ghkvec(Lj,trunpt,above,r,HALTON=FALSE,0)+1.0e-50)) #################################################################################### # note: ghkvec does an entire vector of n probs each with different truncation points but the # same cov matrix. } # # now do obs for y=p # trunpt=as.vector(-mu[,y==(pm1+1)]) Lj=t(chol(Sigma)) above=rep(1,pm1) #################################################################################### # 08/2016 # Keunwoo Kim # now refers rcpp version directly. #logl=logl + sum(log(ghkvec(Lj,trunpt,above,r)+1.0e-50)) logl=logl + sum(log(ghkvec(Lj,trunpt,above,r,HALTON=FALSE,0)+1.0e-50)) #################################################################################### return(logl) } bayesm/R/rordprobitgibbs_rcpp.r0000755000176000001440000001404212566706215016405 0ustar ripleyusersrordprobitGibbs=function(Data,Prior,Mcmc){ # # revision history: # 3/07 Hsiu-Wen Liu # 3/07 fixed naming of dstardraw rossi # # purpose: # draw from posterior for ordered probit using Gibbs Sampler # and metropolis RW # # Arguments: # Data - list of X,y,k # X is nobs x nvar, y is nobs vector of 1,2,.,k (ordinal variable) # Prior - list of A, betabar # A is nvar x nvar prior preci matrix # betabar is nvar x 1 prior mean # Ad is ndstar x ndstar prior preci matrix of dstar (ncut is number of cut-offs being estimated) # dstarbar is ndstar x 1 prior mean of dstar # Mcmc # R is number of draws # keep is thinning parameter # nprint - print estimated time remaining on every nprint'th draw # s is scale parameter of random work Metropolis # # Output: # list of betadraws and cutdraws # # Model: # z=Xbeta + e < 0 e ~N(0,1) # y=1,..,k, if z~c(c[k], c[k+1]) # # cutoffs = c[1],..,c[k+1] # dstar = dstar[1],dstar[k-2] # set c[1]=-100, c[2]=0, ...,c[k+1]=100 # # c[3]=exp(dstar[1]),c[4]=c[3]+exp(dstar[2]),..., # c[k]=c[k-1]+exp(datsr[k-2]) # # Note: 1. length of dstar = length of cutoffs - 3 # 2. Be careful in assessing prior parameter, Ad. .1 is too small for many applications. # # Prior: beta ~ N(betabar,A^-1) # dstar ~ N(dstarbar, Ad^-1) # # # ---------------------------------------------------------------------- # define functions needed # dstartoc is a fuction to transfer dstar to its cut-off value dstartoc=function(dstar) {c(-100, 0, cumsum(exp(dstar)), 100)} # compute conditional likelihood of data given cut-offs # lldstar=function(dstar,y,mu){ gamma=dstartoc(dstar) arg = pnorm(gamma[y+1]-mu)-pnorm(gamma[y]-mu) epsilon=1.0e-50 arg=ifelse(arg < epsilon,epsilon,arg) return(sum(log(arg))) } # # ---------------------------------------------------------------------- # # check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of y and X")} if(is.null(Data$X)) {pandterm("Requires Data element X")} X=Data$X if(is.null(Data$y)) {pandterm("Requires Data element y")} y=Data$y if(is.null(Data$k)) {pandterm("Requires Data element k")} k=Data$k nvar=ncol(X) nobs=length(y) ndstar = k-2 # number of dstar being estimated ncuts = k+1 # number of cut-offs (including zero and two ends) ncut = ncuts-3 # number of cut-offs being estimated c[1]=-100, c[2]=0, c[k+1]=100 # # check data for validity # if(length(y) != nrow(X) ) {pandterm("y and X not of same row dim")} if( sum(unique(y) %in% (1:k) ) < length(unique(y)) ) {pandterm("some value of y is not vaild")} # # check for Prior # if(missing(Prior)) { betabar=c(rep(0,nvar)); A=BayesmConstant.A*diag(nvar); Ad=diag(ndstar); dstarbar=c(rep(0,ndstar))} else { if(is.null(Prior$betabar)) {betabar=c(rep(0,nvar))} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=BayesmConstant.A*diag(nvar)} else {A=Prior$A} if(is.null(Prior$Ad)) {Ad=diag(ndstar)} else {Ad=Prior$Ad} if(is.null(Prior$dstarbar)) {dstarbar=c(rep(0,ndstar))} else {dstarbar=Prior$dstarbar} } # # check dimensions of Priors # if(ncol(A) != nrow(A) || ncol(A) != nvar || nrow(A) != nvar) {pandterm(paste("bad dimensions for A",dim(A)))} if(length(betabar) != nvar) {pandterm(paste("betabar wrong length, length= ",length(betabar)))} if(ncol(Ad) != nrow(Ad) || ncol(Ad) != ndstar || nrow(Ad) != ndstar) {pandterm(paste("bad dimensions for Ad",dim(Ad)))} if(length(dstarbar) != ndstar) {pandterm(paste("dstarbar wrong length, length= ",length(dstarbar)))} # # check MCMC argument # if(missing(Mcmc)) {pandterm("requires Mcmc argument")} else { if(is.null(Mcmc$R)) {pandterm("requires Mcmc element R")} else {R=Mcmc$R} if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} if(is.null(Mcmc$s)) {s=BayesmConstant.RRScaling/sqrt(ndstar)} else {s=Mcmc$s} } # # print out problem # cat(" ", fill=TRUE) cat("Starting Gibbs Sampler for Ordered Probit Model",fill=TRUE) cat(" with ",nobs,"observations",fill=TRUE) cat(" ", fill=TRUE) cat("Table of y values",fill=TRUE) print(table(y)) cat(" ",fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat(" ", fill=TRUE) cat("A",fill=TRUE) print(A) cat(" ", fill=TRUE) cat("dstarbar",fill=TRUE) print(dstarbar) cat(" ", fill=TRUE) cat("Ad",fill=TRUE) print(Ad) cat(" ", fill=TRUE) cat("MCMC parms: ",fill=TRUE) cat("R= ",R," keep= ",keep," nprint= ",nprint,"s= ",s, fill=TRUE) cat(" ",fill=TRUE) # use (-Hessian+Ad)^(-1) evaluated at betahat as the basis of the # covariance matrix for the random walk Metropolis increments betahat = chol2inv(chol(crossprod(X,X)))%*% crossprod(X,y) dstarini = c(cumsum(c( rep(0.1, ndstar)))) # set initial value for dstar dstarout = optim(dstarini, lldstar, method = "BFGS", hessian=T, control = list(fnscale = -1,maxit=500, reltol = 1e-06, trace=0), mu=X%*%betahat, y=y) inc.root=chol(chol2inv(chol((-dstarout$hessian+Ad)))) # chol((H+Ad)^-1) ################################################################### # Keunwoo Kim # 08/20/2014 ################################################################### draws=rordprobitGibbs_rcpp_loop(y,X,k,A,betabar,Ad,s,inc.root,dstarbar,betahat,R,keep,nprint) ################################################################### draws$cutdraw=draws$cutdraw[,2:k] attributes(draws$cutdraw)$class="bayesm.mat" attributes(draws$betadraw)$class="bayesm.mat" attributes(draws$dstardraw)$class="bayesm.mat" attributes(draws$cutdraw)$mcpar=c(1,R,keep) attributes(draws$betadraw)$mcpar=c(1,R,keep) attributes(draws$dstardraw)$mcpar=c(1,R,keep) return(draws) } bayesm/R/rhiernegbinrw_rcpp.r0000644000176000001440000002316313117541521016044 0ustar ripleyusersrhierNegbinRw= function(Data, Prior, Mcmc) { # Revision History # Sridhar Narayanan - 05/2005 # P. Rossi 6/05 # fixed error with nobs not specified and changed llnegbinFract 9/05 # 3/07 added classes # 3/08 fixed fractional likelihood # W. Taylor 4/15 - added nprint option to MCMC argument # # Model # (y_i|lambda_i,alpha) ~ Negative Binomial(Mean = lambda_i, Overdispersion par = alpha) # # ln(lambda_i) = X_i * beta_i # # beta_i = Delta'*z_i + nu_i # nu_i~N(0,Vbeta) # # Priors # vec(Delta|Vbeta) ~ N(vec(Deltabar), Vbeta (x) (Adelta^-1)) # Vbeta ~ Inv Wishart(nu, V) # alpha ~ Gamma(a,b) where mean = a/b and variance = a/(b^2) # # Arguments # Data = list of regdata,Z # regdata is a list of lists each list with members y, X # e.g. regdata[[i]]=list(y=y,X=X) # X has nvar columns including a first column of ones # Z is nreg=length(regdata) x nz with a first column of ones # # Prior - list containing the prior parameters # Deltabar, Adelta - mean of Delta prior, inverse of variance covariance of Delta prior # nu, V - parameters of Vbeta prior # a, b - parameters of alpha prior # # Mcmc - list containing # R is number of draws # keep is thinning parameter (def = 1) # nprint - print estimated time remaining on every nprint'th draw (def = 100) # s_beta - scaling parameter for beta RW (def = 2.93/sqrt(nvar)) # s_alpha - scaling parameter for alpha RW (def = 2.93) # w - fractional weighting parameter (def = .1) # Vbeta0, Delta0 - initial guesses for parameters, if not supplied default values are used # alpha - value of alpha fixed. If it is given, draw only beta # # Definitions of functions used within rhierNegbinRw (but outside of Rcpp loop) # llnegbinR = function(par,X,y, nvar) { # Computes the log-likelihood beta = par[1:nvar] alpha = exp(par[nvar+1])+1.0e-50 mean=exp(X%*%beta) prob=alpha/(alpha+mean) prob=ifelse(prob<1.0e-100,1.0e-100,prob) out=dnbinom(y,size=alpha,prob=prob,log=TRUE) return(sum(out)) } llnegbinFract = function(par,X,y,Xpooled, ypooled, w,wgt, nvar,lnalpha) { # Computes the fractional log-likelihood at the unit level theta = c(par,lnalpha) (1-w)*llnegbinR(theta,X,y,nvar) + w*wgt*llnegbinR(theta,Xpooled,ypooled, nvar) } # # Error Checking # if(missing(Data)) {pandterm("Requires Data argument -- list of regdata and (possibly) Z")} if(is.null(Data$regdata)) { pandterm("Requires Data element regdata -- list of data for each unit : y and X") } regdata=Data$regdata nreg = length(regdata) if (is.null(Data$Z)) { cat("Z not specified - using a column of ones instead", fill = TRUE) Z = matrix(rep(1,nreg),ncol=1) } else { if (!is.matrix(Data$Z)) { pandterm("Z must be a matrix") } else { if (nrow(Data$Z) != nreg) { pandterm(paste("Nrow(Z) ", nrow(Z), "ne number units ",nreg)) } else { Z = Data$Z } } } nz = ncol(Z) for (i in 1:nreg) { if(!is.matrix(regdata[[i]]$X)) {pandterm(paste0("regdata[[",i,"]]$X must be a matrix"))} if(!is.vector(regdata[[i]]$y, mode = "numeric") & !is.vector(regdata[[i]]$y, mode = "logical") & !is.matrix(regdata[[i]]$y)) {pandterm(paste0("regdata[[",i,"]]$y must be a numeric or logical vector or matrix"))} if(is.matrix(regdata[[i]]$y)) { if(ncol(regdata[[i]]$y)>1) {pandterm(paste0("regdata[[",i,"]]$y must be a vector or one-column matrix"))}} } dimfun = function(l) { c(length(l$y),dim(l$X)) } dims=sapply(regdata,dimfun) dims = t(dims) nvar = quantile(dims[,3],prob=0.5) for (i in 1:nreg) { if (dims[i, 1] != dims[i, 2] || dims[i, 3] != nvar) { pandterm(paste("Bad Data dimensions for unit", i, "dims(y,X) =", dims[i, ])) } } ypooled = NULL Xpooled = NULL for (i in 1:nreg) { ypooled = c(ypooled,regdata[[i]]$y) Xpooled = rbind(Xpooled,regdata[[i]]$X) } nobs= length(ypooled) nvar=ncol(Xpooled) # # check for prior elements # if(missing(Prior)) { Deltabar=matrix(rep(0,nvar*nz),nrow=nz) ; Adelta=BayesmConstant.A*diag(nz) ; nu=nvar+BayesmConstant.nuInc; V=nu*diag(nvar); a=0.5; b=0.1; } else { if(is.null(Prior$Deltabar)) {Deltabar=matrix(rep(0,nvar*nz),nrow=nz)} else {Deltabar=Prior$Deltabar} if(is.null(Prior$Adelta)) {Adelta=BayesmConstant.A*diag(nz)} else {Adelta=Prior$Adelta} if(is.null(Prior$nu)) {nu=nvar+BayesmConstant.nuInc} else {nu=Prior$nu} if(is.null(Prior$V)) {V=nu*diag(nvar)} else {V=Prior$V} if(is.null(Prior$a)) {a=BayesmConstant.agammaprior} else {a=Prior$a} if(is.null(Prior$b)) {b=BayesmConstant.bgammaprior} else {b=Prior$b} } if(sum(dim(Deltabar) == c(nz,nvar)) != 2) pandterm("Deltabar is of incorrect dimension") if(sum(dim(Adelta)==c(nz,nz)) != 2) pandterm("Adelta is of incorrect dimension") if(nu < nvar) pandterm("invalid nu value") if(sum(dim(V)==c(nvar,nvar)) != 2) pandterm("V is of incorrect dimension") if((length(a) != 1) | (a <=0)) pandterm("a should be a positive number") if((length(b) != 1) | (b <=0)) pandterm("b should be a positive number") # # check for Mcmc # if(missing(Mcmc)) pandterm("Requires Mcmc argument -- at least R") if(is.null(Mcmc$R)) {pandterm("Requires element R of Mcmc")} else {R=Mcmc$R} if(is.null(Mcmc$Vbeta0)) {Vbeta0=diag(nvar)} else {Vbeta0=Mcmc$Vbeta0} if(sum(dim(Vbeta0) == c(nvar,nvar)) !=2) pandterm("Vbeta0 is not of dimension nvar") if(is.null(Mcmc$Delta0)) {Delta0=matrix(rep(0,nz*nvar),nrow=nz)} else {Delta0=Mcmc$Delta0} if(sum(dim(Delta0) == c(nz,nvar)) !=2) pandterm("Delta0 is not of dimension nvar by nz") if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} if(is.null(Mcmc$s_alpha)) { s_alpha=BayesmConstant.RRScaling} else {s_alpha= Mcmc$s_alpha } if(is.null(Mcmc$s_beta)) { s_beta=BayesmConstant.RRScaling/sqrt(nvar)} else {s_beta=Mcmc$s_beta } if(is.null(Mcmc$w)) { w=BayesmConstant.w} else {w = Mcmc$w} # Wayne Taylor 12/2014 ############################################# if(is.null(Mcmc$alpha)) {fixalpha=FALSE} else {fixalpha=TRUE; alpha=Mcmc$alpha} if(fixalpha & alpha<=0) pandterm("alpha is not positive") ################################################################### # print out problem # cat(" ",fill=TRUE) cat("Starting Random Walk Metropolis Sampler for Hierarchical Negative Binomial Regression",fill=TRUE) cat(" ",nobs," obs; ",nvar," covariates (including the intercept); ",fill=TRUE) cat(" ",nz," individual characteristics (including the intercept) ",fill=TRUE) cat(" ",fill=TRUE) cat("Prior Parameters:",fill=TRUE) cat("Deltabar",fill=TRUE) print(Deltabar) cat("Adelta",fill=TRUE) print(Adelta) cat("nu",fill=TRUE) print(nu) cat("V",fill=TRUE) print(V) if (!fixalpha) { cat("a",fill=TRUE) print(a) cat("b",fill=TRUE) print(b) } cat(" ",fill=TRUE) cat("MCMC Parameters:",fill=TRUE) cat("R= ",R," keep= ",keep," nprint= ",nprint,fill=TRUE) cat("s_alpha = ",s_alpha,fill=TRUE) cat("s_beta = ",s_beta,fill=TRUE) if (fixalpha) { cat("alpha",fill=TRUE) print(alpha) } cat("Fractional Likelihood Weight Parameter = ",w,fill=TRUE) cat(" ",fill=TRUE) par = rep(0,(nvar+1)) cat("initializing Metropolis candidate densities for ",nreg,"units ...",fill=TRUE) fsh() mle = optim(par,llnegbinR, X=Xpooled, y=ypooled, nvar=nvar, method="L-BFGS-B", upper=c(Inf,Inf,Inf,log(100000000)), hessian=TRUE, control=list(fnscale=-1)) fsh() beta_mle=mle$par[1:nvar] alpha_mle = exp(mle$par[nvar+1]) varcovinv = -mle$hessian Delta = Delta0 Beta = t(matrix(rep(beta_mle,nreg),ncol=nreg)) Vbetainv = chol2inv(chol(Vbeta0)) #Wayne: replaced "solve" function Vbeta = Vbeta0 if(!fixalpha) {alpha = alpha_mle} #Dan (7/16): add "if(!fixalpha)" alphacvar = s_alpha/varcovinv[nvar+1,nvar+1] alphacroot = sqrt(alphacvar) cat("beta_mle = ",beta_mle,fill=TRUE) cat("alpha_mle = ",alpha_mle, fill = TRUE) fsh() hess_i=NULL if(nobs > 1000){ sind=sample(c(1:nobs),size=1000) ypooleds=ypooled[sind] Xpooleds=Xpooled[sind,] } else{ ypooleds=ypooled Xpooleds=Xpooled } # Find the individual candidate hessian for (i in 1:nreg) { wgt = length(regdata[[i]]$y)/length(ypooleds) mle2 = optim(mle$par[1:nvar],llnegbinFract, X=regdata[[i]]$X, y=regdata[[i]]$y, Xpooled=Xpooleds, ypooled=ypooleds, w=w,wgt=wgt, nvar=nvar, lnalpha=mle$par[nvar+1], method="BFGS", hessian=TRUE, control=list(fnscale=-1, trace=0,reltol=1e-6)) if (mle2$convergence==0) hess_i[[i]] = list(hess=-mle2$hessian) else hess_i[[i]] = diag(rep(1,nvar)) if(i%%50 ==0) cat(" completed unit #",i,fill=TRUE) fsh() } ################################################################### # Wayne Taylor # 12/01/2014 ################################################################### if (fixalpha) {alpha=Mcmc$alpha} rootA = chol(Vbetainv) draws=rhierNegbinRw_rcpp_loop(regdata, hess_i, Z, Beta, Delta, Deltabar, Adelta, nu, V, a, b, R, keep, s_beta, alphacroot, 1000, rootA, alpha, fixalpha) ################################################################### attributes(draws$alphadraw)$class=c("bayesm.mat","mcmc") attributes(draws$alphadraw)$mcpar=c(1,R,keep) attributes(draws$Deltadraw)$class=c("bayesm.mat","mcmc") attributes(draws$Deltadraw)$mcpar=c(1,R,keep) attributes(draws$Vbetadraw)$class=c("bayesm.var","bayesm.mat","mcmc") attributes(draws$Vbetadraw)$mcpar=c(1,R,keep) attributes(draws$Betadraw)$class=c("bayesm.hcoef") return(draws) }bayesm/R/mixDenBi.R0000755000176000001440000000426610545276104013624 0ustar ripleyusersmixDenBi= function(i,j,xi,xj,pvec,comps) { # Revision History: # P. Rossi 6/05 # vectorized evaluation of bi-variate normal density 12/06 # # purpose: compute marg bivariate density implied by mixture of multivariate normals specified # by pvec,comps # # arguments: # i,j: index of two variables # xi specifies a grid of points for var i # xj specifies a grid of points for var j # pvec: prior probabilities of normal components # comps: list, each member is a list comp with ith normal component ~ N(comp[[1]],Sigma), # Sigma = t(R)%*%R, R^{-1} = comp[[2]] # Output: # matrix with values of density on grid # # --------------------------------------------------------------------------------------------- # define function needed # bivcomps=function(i,j,comps) { # purpose: obtain marginal means and standard deviations from list of normal components # arguments: # i,j: index of elements for bivariate marginal # comps: list, each member is a list comp with ith normal component ~N(comp[[1]],Sigma), # Sigma = t(R)%*%R, R^{-1} = comp[[2]] # returns: # a list with relevant mean vectors and rooti for each compenent # [[2]]=$sigma a matrix whose ith row is the standard deviations for the ith component # result=NULL nc = length(comps) dim = length(comps[[1]][[1]]) ind=matrix(c(i,j,i,j,i,i,j,j),ncol=2) for(comp in 1:nc) { mu = comps[[comp]][[1]][c(i,j)] root= backsolve(comps[[comp]][[2]],diag(dim)) Sigma=crossprod(root) sigma=matrix(Sigma[ind],ncol=2) rooti=backsolve(chol(sigma),diag(2)) result[[comp]]=list(mu=mu,rooti=rooti) } return(result) } # ---------------------------------------------------------------------------------------------- nc = length(comps) marmoms=bivcomps(i,j,comps) ngridxi=length(xi); ngridxj=length(xj) z=cbind(rep(xi,ngridxj),rep(xj,each=ngridxi)) den = matrix(0.0,nrow=ngridxi,ncol=ngridxj) for(comp in 1:nc) { quads=colSums((crossprod(marmoms[[comp]]$rooti,(t(z)-marmoms[[comp]]$mu)))^2) dencomp=exp(-(2/2)*log(2*pi)+sum(log(diag(marmoms[[comp]]$rooti)))-.5*quads) dim(dencomp)=c(ngridxi,ngridxj) den=den+dencomp*pvec[comp] } return(den) } bayesm/R/createX.R0000755000176000001440000000513412566706215013521 0ustar ripleyuserscreateX= function(p,na,nd,Xa,Xd,INT=TRUE,DIFF=FALSE,base=p) { # # Revision History: # P. Rossi 3/05 # # purpose: # function to create X array in format needed MNL and MNP routines # # Arguments: # p is number of choices # na is number of choice attribute variables (choice-specific characteristics) # nd is number of "demo" variables or characteristics of choosers # Xa is a n x (nx*p) matrix of choice attributes. First p cols are # values of attribute #1 for each of p chocies, second p for attribute # # 2 ... # Xd is an n x nd matrix of values of "demo" variables # INT is a logical flag for intercepts # DIFF is a logical flag for differencing wrt to base alternative # (required for MNP) # base is base alternative (default is p) # # note: if either you don't have any attributes or "demos", set # corresponding na, XA or nd,XD to NULL # YOU must specify p,na,nd,XA,XD for the function to work # # Output: # modified X matrix with n*p rows and INT*(p-1)+nd*(p-1) + na cols # # # check arguments # if(missing(p)) pandterm("requires p (# choice alternatives)") if(missing(na)) pandterm("requires na arg (use na=NULL if none)") if(missing(nd)) pandterm("requires nd arg (use nd=NULL if none)") if(missing(Xa)) pandterm("requires Xa arg (use Xa=NULL if none)") if(missing(Xd)) pandterm("requires Xd arg (use Xd=NULL if none)") if(is.null(Xa) && is.null(Xd)) pandterm("both Xa and Xd NULL -- requires one non-null") if(!is.null(na) && !is.null(Xa)) {if(ncol(Xa) != p*na) pandterm(paste("bad Xa dim, dim=",dim(Xa)))} if(!is.null(nd) && !is.null(Xd)) {if(ncol(Xd) != nd) pandterm(paste("ncol(Xd) ne nd, ncol(Xd)=",ncol(Xd)))} if(!is.null(Xa) && !is.null(Xd)) {if(nrow(Xa) != nrow(Xd)) {pandterm(paste("nrow(Xa) ne nrow(Xd),nrow(Xa)= ",nrow(Xa)," nrow(Xd)= ",nrow(Xd)))}} if(is.null(Xa)) {n=nrow(Xd)} else {n=nrow(Xa)} if(INT) {Xd=cbind(c(rep(1,n)),Xd)} if(DIFF) {Imod=diag(p-1)} else {Imod=matrix(0,p,p-1); Imod[-base,]=diag(p-1)} if(!is.null(Xd)) Xone=Xd %x%Imod else Xone=NULL Xtwo=NULL if(!is.null(Xa)) {if(DIFF) {tXa=matrix(t(Xa),nrow=p) Idiff=diag(p); Idiff[,base]=c(rep(-1,p));Idiff=Idiff[-base,] tXa=Idiff%*%tXa Xa=matrix(as.vector(tXa),ncol=(p-1)*na,byrow=TRUE) for (i in 1:na) {Xext=Xa[,((i-1)*(p-1)+1):((i-1)*(p-1)+p-1)] Xtwo=cbind(Xtwo,as.vector(t(Xext)))} } else { for (i in 1:na) { Xext=Xa[,((i-1)*p+1):((i-1)*p+p)] Xtwo=cbind(Xtwo,as.vector(t(Xext)))} } } return(cbind(Xone,Xtwo)) } bayesm/R/plot.bayesm.nmix.R0000755000176000001440000000773211754251324015335 0ustar ripleyusersplot.bayesm.nmix=function(x,names,burnin=trunc(.1*nrow(probdraw)),Grid,bi.sel,nstd=2,marg=TRUE, Data,ngrid=50,ndraw=200,...){ # # S3 method to plot normal mixture marginal and bivariate densities # nmixlist is a list of 3 components, nmixlist[[1]]: array of mix comp prob draws, # mmixlist[[2]] is not used, nmixlist[[3]] is list of draws of components # P. Rossi 2/07 # P. Rossi 3/07 fixed problem with dropping dimensions on probdraw (if ncomp=1) # P. Rossi 2/08 added marg flag to plot marginals # P. Rossi 3/08 added Data argument to paint histograms on the marginal plots # nmixlist=x if(mode(nmixlist) != "list") stop(" Argument must be a list \n") probdraw=nmixlist[[1]]; compdraw=nmixlist[[3]] if(!is.matrix(probdraw)) stop(" First element of list (probdraw) must be a matrix \n") if(mode(compdraw) != "list") stop(" Third element of list (compdraw) must be a list \n") op=par(no.readonly=TRUE) on.exit(par(op)) R=nrow(probdraw) if(R < 100) {cat(" fewer than 100 draws submitted \n"); return(invisible())} datad=length(compdraw[[1]][[1]]$mu) OneDimData=(datad==1) if(missing(bi.sel)) bi.sel=list(c(1,2)) # default to the first pair of variables ind=as.integer(seq(from=(burnin+1),to=R,length.out=max(ndraw,trunc(.05*R)))) if(missing(names)) {names=as.character(1:datad)} if(!missing(Data)){ if(!is.matrix(Data)) stop("Data argument must be a matrix \n") if(ncol(Data)!= datad) stop("Data matrix is of wrong dimension \n") } if(mode(bi.sel) != "list") stop("bi.sel must be as list, e.g. bi.sel=list(c(1,2),c(3,4)) \n") if(missing(Grid)){ Grid=matrix(0,nrow=ngrid,ncol=datad) if(!missing(Data)) {for(i in 1:datad) Grid[,i]=c(seq(from=range(Data[,i])[1],to=range(Data[,i])[2],length=ngrid))} else { out=momMix(probdraw[ind,,drop=FALSE],compdraw[ind]) mu=out$mu sd=out$sd for(i in 1:datad ) Grid[,i]=c(seq(from=(mu[i]-nstd*sd[i]), to=(mu[i]+nstd*sd[i]),length=ngrid)) } } # # plot posterior mean of marginal densities # if(marg){ mden=eMixMargDen(Grid,probdraw[ind,,drop=FALSE],compdraw[ind]) nx=datad if(nx==1) par(mfrow=c(1,1)) if(nx==2) par(mfrow=c(2,1)) if(nx==3) par(mfrow=c(3,1)) if(nx==4) par(mfrow=c(2,2)) if(nx>=5) par(mfrow=c(3,2)) for(index in 1:nx){ if(index == 2) par(ask=dev.interactive()) plot(range(Grid[,index]),c(0,1.1*max(mden[,index])),type="n",xlab="",ylab="density") title(names[index]) if(!missing(Data)){ deltax=(range(Grid[,index])[2]-range(Grid[,index])[1])/nrow(Grid) hist(Data[,index],xlim=range(Grid[,index]), freq=FALSE,col="yellow",breaks=max(20,.1*nrow(Data)),add=TRUE) lines(Grid[,index],mden[,index]/(sum(mden[,index])*deltax),col="red",lwd=2)} else {lines(Grid[,index],mden[,index],col="black",lwd=2) polygon(c(Grid[1,index],Grid[,index],Grid[nrow(Grid),index]),c(0,mden[,index],0),col="magenta")} } } # # now plot bivariates in list bi.sel # if(!OneDimData){ par(ask=dev.interactive()) nsel=length(bi.sel) den=array(0,dim=c(ngrid,ngrid,nsel)) lstxixj=NULL for(sel in 1:nsel){ i=bi.sel[[sel]][1] j=bi.sel[[sel]][2] xi=Grid[,i] xj=Grid[,j] lstxixj[[sel]]=list(xi,xj) for(elt in ind){ den[,,sel]=den[,,sel]+mixDenBi(i,j,xi,xj,probdraw[elt,,drop=FALSE],compdraw[[elt]]) } den[,,sel]=den[,,sel]/sum(den[,,sel]) } nx=nsel par(mfrow=c(1,1)) for(index in 1:nx){ xi=unlist(lstxixj[[index]][1]) xj=unlist(lstxixj[[index]][2]) xlabtxt=names[bi.sel[[index]][1]] ylabtxt=names[bi.sel[[index]][2]] image(xi,xj,den[,,index],col=terrain.colors(100),xlab=xlabtxt,ylab=ylabtxt) contour(xi,xj,den[,,index],add=TRUE,drawlabels=FALSE) } } invisible() } bayesm/R/logMargDenNR.R0000755000176000001440000000071110227516062014370 0ustar ripleyuserslogMargDenNR = function(ll) { # # purpose: compute log marginal density using Newton-Raftery # importance sampling estimator: 1/ (1/g sum_g exp(-log like) ) # where log like is the likelihood of the model evaluated as the # posterior draws (x). # # arguments: # ll -- vector of log-likelihood values evaluated at posterior draws # # output: # estimated log-marginal density med=median(ll) return(med-log(mean(exp(-ll+med)))) } bayesm/R/mnpProb.R0000644000176000001440000000275312533663350013540 0ustar ripleyusersmnpProb= function(beta,Sigma,X,r=100) { # # revision history: # written by Rossi 9/05 # W. Taylor 4/15 - replaced ghkvec call with rcpp version # # purpose: # function to MNP probabilities for a given X matrix (corresponding # to "one" observation # # arguments: # X is p-1 x k array of covariates (including intercepts) # note: X is from the "differenced" system # beta is k x 1 with k = ncol(X) # Sigma is p-1 x p-1 # r is the number of random draws to use in GHK # # output -- probabilities # for each observation w = Xbeta + e e ~N(0,Sigma) # if y=j (j max(w_-j) and w_j >0 # if y=p, w < 0 # # to use GHK we must transform so that these are rectangular regions # e.g. if y=1, w_1 > 0 and w_1 - w_-1 > 0 # # define Aj such that if j=1,..,p-1, Ajw = Ajmu + Aje > 0 is equivalent to y=j # implies Aje > -Ajmu # lower truncation is -Ajmu and cov = AjSigma t(Aj) # # for p, e < - mu # # pm1=ncol(Sigma) k=length(beta) mu=matrix(X%*%beta,nrow=pm1) above=rep(0,pm1) prob=double(pm1+1) for (j in 1:pm1) { Aj=-diag(pm1) Aj[,j]=rep(1,pm1) trunpt=as.vector(-Aj%*%mu) Lj=t(chol(Aj%*%Sigma%*%t(Aj))) # note: rob's routine expects lower triangular root prob[j]=ghkvec(Lj,trunpt,above,r) # note: ghkvec does an entire vector of n probs each with different truncation points but the # same cov matrix. } # # now do pth alternative # prob[pm1+1]=1-sum(prob[1:pm1]) return(prob) } bayesm/R/BayesmFunctions.R0000644000176000001440000000007012524505375015224 0ustar ripleyuserspandterm=function(message) { stop(message,call.=FALSE) }bayesm/R/rdpgibbs_rcpp.r0000644000176000001440000001614312566706215015005 0ustar ripleyusersrDPGibbs=function(Prior,Data,Mcmc){ # # Revision History: # 5/06 add rthetaDP # 7/06 include rthetaDP in main body to avoid copy overhead # 1/08 add scaling # 2/08 add draw of lambda # 3/08 changed nu prior support to dim(y) + exp(unif gird on nulim[1],nulim[2]) # W. Taylor 4/15 - added nprint option to MCMC argument # # purpose: do Gibbs sampling for density estimation using Dirichlet process model # # arguments: # Data is a list of y which is an n x k matrix of data # Prior is a list of (alpha,lambda,Prioralpha) # alpha: starting value # lambda_hyper: hyperparms of prior on lambda # Prioralpha: hyperparms of alpha prior; a list of (Istarmin,Istarmax,power) # if elements of the prior don't exist, defaults are assumed # Mcmc is a list of (R,keep,maxuniq) # R: number of draws # keep: thinning parameter # maxuniq: the maximum number of unique thetaStar values # nprint - print estimated time remaining on every nprint'th draw # # Output: # list with elements # alphadraw: vector of length R/keep, [i] is ith draw of alpha # Istardraw: vector of length R/keep, [i] is the number of unique theta's drawn from ith iteration # adraw # nudraw # vdraw # thetaNp1draws: list, [[i]] is ith draw of theta_{n+1} # inddraw: R x n matrix, [,i] is indicators of identity for each obs in ith iteration # # Model: # y_i ~ f(y|thetai) # thetai|G ~ G # G|lambda,alpha ~ DP(G|G0(lambda),alpha) # # Priors: # alpha: starting value # # lambda: # G0 ~ N(mubar,Sigma (x) Amu^-1) # mubar=vec(mubar) # Sigma ~ IW(nu,nu*v*I) note: mode(Sigma)=nu/(nu+2)*v*I # mubar=0 # amu is uniform on grid specified by alim # nu is log uniform, nu=d-1+exp(Z) z is uniform on seq defined bvy nulim # v is uniform on sequence specificd by vlim # # Prioralpha: # alpha ~ (1-(alpha-alphamin)/(alphamax-alphamin))^power # alphamin=exp(digamma(Istarmin)-log(gamma+log(N))) # alphamax=exp(digamma(Istarmax)-log(gamma+log(N))) # gamma= .5772156649015328606 # # # # check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of y")} if(is.null(Data$y)) {pandterm("Requires Data element y")} y=Data$y # # check data for validity # if(!is.matrix(y)) {pandterm("y must be a matrix")} nobs=nrow(y) dimy=ncol(y) # # check for Prior # alimdef=BayesmConstant.DPalimdef nulimdef=BayesmConstant.DPnulimdef vlimdef=BayesmConstant.DPvlimdef if(missing(Prior)) {pandterm("requires Prior argument ")} else { if(is.null(Prior$lambda_hyper)) {lambda_hyper=list(alim=alimdef,nulim=nulimdef,vlim=vlimdef)} else {lambda_hyper=Prior$lambda_hyper; if(is.null(lambda_hyper$alim)) {lambda_hyper$alim=alimdef} if(is.null(lambda_hyper$nulim)) {lambda_hyper$nulim=nulimdef} if(is.null(lambda_hyper$vlim)) {lambda_hyper$vlim=vlimdef} } if(is.null(Prior$Prioralpha)) {Prioralpha=list(Istarmin=BayesmConstant.DPIstarmin,Istarmax=min(50,0.1*nobs),power=BayesmConstant.DPpower)} else {Prioralpha=Prior$Prioralpha; if(is.null(Prioralpha$Istarmin)) {Prioralpha$Istarmin=BayesmConstant.DPIstarmin} else {Prioralpha$Istarmin=Prioralpha$Istarmin} if(is.null(Prioralpha$Istarmax)) {Prioralpha$Istarmax=min(50,0.1*nobs)} else {Prioralpha$Istarmax=Prioralpha$Istarmax} if(is.null(Prioralpha$power)) {Prioralpha$power=BayesmConstant.DPpower} } } gamma= BayesmConstant.gamma Prioralpha$alphamin=exp(digamma(Prioralpha$Istarmin)-log(gamma+log(nobs))) Prioralpha$alphamax=exp(digamma(Prioralpha$Istarmax)-log(gamma+log(nobs))) Prioralpha$n=nobs # # check Prior arguments for valdity # if(lambda_hyper$alim[1]<0) {pandterm("alim[1] must be >0")} if(lambda_hyper$nulim[1]<0) {pandterm("nulim[1] must be >0")} if(lambda_hyper$vlim[1]<0) {pandterm("vlim[1] must be >0")} if(Prioralpha$Istarmin <1){pandterm("Prioralpha$Istarmin must be >= 1")} if(Prioralpha$Istarmax <= Prioralpha$Istarmin){pandterm("Prioralpha$Istarmin must be > Prioralpha$Istarmax")} # # check MCMC argument # if(missing(Mcmc)) {pandterm("requires Mcmc argument")} else { if(is.null(Mcmc$R)) {pandterm("requires Mcmc element R")} else {R=Mcmc$R} if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} if(is.null(Mcmc$maxuniq)) {maxuniq=BayesmConstant.DPmaxuniq} else {maxuniq=Mcmc$maxuniq} if(is.null(Mcmc$SCALE)) {SCALE=BayesmConstant.DPSCALE} else {SCALE=Mcmc$SCALE} if(is.null(Mcmc$gridsize)) {gridsize=BayesmConstant.DPgridsize} else {gridsize=Mcmc$gridsize} } # # print out the problem # cat(" Starting Gibbs Sampler for Density Estimation Using Dirichlet Process Model",fill=TRUE) cat(" ",nobs," observations on ",dimy," dimensional data",fill=TRUE) cat(" ",fill=TRUE) cat(" SCALE=",SCALE,fill=TRUE) cat(" ",fill=TRUE) cat(" Prior Parms: ",fill=TRUE) cat(" G0 ~ N(mubar,Sigma (x) Amu^-1)",fill=TRUE) cat(" mubar = ",0,fill=TRUE) cat(" Sigma ~ IW(nu,nu*v*I)",fill=TRUE) cat(" Amu ~ uniform[",lambda_hyper$alim[1],",",lambda_hyper$alim[2],"]",fill=TRUE) cat(" nu ~ uniform on log grid on [",dimy-1+exp(lambda_hyper$nulim[1]), ",",dimy-1+exp(lambda_hyper$nulim[2]),"]",fill=TRUE) cat(" v ~ uniform[",lambda_hyper$vlim[1],",",lambda_hyper$vlim[2],"]",fill=TRUE) cat(" ",fill=TRUE) cat(" alpha ~ (1-(alpha-alphamin)/(alphamax-alphamin))^power",fill=TRUE) cat(" Istarmin = ",Prioralpha$Istarmin,fill=TRUE) cat(" Istarmax = ",Prioralpha$Istarmax,fill=TRUE) cat(" alphamin = ",Prioralpha$alphamin,fill=TRUE) cat(" alphamax = ",Prioralpha$alphamax,fill=TRUE) cat(" power = ",Prioralpha$power,fill=TRUE) cat(" ",fill=TRUE) cat(" Mcmc Parms: R= ",R," keep= ",keep," nprint= ",nprint," maxuniq= ",maxuniq," gridsize for lambda hyperparms= ",gridsize, fill=TRUE) cat(" ",fill=TRUE) ################################################################### # Wayne Taylor # 1/29/2015 ################################################################### out = rDPGibbs_rcpp_loop(R,keep,nprint, y, lambda_hyper, SCALE, maxuniq, Prioralpha, gridsize, BayesmConstant.A,BayesmConstant.nuInc,BayesmConstant.DPalpha) ################################################################### nmix=list(probdraw=matrix(c(rep(1,nrow(out$inddraw))),ncol=1),zdraw=out$inddraw,compdraw=out$thetaNp1draw) attributes(nmix)$class="bayesm.nmix" attributes(out$alphadraw)$class=c("bayesm.mat","mcmc") attributes(out$Istardraw)$class=c("bayesm.mat","mcmc") attributes(out$adraw)$class=c("bayesm.mat","mcmc") attributes(out$nudraw)$class=c("bayesm.mat","mcmc") attributes(out$vdraw)$class=c("bayesm.mat","mcmc") return(list(alphadraw=out$alphadraw,Istardraw=out$Istardraw,adraw=out$adraw,nudraw=out$nudraw, vdraw=out$vdraw,nmix=nmix)) } bayesm/R/rmnlIndepMetrop_rcpp.R0000644000176000001440000001042512566706215016265 0ustar ripleyusersrmnlIndepMetrop=function(Data,Prior,Mcmc){ # # revision history: # p. rossi 1/05 # 2/9/05 fixed error in Metrop eval # changed to reflect new argument order in llmnl,mnlHess 9/05 # added return for log-like 11/05 # W. Taylor 4/15 - added nprint option to MCMC argument # # purpose: # draw from posterior for MNL using Independence Metropolis # # Arguments: # Data - list of p,y,X # p is number of alternatives # X is nobs*p x nvar matrix # y is nobs vector of values from 1 to p # Prior - list of A, betabar # A is nvar x nvar prior preci matrix # betabar is nvar x 1 prior mean # Mcmc # R is number of draws # keep is thinning parameter # nprint - print estimated time remaining on every nprint'th draw # nu degrees of freedom parameter for independence # sampling density # # Output: # list of betadraws # # Model: Pr(y=j) = exp(x_j'beta)/sum(exp(x_k'beta) # # Prior: beta ~ N(betabar,A^-1) # # check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of p, y, X")} if(is.null(Data$X)) {pandterm("Requires Data element X")} X=Data$X if(is.null(Data$y)) {pandterm("Requires Data element y")} y=Data$y if(is.null(Data$p)) {pandterm("Requires Data element p")} p=Data$p nvar=ncol(X) nobs=length(y) # # check data for validity # if(length(y) != (nrow(X)/p) ) {pandterm("length(y) ne nrow(X)/p")} if(sum(y %in% (1:p)) < nobs) {pandterm("invalid values in y vector -- must be integers in 1:p")} cat(" table of y values",fill=TRUE) print(table(y)) # # check for Prior # if(missing(Prior)) { betabar=c(rep(0,nvar)); A=BayesmConstant.A*diag(nvar)} else { if(is.null(Prior$betabar)) {betabar=c(rep(0,nvar))} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=BayesmConstant.A*diag(nvar)} else {A=Prior$A} } # # check dimensions of Priors # if(ncol(A) != nrow(A) || ncol(A) != nvar || nrow(A) != nvar) {pandterm(paste("bad dimensions for A",dim(A)))} if(length(betabar) != nvar) {pandterm(paste("betabar wrong length, length= ",length(betabar)))} # # check MCMC argument # if(missing(Mcmc)) {pandterm("requires Mcmc argument")} else { if(is.null(Mcmc$R)) {pandterm("requires Mcmc element R")} else {R=Mcmc$R} if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} if(is.null(Mcmc$nu)) {nu=6} else {nu=Mcmc$nu} } # # print out problem # cat(" ", fill=TRUE) cat("Starting Independence Metropolis Sampler for Multinomial Logit Model",fill=TRUE) cat(" ",length(y)," obs with ",p," alternatives",fill=TRUE) cat(" ", fill=TRUE) cat("Table of y Values",fill=TRUE) print(table(y)) cat("Prior Parms: ",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat("A",fill=TRUE) print(A) cat(" ", fill=TRUE) cat("MCMC parms: ",fill=TRUE) cat("R= ",R," keep= ",keep," nprint= ",nprint," nu (df for st candidates) = ",nu,fill=TRUE) cat(" ",fill=TRUE) # # compute required quantities for indep candidates # beta=c(rep(0,nvar)) mle=optim(beta,llmnl,X=X,y=y,method="BFGS",hessian=TRUE,control=list(fnscale=-1)) beta=mle$par betastar=mle$par mhess=mnlHess(beta,y,X) candcov=chol2inv(chol(mhess)) root=chol(candcov) rooti=backsolve(root,diag(nvar)) priorcov=chol2inv(chol(A)) rootp=chol(priorcov) rootpi=backsolve(rootp,diag(nvar)) oldloglike=llmnl(beta,y,X) oldlpost=oldloglike+lndMvn(beta,betabar,rootpi) oldlimp=lndMvst(beta,nu,betastar,rooti) # note: we don't need the determinants as they cancel in # computation of acceptance prob ################################################################### # Wayne Taylor # 08/21/2014 ################################################################### loopout = rmnlIndepMetrop_rcpp_loop(R,keep,nu,betastar,root,y,X,betabar,rootpi,rooti,oldlimp,oldlpost,nprint); ################################################################### attributes(loopout$betadraw)$class=c("bayesm.mat","mcmc") attributes(loopout$betadraw)$mcpar=c(1,R,keep) return(list(betadraw=loopout$betadraw,loglike=loopout$loglike,acceptr=loopout$naccept/R)) } bayesm/R/rbayesBLP_rcpp.R0000644000176000001440000002405013114117322014751 0ustar ripleyusersrbayesBLP=function(Data, Prior, Mcmc){ # # Keunwoo Kim 02/06/2014 # # Purpose: # draw theta_bar and Sigma via hybrid Gibbs sampler (Jiang, Manchanda, and Rossi, 2009) # # Arguments: # Data # X: J*T by H (if IV is used, the last column is endogeneous variable.) # share: vector of length J*T # J: number of alternatives (excluding outside option) # Z: instrumental variables (optional) # # Prior # sigmasqR # theta_hat # A # deltabar # Ad # nu0 # s0_sq # VOmega # # Mcmc # R: number of MCMC draws # H: number of draws for Monte-Carlo integration # # s: scaling parameter of MH increment # cand_cov: var-cov matrix of MH increment # (minaccep: lower bound of target range of acceptance rate) # (maxaccep: upper bound of target range of acceptance rate) # # theta_bar_initial # r_initial # tau_sq_initial # Omega_initial # delta_initial # # tol: convergence tolerance for the contraction mapping # # Output: # a List of tau_sq (or Omega and delta), # theta_bar, r (equivalent to Sigma) draws, Sigma draws, # relative numerical efficiency of r draws, tunned parameters for MH, and # acceptance rate # pandterm=function(message) {stop(message,call.=FALSE)} # # check for data # if(missing(Data)) {pandterm("Requires Data argument -- list of X and share")} if(is.null(Data$X)) {pandterm("Requires Data element X")} else {X=Data$X} if(is.null(Data$share)) {pandterm("Requires Data element share")} else {share=Data$share} if(is.null(Data$J)) {pandterm("Requires Data element J")} else {J=Data$J} if(is.null(Data$Z)) {IV=FALSE; Z=matrix(0); I=1} else {IV=TRUE; I=ncol(Z)} if(!is.matrix(X)) {pandterm("X must be a matrix")} if(!is.vector(share, mode = "numeric")) {pandterm("share must be a numeric vector")} if(!is.matrix(Z)) {pandterm("Z must be a matrix")} if(length(J) > 1 | floor(J) != J) {pandterm("J must be an integer")} K=ncol(X) if (length(share) != nrow(X)) {pandterm("Mismatch in the number of observations in X and share")} T=length(share)/J # # check for prior # if(missing(Prior)) { c=50 sigmasqRoff=1 sigmasqRdiag=log((1+sqrt(1-4*(2*(c(1:K)-1)*sigmasqRoff-c)))/2)/4 sigmasqR=c(sigmasqRdiag, rep(1, K*(K-1)/2)) A=BayesmConstant.A*diag(K) theta_hat=rep(0,K) nu0=K+1 s0_sq=1 deltabar=rep(0,I) Ad=BayesmConstant.A*diag(I) VOmega=BayesmConstant.BLPVOmega } else { if(is.null(Prior$sigmasqR)) { c=50 sigmasqRoff=1 sigmasqRdiag=log((1+sqrt(1-4*(2*(c(1:K)-1)*sigmasqRoff-c)))/2)/4 sigmasqR=c(sigmasqRdiag, rep(1, K*(K-1)/2)) } else { sigmasqR=Prior$sigmasqR } if(is.null(Prior$A)) {A=BayesmConstant.A*diag(K)} else {A=Prior$A} if(is.null(Prior$theta_hat)) {theta_hat=rep(0,K)} else {theta_hat=Prior$theta_hat} if(is.null(Prior$nu0)) {nu0=K+1} else {nu0=Prior$nu0} if(is.null(Prior$s0_sq)) {s0_sq=1} else {s0_sq=Prior$s0_sq} if(is.null(Prior$deltabar)) {deltabar=rep(0,I)} else {deltabar=Prior$deltabar} if(is.null(Prior$Ad)) {Ad=BayesmConstant.A*diag(I)} else {Ad=Prior$Ad} if(is.null(Prior$VOmega)) {VOmega=BayesmConstant.BLPVOmega} else {VOmega=Prior$VOmega} } if(length(sigmasqR) != K*(K+1)/2) pandterm("sigmasqR is of incorrect dimension") if(sum(dim(A)==c(K,K)) != 2) pandterm("A is of incorrect dimension") if(length(theta_hat) != K) pandterm("theta_hat is of incorrect dimension") if((length(nu0) != 1) | (nu0 <=0)) pandterm("nu0 should be a positive number") if((length(s0_sq) != 1) | (s0_sq <=0)) pandterm("s0_sq should be a positive number") if(length(deltabar) != I) pandterm("deltabar is of incorrect dimension") if(sum(dim(Ad)==c(I,I)) != 2) pandterm("Ad is of incorrect dimension") if(sum(dim(VOmega)==c(2,2)) != 2) pandterm("VOmega is of incorrect dimension") # # check for Mcmc # if(missing(Mcmc)) pandterm("Requires Mcmc argument -- at least R and H") if(is.null(Mcmc$R)) {pandterm("Requires element R of Mcmc")} else {R=Mcmc$R} if(is.null(Mcmc$H)) {pandterm("Requires element H of Mcmc")} else {H=Mcmc$H} if(is.null(Mcmc$initial_theta_bar)) {initial_theta_bar=rep(0,K)} else {initial_theta_bar=Mcmc$initial_theta_bar} if(is.null(Mcmc$initial_r)) {initial_r=rep(0,K*(K+1)/2)} else {initial_r=Mcmc$initial_r} if(is.null(Mcmc$initial_tau_sq)) {initial_tau_sq=0.1} else {initial_tau_sq=Mcmc$initial_tau_sq} if(is.null(Mcmc$initial_Omega)) {initial_Omega=diag(2)} else {initial_Omega=Mcmc$initial_Omega} if(is.null(Mcmc$initial_delta)) {initial_delta=rep(0,I)} else {initial_delta=Mcmc$initial_tau_sq} if(is.null(Mcmc$keep)) {keep=1} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(is.null(Mcmc$s)+is.null(Mcmc$cand_cov)==0){ s=Mcmc$s cand_cov=Mcmc$cand_cov tuning_auto=FALSE } if(is.null(Mcmc$s)+is.null(Mcmc$cand_cov)==1) pandterm("If you want to control tuning parameters, write both parameters.") if(is.null(Mcmc$s)+is.null(Mcmc$cand_cov)==2){ s=BayesmConstant.RRScaling/sqrt(K*(K+1)/2) cand_cov=diag(c(rep(0.1,K),rep(1,K*(K-1)/2))) tuning_auto=TRUE } if(is.null(Mcmc$tol)) {tol=BayesmConstant.BLPtol} else {tol=Mcmc$tol} minaccep=0.3 maxaccep=0.5 if(length(initial_theta_bar)!=K) pandterm("initial_theta_bar is of incorrect dimension") if(length(initial_r)!=(K*(K+1)/2)) pandterm("initial_r is of incorrect dimension") if(initial_tau_sq<0) pandterm("initial_tau_sq should be positive") if(sum(dim(initial_Omega)==c(2,2))!=2) pandterm("initial_Omega is of incorrect dimension") if(length(initial_delta)!=I) pandterm("initial_delta is of incorrect dimension") if(nprint<0) { pandterm('nprint must be >=0') } # # print out problem # cat(" ",fill=TRUE) cat("Data Dimensions:",fill=TRUE) cat(" ",T," market(time); ",J+1," alternatives (including outside option); ",fill=TRUE) cat(" ",fill=TRUE) if (IV==TRUE){ cat(" ",I," instrumental variable(s) ",fill=TRUE) cat(" ",fill=TRUE) } cat("Prior Parameters:",fill=TRUE) cat(" thetahat",fill=TRUE) print(theta_hat) cat(" A",fill=TRUE) print(A) cat(" sigmasqR",fill=TRUE) print(sigmasqR) cat(" nu0",fill=TRUE) print(nu0) if (IV==TRUE){ cat(" VOmega",fill=TRUE) print(VOmega) cat(" deltabar",fill=TRUE) print(deltabar) cat(" Ad",fill=TRUE) print(Ad) } if (IV==FALSE){ cat(" s0_sq",fill=TRUE) print(s0_sq) } cat(" ",fill=TRUE) cat("MCMC Parmameters: ",fill=TRUE) cat(" ",R," reps; keeping every ",keep,"th draw; printing every ",nprint,"th draw",fill=TRUE) cat(" ",H," draws for Monte-Carlo integration",fill=TRUE) cat(" ",fill=TRUE) cat("Contraction Mapping Tolerance: ",fill=TRUE) cat(" until max(abs((mu1-mu0)/mu0)) <",tol,fill=TRUE) cat(" ",fill=TRUE) if (tuning_auto){ cat(" automatically tuning parameters of RW M-H increment",fill=TRUE) cat(" ",fill=TRUE) cat(" target acceptance rate is between ",minaccep*100,"% and ",maxaccep*100,"%",fill=TRUE) cat(" ",fill=TRUE) } else{ cat(" scaling parameter of RW M-H increment is given as",fill=TRUE) print(s) cat(" ",fill=TRUE) cat(" var-cov matrix of RW M-H increment is given as",fill=TRUE) print(cand_cov) cat(" ",fill=TRUE) } # draw for MC integration draw <- matrix(rnorm(K*H), K, H) # # tuning RW Metropolis-Hastings # # if auto-tuning complete1 <- 0 initial_theta_bar2 <- initial_theta_bar initial_r2 <- initial_r initial_tau_sq2 <- initial_tau_sq initial_Omega2 <- initial_Omega initial_delta2 <- initial_delta rdraws <- NULL if (tuning_auto){ cat("Tuning RW Metropolis-Hastings Increment...",fill=TRUE) cat(" ",fill=TRUE) cat("-If acceptance rate < ",minaccep*100,"% => s/5",fill=TRUE) cat("-If acceptance rate > ",maxaccep*100,"% => s*3",fill=TRUE) cat("-If acceptance rate is ",minaccep*100,"~",maxaccep*100,"% => complete tuning",fill=TRUE) cat(" ",fill=TRUE) while (complete1==0){ cat(" try s=",s,fill=TRUE) out1 <- bayesBLP_rcpp_loop(IV, X, Z, share, J, T, draw, 500, sigmasqR, A, theta_hat, deltabar, Ad, nu0, s0_sq, VOmega, s^2, cand_cov, initial_theta_bar2, initial_r2, initial_tau_sq2, initial_Omega2, initial_delta2, tol, 1, 0) initial_theta_bar2 <- as.vector(out1$thetabardraw[,500]) initial_r2 <- as.vector(out1$rdraw[,500]) initial_tau_sq2 <- out1$tausqdraw[500] if (IV==TRUE) {initial_Omega2 <- matrix(out1$Omegadraw[,500],2,2)} if (IV==TRUE) {initial_delta2 <- as.vector(out1$deltadraw[,500])} cat(" acceptance rate is ",out1$acceptrate,fill=TRUE) if (out1$acceptrate>0.20 & out1$acceptrate<0.80){ rdraws <- cbind(rdraws, out1$rdraw) cat(" (r draws stored)",fill=TRUE) } if (out1$acceptratemaxaccep){ s <- s*3 }else{ complete1 <- 1 cat(" ",fill=TRUE) cat(" (tuning completed.)",fill=TRUE) } } # scaling tunned var-cov matrix from r draws scale_opt <- s*sqrt(diag(cand_cov)) Omega <- cov(t(rdraws)) scale_Omega <- sqrt(diag(Omega)) corr_opt <- Omega / (scale_Omega%*%t(scale_Omega)) s <- 1 cand_cov <- corr_opt * (scale_opt%*%t(scale_opt)) cat(" ",fill=TRUE) cat("Tuning Completed:",fill=TRUE) cat(" s=",s,fill=TRUE) cat(" var-cov=",fill=TRUE) print(cand_cov) cat(" ",fill=TRUE) } # # main run # cat("Starting Random Walk Metropolis-Hastings Sampler for BLP",fill=TRUE) out <- bayesBLP_rcpp_loop(IV, X, Z, share, J, T, draw, R, sigmasqR, A, theta_hat, deltabar, Ad, nu0, s0_sq, VOmega, s^2, cand_cov, initial_theta_bar, initial_r, initial_tau_sq, initial_Omega, initial_delta, tol, keep, nprint) out$s <- s out$cand_cov <- cand_cov attributes(out$tausqdraw)$class=c("bayesm.mat","mcmc") attributes(out$tausqdraw)$mcpar=c(1,R,keep) attributes(out$thetabardraw)$class=c("bayesm.mat","mcmc") attributes(out$thetabardraw)$mcpar=c(1,R,keep) attributes(out$rdraw)$class=c("bayesm.mat","mcmc") attributes(out$rdraw)$mcpar=c(1,R,keep) attributes(out$Sigmadraw)$class=c("bayesm.mat","mcmc") attributes(out$Sigmadraw)$mcpar=c(1,R,keep) attributes(out$Omegadraw)$class=c("bayesm.mat","mcmc") attributes(out$Omegadraw)$mcpar=c(1,R,keep) attributes(out$deltadraw)$class=c("bayesm.mat","mcmc") attributes(out$deltadraw)$mcpar=c(1,R,keep) return(out) } bayesm/R/numEff.R0000755000176000001440000000114110240734574013334 0ustar ripleyusersnumEff= function(x,m=as.integer(min(length(x),(100/sqrt(5000))*sqrt(length(x))))) { # # P. Rossi # revision history: 3/27/05 # # purpose: # compute N-W std error and relative numerical efficiency # # Arguments: # x is vector of draws # m is number of lags to truncate acf # def is such that m=100 if length(x)= 5000 and grows with sqrt(length) # # Output: # list with numerical std error and variance multiple (f) # wgt=as.vector(seq(m,1,-1))/(m+1) z=acf(x,lag.max=m,plot=FALSE) f=1+2*wgt%*%as.vector(z$acf[-1]) stderr=sqrt(var(x)*f/length(x)) list(stderr=stderr,f=f,m=m) } bayesm/R/eMixMargDen.R0000755000176000001440000000123410224401101014232 0ustar ripleyuserseMixMargDen= function(grid,probdraw,compdraw) { # # Revision History: # R. McCulloch 11/04 # # purpose: plot the marginal density of a normal mixture averaged over MCMC draws # # arguments: # grid -- array of grid points, grid[,i] are ordinates for ith component # probdraw -- ith row is ith draw of probabilities of mixture comp # compdraw -- list of lists of draws of mixture comp moments (each sublist is from mixgibbs) # # output: # array of same dim as grid with density values # # den=matrix(0,nrow(grid),ncol(grid)) for(i in 1:length(compdraw)) den=den+mixDen(grid,probdraw[i,],compdraw[[i]]) return(den/length(compdraw)) } bayesm/R/mixDen.R0000755000176000001440000000352510554234436013350 0ustar ripleyusersmixDen= function(x,pvec,comps) { # Revision History: # R. McCulloch 11/04 # P. Rossi 3/05 -- put in backsolve # P. Rossi 1/06 -- put in crossprod # # purpose: compute marginal densities for multivariate mixture of normals (given by p and comps) at x # # arguments: # x: ith columns gives evaluations for density of ith variable # pvec: prior probabilities of normal components # comps: list, each member is a list comp with ith normal component ~ N(comp[[1]],Sigma), # Sigma = t(R)%*%R, R^{-1} = comp[[2]] # Output: # matrix with same shape as input, x, ith column gives margial density of ith variable # # --------------------------------------------------------------------------------------------- # define function needed # ums=function(comps) { # purpose: obtain marginal means and standard deviations from list of normal components # arguments: # comps: list, each member is a list comp with ith normal component ~N(comp[[1]],Sigma), # Sigma = t(R)%*%R, R^{-1} = comp[[2]] # returns: # a list with [[1]]=$mu a matrix whose ith row is the means for ith component # [[2]]=$sigma a matrix whose ith row is the standard deviations for the ith component # nc = length(comps) dim = length(comps[[1]][[1]]) mu = matrix(0.0,nc,dim) sigma = matrix(0.0,nc,dim) for(i in 1:nc) { mu[i,] = comps[[i]][[1]] # root = solve(comps[[i]][[2]]) root= backsolve(comps[[i]][[2]],diag(rep(1,dim))) sigma[i,] = sqrt(diag(crossprod(root))) } return(list(mu=mu,sigma=sigma)) } # ---------------------------------------------------------------------------------------------- nc = length(comps) mars = ums(comps) den = matrix(0.0,nrow(x),ncol(x)) for(i in 1:ncol(x)) { for(j in 1:nc) den[,i] = den[,i] + dnorm(x[,i],mean = mars$mu[j,i],sd=mars$sigma[j,i])*pvec[j] } return(den) } bayesm/R/fsh.R0000755000176000001440000000031510225316753012674 0ustar ripleyusersfsh=function() { # # P. Rossi # revision history: 3/27/05 # # Purpose: # function to flush console (needed only under windows) # if (Sys.info()[1] == "Windows") flush.console() return() } bayesm/R/rbprobitgibbs_rcpp.r0000644000176000001440000000654613114117322016032 0ustar ripleyusersrbprobitGibbs= function(Data,Prior,Mcmc) { # # revision history: # p. rossi 1/05 # 3/07 added validity check of values of y and classes # 3/07 fixed error with betabar supplied # W. Taylor 4/15 - added nprint option to MCMC argument # # purpose: # draw from posterior for binary probit using Gibbs Sampler # # Arguments: # Data - list of X,y # X is nobs x nvar, y is nobs vector of 0,1 # Prior - list of A, betabar # A is nvar x nvar prior preci matrix # betabar is nvar x 1 prior mean # Mcmc # R is number of draws # keep is thinning parameter # nprint - print estimated time remaining on every nprint'th draw # # Output: # list of betadraws # # Model: y = 1 if w=Xbeta + e > 0 e ~N(0,1) # # Prior: beta ~ N(betabar,A^-1) # # # # check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of y and X")} if(is.null(Data$X)) {pandterm("Requires Data element X")} X=Data$X if(is.null(Data$y)) {pandterm("Requires Data element y")} y=Data$y nvar=ncol(X) nobs=length(y) # # check data for validity # if(length(y) != nrow(X) ) {pandterm("y and X not of same row dim")} if(sum(unique(y) %in% c(0:1)) < length(unique(y))) {pandterm("Invalid y, must be 0,1")} # # check for Prior # if(missing(Prior)) { betabar=c(rep(0,nvar)); A=BayesmConstant.A*diag(nvar)} else { if(is.null(Prior$betabar)) {betabar=c(rep(0,nvar))} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=BayesmConstant.A*diag(nvar)} else {A=Prior$A} } # # check dimensions of Priors # if(ncol(A) != nrow(A) || ncol(A) != nvar || nrow(A) != nvar) {pandterm(paste("bad dimensions for A",dim(A)))} if(length(betabar) != nvar) {pandterm(paste("betabar wrong length, length= ",length(betabar)))} # # check MCMC argument # if(missing(Mcmc)) {pandterm("requires Mcmc argument")} else { if(is.null(Mcmc$R)) {pandterm("requires Mcmc element R")} else {R=Mcmc$R} if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} } # # print out problem # cat(" ", fill=TRUE) cat("Starting Gibbs Sampler for Binary Probit Model",fill=TRUE) cat(" with ",length(y)," observations",fill=TRUE) cat("Table of y Values",fill=TRUE) print(table(y)) cat(" ", fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat("A",fill=TRUE) print(A) cat(" ", fill=TRUE) cat("MCMC parms: ",fill=TRUE) cat("R= ",R," keep= ",keep," nprint= ",nprint,fill=TRUE) cat(" ",fill=TRUE) beta=c(rep(0,nvar)) sigma=c(rep(1,nrow(X))) root=chol(chol2inv(chol((crossprod(X,X)+A)))) Abetabar=crossprod(A,betabar) #a=ifelse(y == 0,-100, 0) #b=ifelse(y == 0, 0, 100) above=ifelse(y == 0, 1, 0) trunpt=0 ################################################################### # Keunwoo Kim # 08/05/2014 ################################################################### #draws=rbprobitGibbs_rcpp_loop(y,X,Abetabar,root,beta,sigma,a,b,R,keep,nprint) draws=rbprobitGibbs_rcpp_loop(y,X,Abetabar,root,beta,sigma,trunpt,above,R,keep,nprint) ################################################################### attributes(draws$betadraw)$class=c("bayesm.mat","mcmc") attributes(draws$betadraw)$mcpar=c(1,R,keep) return(draws) } bayesm/R/summary.bayesm.mat.R0000755000176000001440000000356011754537723015667 0ustar ripleyuserssummary.bayesm.mat=function(object,names,burnin=trunc(.1*nrow(X)),tvalues,QUANTILES=TRUE,TRAILER=TRUE,...){ # # S3 method to compute and print posterior summaries for a matrix of draws # P. Rossi 2/07 # X=object if(mode(X) == "list") stop("list entered \n Possible Fixup: extract from list \n") if(mode(X) !="numeric") stop("Requires numeric argument \n") if(is.null(attributes(X)$dim)) X=as.matrix(X) nx=ncol(X) if(missing(names)) names=as.character(1:nx) if(nrow(X) < 100) {cat("fewer than 100 draws submitted \n"); return(invisible())} X=X[(burnin+1):nrow(X),,drop=FALSE] mat=matrix(apply(X,2,mean),nrow=1) mat=rbind(mat,sqrt(matrix(apply(X,2,var),nrow=1))) num_se=double(nx); rel_eff=double(nx); eff_s_size=double(nx) for(i in 1:nx) {out=numEff(X[,i]) if(is.nan(out$stderr)) {num_se[i]=-9999; rel_eff[i]=-9999; eff_s_size[i]=-9999} else {num_se[i]=out$stderr; rel_eff[i]=out$f; eff_s_size[i]=nrow(X)/ceiling(out$f)} } mat=rbind(mat,num_se,rel_eff,eff_s_size) colnames(mat)=names rownames(mat)[1]="mean" rownames(mat)[2]="std dev" rownames(mat)[3]="num se" rownames(mat)[4]="rel eff" rownames(mat)[5]="sam size" if(!missing(tvalues)) {if(mode(tvalues)!="numeric") stop("true values arguments must be numeric \n") if(length(tvalues) != nx) stop("true values argument is wrong length \n") mat=rbind(tvalues,mat) } cat("Summary of Posterior Marginal Distributions ") cat("\nMoments \n") print(t(mat),digits=2) if(QUANTILES){ qmat=apply(X,2,quantile,probs=c(.025,.05,.5,.95,.975)) colnames(qmat)=names if(!missing(tvalues)) { qmat=rbind(tvalues,qmat)} cat("\nQuantiles \n") print(t(qmat),digits=2)} if(TRAILER) cat(paste(" based on ",nrow(X)," valid draws (burn-in=",burnin,") \n",sep="")) invisible(t(mat)) } bayesm/R/rsurgibbs_rcpp.r0000644000176000001440000001165712566706215015220 0ustar ripleyusersrsurGibbs= function(Data,Prior,Mcmc) { # # revision history: # P. Rossi 9/05 # 3/07 added classes # 9/14 changed to improve computations by avoiding Kronecker products # W. Taylor 4/15 - added nprint option to MCMC argument # Purpose: # implement Gibbs Sampler for SUR # # Arguments: # Data -- regdata # regdata is a list of lists of data for each regression # regdata[[i]] contains data for regression equation i # regdata[[i]]$y is y, regdata[[i]]$X is X # note: each regression can have differing numbers of X vars # but you must have same no of obs in each equation. # Prior -- list of prior hyperparameters # betabar,A prior mean, prior precision # nu, V prior on Sigma # Mcmc -- list of MCMC parms # R number of draws # keep -- thinning parameter # nprint - print estimated time remaining on every nprint'th draw # # Output: # list of betadraw,Sigmadraw # # Model: # y_i = X_ibeta + e_i # y is nobs x 1 # X is nobs x k_i # beta is k_i x 1 vector of coefficients # i=1,nreg total regressions # # (e_1,k,...,e_nreg,k) ~ N(0,Sigma) k=1,...,nobs # # we can also write as stacked regression # y = Xbeta+e # y is nobs*nreg x 1,X is nobs*nreg x (sum(k_i)) # routine draws beta -- the stacked vector of all coefficients # # Priors: beta ~ N(betabar,A^-1) # Sigma ~ IW(nu,V) # # # check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of regdata")} if(is.null(Data$regdata)) {pandterm("Requires Data element regdata")} regdata=Data$regdata # # check regdata for validity # nreg=length(regdata) nobs=length(regdata[[1]]$y) nvar=0 indreg=double(nreg+1) y=NULL for (reg in 1:nreg) { if(length(regdata[[reg]]$y) != nobs || nrow(regdata[[reg]]$X) != nobs) {pandterm(paste("incorrect dimensions for regression",reg))} else {indreg[reg]=nvar+1 nvar=nvar+ncol(regdata[[reg]]$X); y=c(y,regdata[[reg]]$y)} } indreg[nreg+1]=nvar+1 # # check for Prior # if(missing(Prior)) { betabar=c(rep(0,nvar)); A=BayesmConstant.A*diag(nvar); nu=nreg+BayesmConstant.nuInc; V=nu*diag(nreg)} else { if(is.null(Prior$betabar)) {betabar=c(rep(0,nvar))} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=BayesmConstant.A*diag(nvar)} else {A=Prior$A} if(is.null(Prior$nu)) {nu=nreg+BayesmConstant.nuInc} else {nu=Prior$nu} if(is.null(Prior$V)) {V=nu*diag(nreg)} else {ssq=Prior$V} } # # check dimensions of Priors # if(ncol(A) != nrow(A) || ncol(A) != nvar || nrow(A) != nvar) {pandterm(paste("bad dimensions for A",dim(A)))} if(length(betabar) != nvar) {pandterm(paste("betabar wrong length, length= ",length(betabar)))} # # check MCMC argument # if(missing(Mcmc)) {pandterm("requires Mcmc argument")} else { if(is.null(Mcmc$R)) {pandterm("requires Mcmc element R")} else {R=Mcmc$R} if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} } # # print out problem # cat(" ", fill=TRUE) cat("Starting Gibbs Sampler for SUR Regression Model",fill=TRUE) cat(" with ",nreg," regressions",fill=TRUE) cat(" and ",nobs," observations for each regression",fill=TRUE) cat(" ", fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat("A",fill=TRUE) print(A) cat("nu = ",nu,fill=TRUE) cat("V = ",fill=TRUE) print(V) cat(" ", fill=TRUE) cat("MCMC parms: ",fill=TRUE) cat("R= ",R," keep= ",keep," nprint= ",nprint,fill=TRUE) cat(" ",fill=TRUE) # # set initial value of Sigma # E=matrix(double(nobs*nreg),ncol=nreg) for (reg in 1:nreg) { E[,reg]=lm(y~.-1,data=data.frame(y=regdata[[reg]]$y,regdata[[reg]]$X))$residuals } Sigma=(crossprod(E)+diag(.01,nreg))/nobs Sigmainv=chol2inv(chol(Sigma)) # # precompute various moments and indices into moment matrix and Abetabar nk=integer(nreg) Xstar=NULL Y=NULL for(i in 1:nreg){ nk[i]=ncol(regdata[[i]]$X) Xstar=cbind(Xstar,regdata[[i]]$X) Y=cbind(Y,regdata[[i]]$y) } cumnk=cumsum(nk) XspXs=crossprod(Xstar) Abetabar=A%*%betabar ################################################################### # Keunwoo Kim # 09/19/2014 ################################################################### draws=rsurGibbs_rcpp_loop(regdata,indreg,cumnk,nk,XspXs,Sigmainv,A,Abetabar,nu,V,nvar,E,Y,R,keep,nprint) ################################################################### attributes(draws$betadraw)$class=c("bayesm.mat","mcmc") attributes(draws$betadraw)$mcpar=c(1,R,keep) attributes(draws$Sigmadraw)$class=c("bayesm.var","bayesm.mat","mcmc") attributes(draws$Sigmadraw)$mcpar=c(1,R,keep) return(draws) } bayesm/R/rivGibbs_rcpp.R0000755000176000001440000001222012566706215014713 0ustar ripleyusersrivGibbs=function(Data,Prior,Mcmc) { # # revision history: # R. McCulloch original version 2/05 # p. rossi 3/05 # p. rossi 1/06 -- fixed error in nins # p. rossi 1/06 -- fixed def Prior settings for nu,V # 3/07 added classes # W. Taylor 4/15 - added nprint option to MCMC argument # # # purpose: # draw from posterior for linear I.V. model # # Arguments: # Data -- list of z,w,x,y # y is vector of obs on lhs var in structural equation # x is "endogenous" var in structural eqn # w is matrix of obs on "exogenous" vars in the structural eqn # z is matrix of obs on instruments # Prior -- list of md,Ad,mbg,Abg,nu,V # md is prior mean of delta # Ad is prior prec # mbg is prior mean vector for beta,gamma # Abg is prior prec of same # nu,V parms for IW on Sigma # # Mcmc -- list of R,keep # R is number of draws # keep is thinning parameter # nprint - print estimated time remaining on every nprint'th draw # # Output: # list of draws of delta,beta,gamma and Sigma # # Model: # # x=z'delta + e1 # y=beta*x + w'gamma + e2 # e1,e2 ~ N(0,Sigma) # # Priors # delta ~ N(md,Ad^-1) # vec(beta,gamma) ~ N(mbg,Abg^-1) # Sigma ~ IW(nu,V) # # check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of z,w,x,y")} if(is.null(Data$z)) {pandterm("Requires Data element z")} z=Data$z if(is.null(Data$w)) {pandterm("Requires Data element w")} w=Data$w if(is.null(Data$x)) {pandterm("Requires Data element x")} x=Data$x if(is.null(Data$y)) {pandterm("Requires Data element y")} y=Data$y # # check data for validity # if(!is.vector(x)) {pandterm("x must be a vector")} if(!is.vector(y)) {pandterm("y must be a vector")} n=length(y) if(!is.matrix(w)) {pandterm("w is not a matrix")} if(!is.matrix(z)) {pandterm("z is not a matrix")} dimd=ncol(z) dimg=ncol(w) if(n != length(x) ) {pandterm("length(y) ne length(x)")} if(n != nrow(w) ) {pandterm("length(y) ne nrow(w)")} if(n != nrow(z) ) {pandterm("length(y) ne nrow(z)")} # # check for Prior # if(missing(Prior)) { md=c(rep(0,dimd));Ad=BayesmConstant.A*diag(dimd); mbg=c(rep(0,(1+dimg))); Abg=BayesmConstant.A*diag((1+dimg)); nu=3; V=diag(2)} else { if(is.null(Prior$md)) {md=c(rep(0,dimd))} else {md=Prior$md} if(is.null(Prior$Ad)) {Ad=BayesmConstant.A*diag(dimd)} else {Ad=Prior$Ad} if(is.null(Prior$mbg)) {mbg=c(rep(0,(1+dimg)))} else {mbg=Prior$mbg} if(is.null(Prior$Abg)) {Abg=BayesmConstant.A*diag((1+dimg))} else {Abg=Prior$Abg} if(is.null(Prior$nu)) {nu=3} else {nu=Prior$nu} if(is.null(Prior$V)) {V=nu*diag(2)} else {V=Prior$V} } # # check dimensions of Priors # if(ncol(Ad) != nrow(Ad) || ncol(Ad) != dimd || nrow(Ad) != dimd) {pandterm(paste("bad dimensions for Ad",dim(Ad)))} if(length(md) != dimd) {pandterm(paste("md wrong length, length= ",length(md)))} if(ncol(Abg) != nrow(Abg) || ncol(Abg) != (1+dimg) || nrow(Abg) != (1+dimg)) {pandterm(paste("bad dimensions for Abg",dim(Abg)))} if(length(mbg) != (1+dimg)) {pandterm(paste("mbg wrong length, length= ",length(mbg)))} # # check MCMC argument # if(missing(Mcmc)) {pandterm("requires Mcmc argument")} else { if(is.null(Mcmc$R)) {pandterm("requires Mcmc element R")} else {R=Mcmc$R} if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} } # # print out model # cat(" ",fill=TRUE) cat("Starting Gibbs Sampler for Linear IV Model",fill=TRUE) cat(" ",fill=TRUE) cat(" nobs= ",n,"; ",ncol(z)," instruments; ",ncol(w)," included exog vars",fill=TRUE) cat(" Note: the numbers above include intercepts if in z or w",fill=TRUE) cat(" ",fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("mean of delta ",fill=TRUE) print(md) cat("Adelta",fill=TRUE) print(Ad) cat("mean of beta/gamma",fill=TRUE) print(mbg) cat("Abeta/gamma",fill=TRUE) print(Abg) cat("Sigma Prior Parms",fill=TRUE) cat("nu= ",nu," V=",fill=TRUE) print(V) cat(" ",fill=TRUE) cat("MCMC parms: ",fill=TRUE) cat("R= ",R," keep= ",keep," nprint= ",nprint,fill=TRUE) cat(" ",fill=TRUE) ################################################################### # Keunwoo Kim # 09/03/2014 ################################################################### draws=rivGibbs_rcpp_loop(y, x, z, w, mbg, Abg, md, Ad, V, nu, R, keep, nprint) ################################################################### attributes(draws$deltadraw)$class=c("bayesm.mat","mcmc") attributes(draws$deltadraw)$mcpar=c(1,R,keep) attributes(draws$betadraw)$class=c("bayesm.mat","mcmc") attributes(draws$betadraw)$mcpar=c(1,R,keep) attributes(draws$gammadraw)$class=c("bayesm.mat","mcmc") attributes(draws$gammadraw)$mcpar=c(1,R,keep) attributes(draws$Sigmadraw)$class=c("bayesm.var","bayesm.mat","mcmc") attributes(draws$Sigmadraw)$mcpar=c(1,R,keep) return(draws) } bayesm/R/rmnpgibbs_rcpp.r0000644000176000001440000001123412566706215015170 0ustar ripleyusersrmnpGibbs=function(Data,Prior,Mcmc) { # # Revision History: # modified by rossi 12/18/04 to include error checking # 3/07 added classes # W. Taylor 4/15 - added nprint option to MCMC argument # # purpose: Gibbs MNP model with full covariance matrix # # Arguments: # Data contains # p the number of choice alternatives # y -- a vector of length n with choices (takes on values from 1, .., p) # X -- n(p-1) x k matrix of covariates (including intercepts) # note: X is the differenced matrix unlike MNL X=stack(X_1,..,X_n) # each X_i is (p-1) x nvar # # Prior contains a list of (betabar, A, nu, V) # if elements of prior do not exist, defaults are used # # Mcmc is a list of (beta0,sigma0,R,keep) # beta0,sigma0 are intial values, if not supplied defaults are used # R is number of draws # keep is thinning parm, keep every keepth draw # nprint - print estimated time remaining on every nprint'th draw # # Output: a list of every keepth betadraw and sigmsdraw # # model: # w_i = X_ibeta + e e~N(0,Sigma) note w_i,e are (p-1) x 1 # y_i = j if w_ij > w_i-j j=1,...,p-1 # y_i = p if all w_i < 0 # # priors: # beta ~ N(betabar,A^-1) # Sigma ~ IW(nu,V) # # Check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of p, y, X")} if(is.null(Data$p)) {pandterm("Requires Data element p -- number of alternatives")} p=Data$p if(is.null(Data$y)) {pandterm("Requires Data element y -- number of alternatives")} y=Data$y if(is.null(Data$X)) {pandterm("Requires Data element X -- matrix of covariates")} X=Data$X # # check data for validity # levely=as.numeric(levels(as.factor(y))) if(length(levely) != p) {pandterm(paste("y takes on ",length(levely), " values -- must be ",p))} bady=FALSE for (i in 1:p) { if(levely[i] != i) bady=TRUE } cat("Table of y values",fill=TRUE) print(table(y)) if (bady) {pandterm("Invalid y")} n=length(y) k=ncol(X) pm1=p-1 if(nrow(X)/n != pm1) {pandterm(paste("X has ",nrow(X)," rows; must be = (p-1)n"))} # # check for prior elements # if(missing(Prior)) { betabar=rep(0,k) ; A=BayesmConstant.A*diag(k) ; nu=pm1+3; V=nu*diag(pm1)} else {if(is.null(Prior$betabar)) {betabar=rep(0,k)} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=BayesmConstant.A*diag(k)} else {A=Prior$A} if(is.null(Prior$nu)) {nu=pm1+BayesmConstant.nuInc} else {nu=Prior$nu} if(is.null(Prior$V)) {V=nu*diag(pm1)} else {V=Prior$V}} if(length(betabar) != k) pandterm("length betabar ne k") if(sum(dim(A)==c(k,k)) != 2) pandterm("A is of incorrect dimension") if(nu < 1) pandterm("invalid nu value") if(sum(dim(V)==c(pm1,pm1)) != 2) pandterm("V is of incorrect dimension") # # check for Mcmc # if(missing(Mcmc)) pandterm("Requires Mcmc argument -- at least R must be included") if(is.null(Mcmc$R)) {pandterm("Requires element R of Mcmc")} else {R=Mcmc$R} if(is.null(Mcmc$beta0)) {beta0=rep(0,k)} else {beta0=Mcmc$beta0} if(is.null(Mcmc$sigma0)) {sigma0=diag(pm1)} else {sigma0=Mcmc$sigma0} if(length(beta0) != k) pandterm("beta0 is not of length k") if(sum(dim(sigma0) == c(pm1,pm1)) != 2) pandterm("sigma0 is of incorrect dimension") if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} # # print out problem # cat(" ",fill=TRUE) cat("Starting Gibbs Sampler for MNP",fill=TRUE) cat(" ",n," obs; ",p," choice alternatives; ",k," indep vars (including intercepts)",fill=TRUE) cat(" ",fill=TRUE) cat("Table of y values",fill=TRUE) print(table(y)) cat("Prior Parms:",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat("A",fill=TRUE) print(A) cat("nu",fill=TRUE) print(nu) cat("V",fill=TRUE) print(V) cat(" ",fill=TRUE) cat("MCMC Parms:",fill=TRUE) cat(" ",R," reps; keeping every ",keep,"th draw"," nprint= ",nprint,fill=TRUE) cat("initial beta= ",beta0,fill=TRUE) cat("initial sigma= ",sigma0,fill=TRUE) cat(" ",fill=TRUE) ################################################################### # Wayne Taylor # 09/03/2014 ################################################################### loopout = rmnpGibbs_rcpp_loop(R,keep,nprint,pm1,y,X,beta0,sigma0,V,nu,betabar,A); ################################################################### attributes(loopout$betadraw)$class=c("bayesm.mat","mcmc") attributes(loopout$betadraw)$mcpar=c(1,R,keep) attributes(loopout$sigmadraw)$class=c("bayesm.var","bayesm.mat","mcmc") attributes(loopout$sigmadraw)$mcpar=c(1,R,keep) return(loopout) } bayesm/R/BayesmConstants.R0000644000176000001440000000345212566706215015241 0ustar ripleyusers#MCMC BayesmConstant.keep = 1 #keep every keepth draw for MCMC routines BayesmConstant.nprint = 100 #print the remaining time on every nprint'th draw BayesmConstant.RRScaling = 2.38 #Roberts and Rosenthal optimal scaling constant BayesmConstant.w = .1 #fractional likelihood weighting parameter #Priors BayesmConstant.A = .01 #scaling factor for the prior precision matrix BayesmConstant.nuInc = 3 #Increment for nu BayesmConstant.a = 5 #Dirichlet parameter for mixture models BayesmConstant.nu.e = 3.0 #degrees of freedom parameter for regression error variance prior BayesmConstant.nu = 3.0 #degrees of freedom parameter for Inverted Wishart prior BayesmConstant.agammaprior = .5 #Gamma prior parameter BayesmConstant.bgammaprior = .1 #Gamma prior parameter #DP BayesmConstant.DPalimdef=c(.01,10) #defines support of 'a' distribution BayesmConstant.DPnulimdef=c(.01,3) #defines support of nu distribution BayesmConstant.DPvlimdef=c(.1,4) #defines support of v distribution BayesmConstant.DPIstarmin = 1 #expected number of components at lower bound of support of alpha BayesmConstant.DPpower = .8 #power parameter for alpha prior BayesmConstant.DPalpha = 1.0 #intitalized value for alpha draws BayesmConstant.DPmaxuniq = 200 #storage constraint on the number of unique components BayesmConstant.DPSCALE = TRUE #should data be scaled by mean,std deviation before posterior draws BayesmConstant.DPgridsize = 20 #number of discrete points for hyperparameter priors #Mathematical Constants BayesmConstant.gamma = .5772156649015328606 #BayesBLP BayesmConstant.BLPVOmega = matrix(c(1,0.5,0.5,1),2,2) #IW prior parameter of correlated shocks in IV bayesBLP BayesmConstant.BLPtol = 1e-6bayesm/R/RcppExports.R0000644000176000001440000002013013117541521014373 0ustar ripleyusers# Generated by using Rcpp::compileAttributes() -> do not edit by hand # Generator token: 10BE3573-1514-4C36-9D1C-5A225CD40393 bayesBLP_rcpp_loop <- function(IV, X, Z, share, J, T, v, R, sigmasqR, A, theta_hat, deltabar, Ad, nu0, s0_sq, VOmega, ssq, cand_cov, theta_bar_initial, r_initial, tau_sq_initial, Omega_initial, delta_initial, tol, keep, nprint) { .Call('bayesm_bayesBLP_rcpp_loop', PACKAGE = 'bayesm', IV, X, Z, share, J, T, v, R, sigmasqR, A, theta_hat, deltabar, Ad, nu0, s0_sq, VOmega, ssq, cand_cov, theta_bar_initial, r_initial, tau_sq_initial, Omega_initial, delta_initial, tol, keep, nprint) } breg <- function(y, X, betabar, A) { .Call('bayesm_breg', PACKAGE = 'bayesm', y, X, betabar, A) } cgetC <- function(e, k) { .Call('bayesm_cgetC', PACKAGE = 'bayesm', e, k) } clusterMix_rcpp_loop <- function(zdraw, cutoff, SILENT, nprint) { .Call('bayesm_clusterMix_rcpp_loop', PACKAGE = 'bayesm', zdraw, cutoff, SILENT, nprint) } ghkvec <- function(L, trunpt, above, r, HALTON = TRUE, pn = as.integer( c(0))) { .Call('bayesm_ghkvec', PACKAGE = 'bayesm', L, trunpt, above, r, HALTON, pn) } llmnl <- function(beta, y, X) { .Call('bayesm_llmnl', PACKAGE = 'bayesm', beta, y, X) } lndIChisq <- function(nu, ssq, X) { .Call('bayesm_lndIChisq', PACKAGE = 'bayesm', nu, ssq, X) } lndIWishart <- function(nu, V, IW) { .Call('bayesm_lndIWishart', PACKAGE = 'bayesm', nu, V, IW) } lndMvn <- function(x, mu, rooti) { .Call('bayesm_lndMvn', PACKAGE = 'bayesm', x, mu, rooti) } lndMvst <- function(x, nu, mu, rooti, NORMC = FALSE) { .Call('bayesm_lndMvst', PACKAGE = 'bayesm', x, nu, mu, rooti, NORMC) } rbprobitGibbs_rcpp_loop <- function(y, X, Abetabar, root, beta, sigma, trunpt, above, R, keep, nprint) { .Call('bayesm_rbprobitGibbs_rcpp_loop', PACKAGE = 'bayesm', y, X, Abetabar, root, beta, sigma, trunpt, above, R, keep, nprint) } rdirichlet <- function(alpha) { .Call('bayesm_rdirichlet', PACKAGE = 'bayesm', alpha) } rDPGibbs_rcpp_loop <- function(R, keep, nprint, y, lambda_hyper, SCALE, maxuniq, PrioralphaList, gridsize, BayesmConstantA, BayesmConstantnuInc, BayesmConstantDPalpha) { .Call('bayesm_rDPGibbs_rcpp_loop', PACKAGE = 'bayesm', R, keep, nprint, y, lambda_hyper, SCALE, maxuniq, PrioralphaList, gridsize, BayesmConstantA, BayesmConstantnuInc, BayesmConstantDPalpha) } rhierLinearMixture_rcpp_loop <- function(regdata, Z, deltabar, Ad, mubar, Amu, nu, V, nu_e, ssq, R, keep, nprint, drawdelta, olddelta, a, oldprob, ind, tau) { .Call('bayesm_rhierLinearMixture_rcpp_loop', PACKAGE = 'bayesm', regdata, Z, deltabar, Ad, mubar, Amu, nu, V, nu_e, ssq, R, keep, nprint, drawdelta, olddelta, a, oldprob, ind, tau) } rhierLinearModel_rcpp_loop <- function(regdata, Z, Deltabar, A, nu, V, nu_e, ssq, tau, Delta, Vbeta, R, keep, nprint) { .Call('bayesm_rhierLinearModel_rcpp_loop', PACKAGE = 'bayesm', regdata, Z, Deltabar, A, nu, V, nu_e, ssq, tau, Delta, Vbeta, R, keep, nprint) } rhierMnlDP_rcpp_loop <- function(R, keep, nprint, lgtdata, Z, deltabar, Ad, PrioralphaList, lambda_hyper, drawdelta, nvar, oldbetas, s, maxuniq, gridsize, BayesmConstantA, BayesmConstantnuInc, BayesmConstantDPalpha) { .Call('bayesm_rhierMnlDP_rcpp_loop', PACKAGE = 'bayesm', R, keep, nprint, lgtdata, Z, deltabar, Ad, PrioralphaList, lambda_hyper, drawdelta, nvar, oldbetas, s, maxuniq, gridsize, BayesmConstantA, BayesmConstantnuInc, BayesmConstantDPalpha) } llmnl_con <- function(betastar, y, X, SignRes = as.numeric( c(0))) { .Call('bayesm_llmnl_con', PACKAGE = 'bayesm', betastar, y, X, SignRes) } rhierMnlRwMixture_rcpp_loop <- function(lgtdata, Z, deltabar, Ad, mubar, Amu, nu, V, s, R, keep, nprint, drawdelta, olddelta, a, oldprob, oldbetas, ind, SignRes) { .Call('bayesm_rhierMnlRwMixture_rcpp_loop', PACKAGE = 'bayesm', lgtdata, Z, deltabar, Ad, mubar, Amu, nu, V, s, R, keep, nprint, drawdelta, olddelta, a, oldprob, oldbetas, ind, SignRes) } rhierNegbinRw_rcpp_loop <- function(regdata, hessdata, Z, Beta, Delta, Deltabar, Adelta, nu, V, a, b, R, keep, sbeta, alphacroot, nprint, rootA, alpha, fixalpha) { .Call('bayesm_rhierNegbinRw_rcpp_loop', PACKAGE = 'bayesm', regdata, hessdata, Z, Beta, Delta, Deltabar, Adelta, nu, V, a, b, R, keep, sbeta, alphacroot, nprint, rootA, alpha, fixalpha) } rivDP_rcpp_loop <- function(R, keep, nprint, dimd, mbg, Abg, md, Ad, y, isgamma, z, x, w, delta, PrioralphaList, gridsize, SCALE, maxuniq, scalex, scaley, lambda_hyper, BayesmConstantA, BayesmConstantnu) { .Call('bayesm_rivDP_rcpp_loop', PACKAGE = 'bayesm', R, keep, nprint, dimd, mbg, Abg, md, Ad, y, isgamma, z, x, w, delta, PrioralphaList, gridsize, SCALE, maxuniq, scalex, scaley, lambda_hyper, BayesmConstantA, BayesmConstantnu) } rivGibbs_rcpp_loop <- function(y, x, z, w, mbg, Abg, md, Ad, V, nu, R, keep, nprint) { .Call('bayesm_rivGibbs_rcpp_loop', PACKAGE = 'bayesm', y, x, z, w, mbg, Abg, md, Ad, V, nu, R, keep, nprint) } rmixGibbs <- function(y, Bbar, A, nu, V, a, p, z) { .Call('bayesm_rmixGibbs', PACKAGE = 'bayesm', y, Bbar, A, nu, V, a, p, z) } rmixture <- function(n, pvec, comps) { .Call('bayesm_rmixture', PACKAGE = 'bayesm', n, pvec, comps) } rmnlIndepMetrop_rcpp_loop <- function(R, keep, nu, betastar, root, y, X, betabar, rootpi, rooti, oldlimp, oldlpost, nprint) { .Call('bayesm_rmnlIndepMetrop_rcpp_loop', PACKAGE = 'bayesm', R, keep, nu, betastar, root, y, X, betabar, rootpi, rooti, oldlimp, oldlpost, nprint) } rmnpGibbs_rcpp_loop <- function(R, keep, nprint, pm1, y, X, beta0, sigma0, V, nu, betabar, A) { .Call('bayesm_rmnpGibbs_rcpp_loop', PACKAGE = 'bayesm', R, keep, nprint, pm1, y, X, beta0, sigma0, V, nu, betabar, A) } rmultireg <- function(Y, X, Bbar, A, nu, V) { .Call('bayesm_rmultireg', PACKAGE = 'bayesm', Y, X, Bbar, A, nu, V) } rmvpGibbs_rcpp_loop <- function(R, keep, nprint, p, y, X, beta0, sigma0, V, nu, betabar, A) { .Call('bayesm_rmvpGibbs_rcpp_loop', PACKAGE = 'bayesm', R, keep, nprint, p, y, X, beta0, sigma0, V, nu, betabar, A) } rmvst <- function(nu, mu, root) { .Call('bayesm_rmvst', PACKAGE = 'bayesm', nu, mu, root) } rnegbinRw_rcpp_loop <- function(y, X, betabar, rootA, a, b, beta, alpha, fixalpha, betaroot, alphacroot, R, keep, nprint) { .Call('bayesm_rnegbinRw_rcpp_loop', PACKAGE = 'bayesm', y, X, betabar, rootA, a, b, beta, alpha, fixalpha, betaroot, alphacroot, R, keep, nprint) } rnmixGibbs_rcpp_loop <- function(y, Mubar, A, nu, V, a, p, z, R, keep, nprint) { .Call('bayesm_rnmixGibbs_rcpp_loop', PACKAGE = 'bayesm', y, Mubar, A, nu, V, a, p, z, R, keep, nprint) } rordprobitGibbs_rcpp_loop <- function(y, X, k, A, betabar, Ad, s, inc_root, dstarbar, betahat, R, keep, nprint) { .Call('bayesm_rordprobitGibbs_rcpp_loop', PACKAGE = 'bayesm', y, X, k, A, betabar, Ad, s, inc_root, dstarbar, betahat, R, keep, nprint) } rscaleUsage_rcpp_loop <- function(k, x, p, n, R, keep, ndghk, nprint, y, mu, Sigma, tau, sigma, Lambda, e, domu, doSigma, dosigma, dotau, doLambda, doe, nu, V, mubar, Am, gsigma, gl11, gl22, gl12, nuL, VL, ge) { .Call('bayesm_rscaleUsage_rcpp_loop', PACKAGE = 'bayesm', k, x, p, n, R, keep, ndghk, nprint, y, mu, Sigma, tau, sigma, Lambda, e, domu, doSigma, dosigma, dotau, doLambda, doe, nu, V, mubar, Am, gsigma, gl11, gl22, gl12, nuL, VL, ge) } rsurGibbs_rcpp_loop <- function(regdata, indreg, cumnk, nk, XspXs, Sigmainv, A, Abetabar, nu, V, nvar, E, Y, R, keep, nprint) { .Call('bayesm_rsurGibbs_rcpp_loop', PACKAGE = 'bayesm', regdata, indreg, cumnk, nk, XspXs, Sigmainv, A, Abetabar, nu, V, nvar, E, Y, R, keep, nprint) } rtrun <- function(mu, sigma, a, b) { .Call('bayesm_rtrun', PACKAGE = 'bayesm', mu, sigma, a, b) } runireg_rcpp_loop <- function(y, X, betabar, A, nu, ssq, R, keep, nprint) { .Call('bayesm_runireg_rcpp_loop', PACKAGE = 'bayesm', y, X, betabar, A, nu, ssq, R, keep, nprint) } runiregGibbs_rcpp_loop <- function(y, X, betabar, A, nu, ssq, sigmasq, R, keep, nprint) { .Call('bayesm_runiregGibbs_rcpp_loop', PACKAGE = 'bayesm', y, X, betabar, A, nu, ssq, sigmasq, R, keep, nprint) } rwishart <- function(nu, V) { .Call('bayesm_rwishart', PACKAGE = 'bayesm', nu, V) } callroot <- function(c1, c2, tol, iterlim) { .Call('bayesm_callroot', PACKAGE = 'bayesm', c1, c2, tol, iterlim) } bayesm/R/plot.bayesm.hcoef.R0000755000176000001440000000317512566706215015451 0ustar ripleyusersplot.bayesm.hcoef=function(x,names,burnin=trunc(.1*R),...){ # # S3 method to plot arrays of draws of coefs in hier models # 3 dimensional arrays: unit x var x draw # P. Rossi 2/07 # X=x if(mode(X) == "list") stop("list entered \n Possible Fixup: extract from list \n") if(mode(X) !="numeric") stop("Requires numeric argument \n") d=dim(X) if(length(d) !=3) stop("Requires 3-dim array \n") op=par(no.readonly=TRUE) on.exit(par(op)) on.exit(devAskNewPage(FALSE),add=TRUE) nunits=d[1] nvar=d[2] R=d[3] if(missing(names)) {names=as.character(1:nvar)} if(R < 100) {cat("fewer than 100 draws submitted \n"); return(invisible())} # # plot posterior distributions of nvar coef for 30 rand units # rsam=sort(sample(c(1:nunits),30)) # randomly sample 30 cross-sectional units par(mfrow=c(1,1)) par(las=3) # horizontal labeling devAskNewPage(TRUE) for(var in 1:nvar){ ext=X[rsam,var,(burnin+1):R]; ext=data.frame(t(ext)) colnames(ext)=as.character(rsam) out=boxplot(ext,plot=FALSE,...) out$stats=apply(ext,2,quantile,probs=c(0,.05,.95,1)) bxp(out,xlab="Cross-sectional Unit",main=paste("Coefficients on Var ",names[var],sep=""),boxfill="magenta",...) } # # plot posterior means for each var # par(las=1) pmeans=matrix(0,nrow=nunits,ncol=nvar) for(i in 1:nunits) pmeans[i,]=apply(X[i,,(burnin+1):R],1,mean) attributes(pmeans)$class="bayesm.mat" for(var in 1:nvar) names[var]=paste("Posterior Means of Coef ",names[var],sep="") plot(pmeans,names,TRACEPLOT=FALSE,INT=FALSE,DEN=FALSE,CHECK_NDRAWS=FALSE,...) invisible() } bayesm/R/plot.bayesm.mat.R0000755000176000001440000000437712566706215015153 0ustar ripleyusersplot.bayesm.mat=function(x,names,burnin=trunc(.1*nrow(X)),tvalues,TRACEPLOT=TRUE,DEN=TRUE,INT=TRUE, CHECK_NDRAWS=TRUE,...){ # # S3 method to print matrices of draws the object X is of class "bayesm.mat" # # P. Rossi 2/07 # X=x if(mode(X) == "list") stop("list entered \n Possible Fixup: extract from list \n") if(mode(X) !="numeric") stop("Requires numeric argument \n") op=par(no.readonly=TRUE) on.exit(par(op)) on.exit(devAskNewPage(FALSE),add=TRUE) if(is.null(attributes(X)$dim)) X=as.matrix(X) nx=ncol(X) if(nrow(X) < 100 & CHECK_NDRAWS) {cat("fewer than 100 draws submitted \n"); return(invisible())} if(!missing(tvalues)){ if(mode(tvalues) !="numeric") {stop("tvalues must be a numeric vector \n")} else {if(length(tvalues)!=nx) stop("tvalues are wrong length \n")} } if(nx==1) par(mfrow=c(1,1)) if(nx==2) par(mfrow=c(2,1)) if(nx==3) par(mfrow=c(3,1)) if(nx==4) par(mfrow=c(2,2)) if(nx>=5) par(mfrow=c(3,2)) if(missing(names)) {names=as.character(1:nx)} if (DEN) ylabtxt="density" else ylabtxt="freq" devAskNewPage(TRUE) for(index in 1:nx){ hist(X[(burnin+1):nrow(X),index],xlab="",ylab=ylabtxt,main=names[index],freq=!DEN,col="magenta",...) if(!missing(tvalues)) abline(v=tvalues[index],lwd=2,col="blue") if(INT){ quants=quantile(X[(burnin+1):nrow(X),index],prob=c(.025,.975)) mean=mean(X[(burnin+1):nrow(X),index]) semean=numEff(X[(burnin+1):nrow(X),index])$stderr text(quants[1],0,"|",cex=3.0,col="green") text(quants[2],0,"|",cex=3.0,col="green") text(mean,0,"|",cex=3.0,col="red") text(mean-2*semean,0,"|",cex=2,col="yellow") text(mean+2*semean,0,"|",cex=2,col="yellow") } } if(TRACEPLOT){ if(nx==1) par(mfrow=c(1,2)) if(nx==2) par(mfrow=c(2,2)) if(nx>=3) par(mfrow=c(3,2)) for(index in 1:nx){ plot(as.vector(X[,index]),xlab="",ylab="",main=names[index],type="l",col="red") if(!missing(tvalues)) abline(h=tvalues[index],lwd=2,col="blue") if(var(X[,index])>1.0e-20) {acf(as.vector(X[,index]),xlab="",ylab="",main="")} else {plot.default(X[,index],xlab="",ylab="",type="n",main="No ACF Produced")} } } invisible() } bayesm/R/rhierLinearModel_rcpp.R0000644000176000001440000001560013117541521016361 0ustar ripleyusersrhierLinearModel= function(Data,Prior,Mcmc) { # # Revision History # 1/17/05 P. Rossi # 10/05 fixed error in setting prior if Prior argument is missing # 3/07 added classes # W. Taylor 4/15 - added nprint option to MCMC argument # # Purpose: # run hiearchical regression model # # Arguments: # Data list of regdata,Z # regdata is a list of lists each list with members y, X # e.g. regdata[[i]]=list(y=y,X=X) # X has nvar columns # Z is nreg=length(regdata) x nz # Prior list of prior hyperparameters # Deltabar,A, nu.e,ssq,nu,V # note: ssq is a nreg x 1 vector! # Mcmc # list of Mcmc parameters # R is number of draws # keep is thining parameter -- keep every keepth draw # nprint - print estimated time remaining on every nprint'th draw # # Output: # list of # betadraw -- nreg x nvar x R/keep array of individual regression betas # taudraw -- R/keep x nreg array of error variances for each regression # Deltadraw -- R/keep x nz x nvar array of Delta draws # Vbetadraw -- R/keep x nvar*nvar array of Vbeta draws # # Model: # nreg regression equations # y_i = X_ibeta_i + epsilon_i # epsilon_i ~ N(0,tau_i) # nvar X vars in each equation # # Priors: # tau_i ~ nu.e*ssq_i/chisq(nu.e) tau_i is the variance of epsilon_i # beta_i ~ N(ZDelta[i,],V_beta) # Note: ZDelta is the matrix Z * Delta; [i,] refers to ith row of this product! # # vec(Delta) | V_beta ~ N(vec(Deltabar),Vbeta (x) A^-1) # V_beta ~ IW(nu,V) or V_beta^-1 ~ W(nu,V^-1) # Delta, Deltabar are nz x nvar # A is nz x nz # Vbeta is nvar x nvar # # NOTE: if you don't have any z vars, set Z=iota (nreg x 1) # # # create needed functions # #------------------------------------------------------------------------------ append=function(l) { l=c(l,list(XpX=crossprod(l$X),Xpy=crossprod(l$X,l$y)))} # getvar=function(l) { v=var(l$y) if(is.na(v)) return(1) if(v>0) return (v) else return (1)} # #------------------------------------------------------------------------------ # # # check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of regdata and Z")} if(is.null(Data$regdata)) {pandterm("Requires Data element regdata")} regdata=Data$regdata nreg=length(regdata) if(is.null(Data$Z)) { cat("Z not specified -- putting in iota",fill=TRUE); fsh() ; Z=matrix(rep(1,nreg),ncol=1)} else {if (!is.matrix(Data$Z)) {pandterm("Z must be a matrix")} else {if (nrow(Data$Z) != nreg) {pandterm(paste("Nrow(Z) ",nrow(Z),"ne number regressions ",nreg))} else {Z=Data$Z}}} nz=ncol(Z) # # check data for validity # for (i in 1:nreg) { if(!is.matrix(regdata[[i]]$X)) {pandterm(paste0("regdata[[",i,"]]$X must be a matrix"))} if(!is.vector(regdata[[i]]$y, mode = "numeric") & !is.vector(regdata[[i]]$y, mode = "logical") & !is.matrix(regdata[[i]]$y)) {pandterm(paste0("regdata[[",i,"]]$y must be a numeric or logical vector or matrix"))} if(is.matrix(regdata[[i]]$y)){ if(ncol(regdata[[i]]$y)>1) {pandterm(paste0("regdata[[",i,"]]$y must be a vector or one-column matrix"))}} } dimfun=function(l) {c(length(l$y),dim(l$X))} dims=sapply(regdata,dimfun) dims=t(dims) nvar=quantile(dims[,3],prob=.5) for (i in 1:nreg) { if(dims[i,1] != dims[i,2] || dims[i,3] !=nvar) {pandterm(paste("Bad Data dimensions for unit ",i," dims(y,X) =",dims[i,]))} } # # check for Prior # if(missing(Prior)) { Deltabar=matrix(rep(0,nz*nvar),ncol=nvar); A=BayesmConstant.A*diag(nz); nu.e=BayesmConstant.nu.e; ssq=sapply(regdata,getvar) ; nu=nvar+BayesmConstant.nuInc ; V= nu*diag(nvar)} else { if(is.null(Prior$Deltabar)) {Deltabar=matrix(rep(0,nz*nvar),ncol=nvar)} else {Deltabar=Prior$Deltabar} if(is.null(Prior$A)) {A=BayesmConstant.A*diag(nz)} else {A=Prior$A} if(is.null(Prior$nu.e)) {nu.e=BayesmConstant.nu.e} else {nu.e=Prior$nu.e} if(is.null(Prior$ssq)) {ssq=sapply(regdata,getvar)} else {ssq=Prior$ssq} if(is.null(Prior$nu)) {nu=nvar+BayesmConstant.nuInc} else {nu=Prior$nu} if(is.null(Prior$V)) {V=nu*diag(nvar)} else {V=Prior$V} } # # check dimensions of Priors # if(ncol(A) != nrow(A) || ncol(A) != nz || nrow(A) != nz) {pandterm(paste("bad dimensions for A",dim(A)))} if(nrow(Deltabar) != nz || ncol(Deltabar) != nvar) {pandterm(paste("bad dimensions for Deltabar ",dim(Deltabar)))} if(length(ssq) != nreg) {pandterm(paste("bad length for ssq ",length(ssq)))} if(ncol(V) != nvar || nrow(V) != nvar) {pandterm(paste("bad dimensions for V ",dim(V)))} # # check MCMC argument # if(missing(Mcmc)) {pandterm("requires Mcmc argument")} else { if(is.null(Mcmc$R)) {pandterm("requires Mcmc element R")} else {R=Mcmc$R} if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} } # # print out problem # cat(" ", fill=TRUE) cat("Starting Gibbs Sampler for Linear Hierarchical Model",fill=TRUE) cat(" ",nreg," Regressions",fill=TRUE) cat(" ",ncol(Z)," Variables in Z (if 1, then only intercept)",fill=TRUE) cat(" ", fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("Deltabar",fill=TRUE) print(Deltabar) cat("A",fill=TRUE) print(A) cat("nu.e (d.f. parm for regression error variances)= ",nu.e,fill=TRUE) cat("Vbeta ~ IW(nu,V)",fill=TRUE) cat("nu = ",nu,fill=TRUE) cat("V ",fill=TRUE) print(V) cat(" ", fill=TRUE) cat("MCMC parms: ",fill=TRUE) cat("R= ",R," keep= ",keep," nprint= ",nprint,fill=TRUE) cat(" ",fill=TRUE) # # allocate space for the draws and set initial values of Vbeta and Delta # tau=double(nreg) Delta=matrix(0,nz,nvar) Vbeta=diag(nvar) # # set up fixed parms for the draw of Vbeta,Delta # # note: in the notation of the MVR Y = X B # n x m n x k k x m # "n" = nreg # "m" = nvar # "k" = nz # general model: Beta = Z Delta + U # # Create XpX elements of regdata and initialize tau # regdata=lapply(regdata,append) tau=sapply(regdata,getvar) ################################################################### # Keunwoo Kim # 08/20/2014 ################################################################### draws=rhierLinearModel_rcpp_loop(regdata,Z,Deltabar,A,nu,V,nu.e,ssq,tau,Delta,Vbeta,R,keep,nprint) ################################################################### attributes(draws$taudraw)$class=c("bayesm.mat","mcmc") attributes(draws$taudraw)$mcpar=c(1,R,keep) attributes(draws$Deltadraw)$class=c("bayesm.mat","mcmc") attributes(draws$Deltadraw)$mcpar=c(1,R,keep) attributes(draws$Vbetadraw)$class=c("bayesm.var","bayesm.mat","mcmc") attributes(draws$Vbetadraw)$mcpar=c(1,R,keep) attributes(draws$betadraw)$class=c("bayesm.hcoef") return(draws) }bayesm/R/rnmixgibbs_rcpp.r0000644000176000001440000001343312566706215015354 0ustar ripleyusersrnmixGibbs= function(Data,Prior,Mcmc){ # # Revision History: # P. Rossi 3/05 # add check to see if Mubar is a vector 9/05 # fixed bug in saving comps draw comps[[mkeep]]= 9/05 # fixed so that ncomp can be =1; added check that nobs >= 2*ncomp 12/06 # 3/07 added classes # added log-likelihood 9/08 # W. Taylor 4/15 - added nprint option to MCMC argument # # purpose: do Gibbs sampling inference for a mixture of multivariate normals # # arguments: # Data is a list of y which is an n x k matrix of data -- each row # is an iid draw from the normal mixture # Prior is a list of (Mubar,A,nu,V,a,ncomp) # ncomp is required # if elements of the prior don't exist, defaults are assumed # Mcmc is a list of R, keep (thinning parameter), and nprint # Output: # list with elements # pdraw -- R/keep x ncomp array of mixture prob draws # zdraw -- R/keep x nobs array of indicators of mixture comp identity for each obs # compsdraw -- list of R/keep lists of lists of comp parm draws # e.g. compsdraw[[i]] is ith draw -- list of ncomp lists # compsdraw[[i]][[j]] is list of parms for jth normal component # if jcomp=compsdraw[[i]][j]] # ~N(jcomp[[1]],Sigma), Sigma = t(R)%*%R, R^{-1} = jcomp[[2]] # # Model: # y_i ~ N(mu_ind,Sigma_ind) # ind ~ iid multinomial(p) p is a 1x ncomp vector of probs # Priors: # mu_j ~ N(mubar,Sigma (x) A^-1) # mubar=vec(Mubar) # Sigma_j ~ IW(nu,V) # note: this is the natural conjugate prior -- a special case of multivariate # regression # p ~ Dirchlet(a) # # check arguments # # # ----------------------------------------------------------------------------------------- llnmix=function(Y,z,comps){ # # evaluate likelihood for mixture of normals # zu=unique(z) ll=0.0 for(i in 1:length(zu)){ Ysel=Y[z==zu[i],,drop=FALSE] ll=ll+sum(apply(Ysel,1,lndMvn,mu=comps[[zu[i]]]$mu,rooti=comps[[zu[i]]]$rooti)) } return(ll) } # ----------------------------------------------------------------------------------------- if(missing(Data)) {pandterm("Requires Data argument -- list of y")} if(is.null(Data$y)) {pandterm("Requires Data element y")} y=Data$y # # check data for validity # if(!is.matrix(y)) {pandterm("y must be a matrix")} nobs=nrow(y) dimy=ncol(y) # # check for Prior # if(missing(Prior)) {pandterm("requires Prior argument ")} else { if(is.null(Prior$ncomp)) {pandterm("requires number of mix comps -- Prior$ncomp")} else {ncomp=Prior$ncomp} if(is.null(Prior$Mubar)) {Mubar=matrix(rep(0,dimy),nrow=1)} else {Mubar=Prior$Mubar; if(is.vector(Mubar)) {Mubar=matrix(Mubar,nrow=1)}} if(is.null(Prior$A)) {A=matrix(BayesmConstant.A,ncol=1)} else {A=Prior$A} if(is.null(Prior$nu)) {nu=dimy+BayesmConstant.nuInc} else {nu=Prior$nu} if(is.null(Prior$V)) {V=nu*diag(dimy)} else {V=Prior$V} if(is.null(Prior$a)) {a=c(rep(BayesmConstant.a,ncomp))} else {a=Prior$a} } # # check for adequate no. of observations # if(nobs<2*ncomp) {pandterm("too few obs, nobs should be >= 2*ncomp")} # # check dimensions of Priors # if(ncol(A) != nrow(A) || ncol(A) != 1) {pandterm(paste("bad dimensions for A",dim(A)))} if(!is.matrix(Mubar)) {pandterm("Mubar must be a matrix")} if(nrow(Mubar) != 1 || ncol(Mubar) != dimy) {pandterm(paste("bad dimensions for Mubar",dim(Mubar)))} if(ncol(V) != nrow(V) || ncol(V) != dimy) {pandterm(paste("bad dimensions for V",dim(V)))} if(length(a) != ncomp) {pandterm(paste("a wrong length, length= ",length(a)))} bada=FALSE for(i in 1:ncomp){if(a[i] < 0) bada=TRUE} if(bada) pandterm("invalid values in a vector") # # check MCMC argument # if(missing(Mcmc)) {pandterm("requires Mcmc argument")} else { if(is.null(Mcmc$R)) {pandterm("requires Mcmc element R")} else {R=Mcmc$R} if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} if(is.null(Mcmc$LogLike)) {LogLike=FALSE} else {LogLike=Mcmc$LogLike} } # # print out the problem # cat(" Starting Gibbs Sampler for Mixture of Normals",fill=TRUE) cat(" ",nobs," observations on ",dimy," dimensional data",fill=TRUE) cat(" using ",ncomp," mixture components",fill=TRUE) cat(" ",fill=TRUE) cat(" Prior Parms: ",fill=TRUE) cat(" mu_j ~ N(mubar,Sigma (x) A^-1)",fill=TRUE) cat(" mubar = ",fill=TRUE) print(Mubar) cat(" precision parm for prior variance of mu vectors (A)= ",A,fill=TRUE) cat(" Sigma_j ~ IW(nu,V) nu= ",nu,fill=TRUE) cat(" V =",fill=TRUE) print(V) cat(" Dirichlet parameters ",fill=TRUE) print(a) cat(" ",fill=TRUE) cat(" Mcmc Parms: R= ",R," keep= ",keep," nprint= ",nprint," LogLike= ",LogLike,fill=TRUE) # pdraw=matrix(double(floor(R/keep)*ncomp),ncol=ncomp) # zdraw=matrix(double(floor(R/keep)*nobs),ncol=nobs) # compdraw=list() compsd=list() if(LogLike) ll=double(floor(R/keep)) # # set initial values of z # z=rep(c(1:ncomp),(floor(nobs/ncomp)+1)) z=z[1:nobs] cat(" ",fill=TRUE) cat("starting value for z",fill=TRUE) print(table(z)) cat(" ",fill=TRUE) p=c(rep(1,ncomp))/ncomp # note this is not used fsh() #Wayne Taylor 8/18/14##################################################### nmix = rnmixGibbs_rcpp_loop(y, Mubar, A, nu, V, a, p, z, R, keep, nprint); ########################################################################## attributes(nmix)$class="bayesm.nmix" if(LogLike){ zdraw = nmix$zdraw compdraw = nmix$compdraw ll = lapply(seq_along(compdraw), function(i) llnmix(y, zdraw[i,], compdraw[[i]])) return(list(ll=ll,nmix=nmix)) }else{ return(list(nmix=nmix)) } }bayesm/R/rbiNormGibbs.R0000755000176000001440000000635712566706215014515 0ustar ripleyusersrbiNormGibbs=function(initx=2,inity=-2,rho,burnin=100,R=500) { # # revision history: # P. Rossi 1/05 # # purpose: # illustrate the function of bivariate normal gibbs sampler # # arguments: # initx,inity initial values for draw sequence # rho correlation # burnin draws to be discarded in final paint # R -- number of draws # # output: # opens graph window and paints all moves and normal contours # list containing draw matrix # # model: # theta is bivariate normal with zero means, unit variances and correlation rho # # define needed functions # kernel= function(x,mu,rooti){ # function to evaluate -.5*log of MV NOrmal density kernel with mean mu, var Sigma # and with sigma^-1=rooti%*%t(rooti) # rooti is in the inverse of upper triangular chol root of sigma # note: this is the UL decomp of sigmai not LU! # Sigma=root'root root=inv(rooti) z=as.vector(t(rooti)%*%(x-mu)) (z%*%z) } # # check input arguments # if(missing(rho)) {pandterm("Requires rho argument ")} # # print out settings # cat("Bivariate Normal Gibbs Sampler",fill=TRUE) cat("rho= ",rho,fill=TRUE) cat("initial x,y coordinates= (",initx,",",inity,")",fill=TRUE) cat("burn-in= ",burnin," R= ",R,fill=TRUE) cat(" ",fill=TRUE) cat(" ",fill=TRUE) sd=(1-rho**2)**(.5) sigma=matrix(c(1,rho,rho,1),ncol=2) rooti=backsolve(chol(sigma),diag(2)) mu=c(0,0) x=seq(-3.5,3.5,length=100) y=x z=matrix(double(100*100),ncol=100) for (i in 1:length(x)) { for(j in 1:length(y)) { z[i,j]=kernel(c(x[i],y[j]),mu,rooti) } } prob=c(.1,.3,.5,.7,.9,.99) lev=qchisq(prob,2) par(mfrow=c(1,1)) contour(x,y,z,levels=lev,labels=prob, xlab="theta1",ylab="theta2",drawlabels=TRUE,col="green",labcex=1.3,lwd=2.0) title(paste("Gibbs Sampler with Intermediate Moves: Rho =",rho)) points(initx,inity,pch="B",cex=1.5) oldx=initx oldy=inity continue="y" r=0 draws=matrix(double(R*2),ncol=2) draws[1,]=c(initx,inity) cat(" ") cat("Starting Gibbs Sampler ....",fill=TRUE) cat("(hit enter or y to display moves one-at-a-time)",fill=TRUE) cat("('go' to paint all moves without stopping to prompt)",fill=TRUE) cat(" ",fill=TRUE) while(continue != "n"&& r < R) { if(continue != "go") continue=readline("cont?") newy=sd*rnorm(1) + rho*oldx lines(c(oldx,oldx),c(oldy,newy),col="magenta",lwd=1.5) newx=sd*rnorm(1)+rho*newy lines(c(oldx,newx),c(newy,newy),col="magenta",lwd=1.5) oldy=newy oldx=newx r=r+1 draws[r,]=c(newx,newy) } continue=readline("Show Comparison to iid Sampler?") if(continue != "n" & continue != "No" & continue != "no"){ par(mfrow=c(1,2)) contour(x,y,z,levels=lev, xlab="theta1",ylab="theta2",drawlabels=TRUE,labels=prob,labcex=1.1,col="green",lwd=2.0) title(paste("Gibbs Draws: Rho =",rho)) points(draws[(burnin+1):R,],pch=20,col="magenta",cex=.7) idraws=t(chol(sigma))%*%matrix(rnorm(2*(R-burnin)),nrow=2) idraws=t(idraws) contour(x,y,z,levels=lev, xlab="theta1",ylab="theta2",drawlabels=TRUE,labels=prob,labcex=1.1,col="green",lwd=2.0) title(paste("IID draws: Rho =",rho)) points(idraws,pch=20,col="magenta",cex=.7) } attributes(draws)$class=c("bayesm.mat","mcmc") attributes(draws)$mcpar=c(1,R,1) return(draws) } bayesm/R/summary.bayesm.var.R0000755000176000001440000000272412135054024015655 0ustar ripleyuserssummary.bayesm.var=function(object,names,burnin=trunc(.1*nrow(Vard)),tvalues,QUANTILES=FALSE,...){ # # S3 method to summarize draws of var-cov matrix (stored as a vector) # Vard is R x d**2 array of draws # P. Rossi 2/07 # Vard=object if(mode(Vard) == "list") stop("list entered \n Possible Fixup: extract from list \n") if(!is.matrix(Vard)) stop("Requires matrix argument \n") if(trunc(sqrt(ncol(Vard)))!=sqrt(ncol(Vard))) stop("Argument cannot be draws from a square matrix \n") if(nrow(Vard) < 100) {cat("fewer than 100 draws submitted \n"); return(invisible())} d=sqrt(ncol(Vard)) corrd=t(apply(Vard[(burnin+1):nrow(Vard),],1,nmat)) pmeancorr=apply(corrd,2,mean) dim(pmeancorr)=c(d,d) indexdiag=(0:(d-1))*d+1:d var=Vard[(burnin+1):nrow(Vard),indexdiag] sdd=sqrt(var) pmeansd=apply(sdd,2,mean) mat=cbind(pmeansd,pmeancorr) if(missing(names)) names=as.character(1:d) cat("Posterior Means of Std Deviations and Correlation Matrix \n") rownames(mat)=names colnames(mat)=c("Std Dev",names) print(mat,digits=2) cat("\nUpper Triangle of Var-Cov Matrix \n") ind=as.vector(upper.tri(matrix(0,ncol=d,nrow=d),diag=TRUE)) labels=cbind(rep(c(1:d),d),rep(c(1:d),each=d)) labels=labels[ind,] plabels=paste(labels[,1],labels[,2],sep=",") uppertri=as.matrix(Vard[,ind]) attributes(uppertri)$class="bayesm.mat" summary(uppertri,names=plabels,burnin=burnin,tvalues=tvalues,QUANTILES=QUANTILES) invisible() } bayesm/R/rhierLinearMixture_rcpp.r0000644000176000001440000002024613117541521017020 0ustar ripleyusersrhierLinearMixture=function(Data,Prior,Mcmc){ # # revision history: # changed 12/17/04 by rossi to fix bug in drawdelta when there is zero/one unit # in a mixture component # adapted to linear model by Vicky Chen 6/06 # put in classes 3/07 # changed a check 9/08 # W. Taylor 4/15 - added nprint option to MCMC argument # # purpose: run hierarchical linear model with mixture of normals # # Arguments: # Data contains a list of (regdata, and possibly Z) # regdata is a list of lists (one list per unit) # regdata[[i]]=list(y,X) # y is a vector of observations # X is a length(y) x nvar matrix of values of # X vars including intercepts # Z is an nreg x nz matrix of values of variables # note: Z should NOT contain an intercept # Prior contains a list of (nu.e,ssq,deltabar,Ad,mubar,Amu,nu,V,ncomp,a) # ncomp is the number of components in normal mixture # if elements of Prior (other than ncomp) do not exist, defaults are used # Mcmc contains a list of (s,c,R,keep,nprint) # # Output: as list containing # taodraw is R/keep x nreg array of error variances for each regression # Deltadraw R/keep x nz*nvar matrix of draws of Delta, first row is initial value # betadraw is nreg x nvar x R/keep array of draws of betas # probdraw is R/keep x ncomp matrix of draws of probs of mixture components # compdraw is a list of list of lists (length R/keep) # compdraw[[rep]] is the repth draw of components for mixtures # # Priors: # tau_i ~ nu.e*ssq_i/chisq(nu.e) tau_i is the variance of epsilon_i # beta_i = delta %*% z[i,] + u_i # u_i ~ N(mu_ind[i],Sigma_ind[i]) # ind[i] ~multinomial(p) # p ~ dirichlet (a) # a: Dirichlet parameters for prior on p # delta is a k x nz array # delta= vec(D) ~ N(deltabar,A_d^-1) # mu_j ~ N(mubar,A_mu^-1(x)Sigma_j) # Sigma_j ~ IW(nu,V^-1) # ncomp is number of components # # MCMC parameters # R is number of draws # keep is thinning parameter, keep every keepth draw # nprint - print estimated time remaining on every nprint'th draw # # check arguments # #-------------------------------------------------------------------------------------------------- # # create functions needed # append=function(l) { l=c(l,list(XpX=crossprod(l$X),Xpy=crossprod(l$X,l$y)))} # getvar=function(l) { v=var(l$y) if(is.na(v)) return(1) if(v>0) return (v) else return (1)} # if(missing(Data)) {pandterm("Requires Data argument -- list of regdata, and (possibly) Z")} if(is.null(Data$regdata)) {pandterm("Requires Data element regdata (list of data for each unit)")} regdata=Data$regdata nreg=length(regdata) drawdelta=TRUE if(is.null(Data$Z)) { cat("Z not specified",fill=TRUE); fsh() ; drawdelta=FALSE} else {if (!is.matrix(Data$Z)) {pandterm("Z must be a matrix")} else {if (nrow(Data$Z) != nreg) {pandterm(paste("Nrow(Z) ",nrow(Z),"ne number regressions ",nreg))} else {Z=Data$Z}}} if(drawdelta) { nz=ncol(Z) colmeans=apply(Z,2,mean) if(sum(colmeans) > .00001) {pandterm(paste("Z does not appear to be de-meaned: colmeans= ",colmeans))} } # # check regdata for validity # for (i in 1:nreg) { if(!is.matrix(regdata[[i]]$X)) {pandterm(paste0("regdata[[",i,"]]$X must be a matrix"))} if(!is.vector(regdata[[i]]$y, mode = "numeric") & !is.vector(regdata[[i]]$y, mode = "logical") & !is.matrix(regdata[[i]]$y)) {pandterm(paste0("regdata[[",i,"]]$y must be a numeric or logical vector or matrix"))} if(is.matrix(regdata[[i]]$y)){ if(ncol(regdata[[i]]$y)>1) {pandterm(paste0("regdata[[",i,"]]$y must be a vector or one-column matrix"))}} } dimfun=function(l) {c(length(l$y),dim(l$X))} dims=sapply(regdata,dimfun) dims=t(dims) nvar=quantile(dims[,3],prob=.5) for (i in 1:nreg) { if(dims[i,1] != dims[i,2] || dims[i,3] !=nvar) {pandterm(paste("Bad Data dimensions for unit ",i," dims(y,X) =",dims[i,]))} } # # check on prior # if(missing(Prior)) {pandterm("Requires Prior list argument (at least ncomp)")} if(is.null(Prior$nu.e)) {nu.e=BayesmConstant.nu.e} else {nu.e=Prior$nu.e} if(is.null(Prior$ssq)) {ssq=sapply(regdata,getvar)} else {ssq=Prior$ssq} if(is.null(Prior$ncomp)) {pandterm("Requires Prior element ncomp (num of mixture components)")} else {ncomp=Prior$ncomp} if(is.null(Prior$mubar)) {mubar=matrix(rep(0,nvar),nrow=1)} else { mubar=matrix(Prior$mubar,nrow=1)} if(ncol(mubar) != nvar) {pandterm(paste("mubar must have ncomp cols, ncol(mubar)= ",ncol(mubar)))} if(is.null(Prior$Amu)) {Amu=matrix(BayesmConstant.A,ncol=1)} else {Amu=matrix(Prior$Amu,ncol=1)} if(ncol(Amu) != 1 | nrow(Amu) != 1) {pandterm("Am must be a 1 x 1 array")} if(is.null(Prior$nu)) {nu=nvar+BayesmConstant.nuInc} else {nu=Prior$nu} if(nu < 1) {pandterm("invalid nu value")} if(is.null(Prior$V)) {V=nu*diag(nvar)} else {V=Prior$V} if(sum(dim(V)==c(nvar,nvar)) !=2) pandterm("Invalid V in prior") if(is.null(Prior$Ad) & drawdelta) {Ad=BayesmConstant.A*diag(nvar*nz)} else {Ad=Prior$Ad} if(drawdelta) {if(ncol(Ad) != nvar*nz | nrow(Ad) != nvar*nz) {pandterm("Ad must be nvar*nz x nvar*nz")}} if(is.null(Prior$deltabar)& drawdelta) {deltabar=rep(0,nz*nvar)} else {deltabar=Prior$deltabar} if(drawdelta) {if(length(deltabar) != nz*nvar) {pandterm("deltabar must be of length nvar*nz")}} if(is.null(Prior$a)) { a=rep(BayesmConstant.a,ncomp)} else {a=Prior$a} if(length(a) != ncomp) {pandterm("Requires dim(a)= ncomp (no of components)")} bada=FALSE for(i in 1:ncomp) { if(a[i] < 0) bada=TRUE} if(bada) pandterm("invalid values in a vector") # # check on Mcmc # if(missing(Mcmc)) {pandterm("Requires Mcmc list argument")} else { if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$R)) {pandterm("Requires R argument in Mcmc list")} else {R=Mcmc$R} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} } # # print out problem # cat(" ",fill=TRUE) cat("Starting MCMC Inference for Hierarchical Linear Model:",fill=TRUE) cat(" Normal Mixture with",ncomp,"components for first stage prior",fill=TRUE) cat(paste(" for ",nreg," cross-sectional units"),fill=TRUE) cat(" ",fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("nu.e =",nu.e,fill=TRUE) cat("nu =",nu,fill=TRUE) cat("V ",fill=TRUE) print(V) cat("mubar ",fill=TRUE) print(mubar) cat("Amu ", fill=TRUE) print(Amu) cat("a ",fill=TRUE) print(a) if(drawdelta) { cat("deltabar",fill=TRUE) print(deltabar) cat("Ad",fill=TRUE) print(Ad) } cat(" ",fill=TRUE) cat("MCMC Parms: ",fill=TRUE) cat("R= ",R," keep= ",keep," nprint= ",nprint,fill=TRUE) cat("",fill=TRUE) # initialize values # # Create XpX elements of regdata and initialize tau # regdata=lapply(regdata,append) tau=sapply(regdata,getvar) # # set initial values for the indicators # ind is of length(nreg) and indicates which mixture component this obs # belongs to. # ind=NULL ninc=floor(nreg/ncomp) for (i in 1:(ncomp-1)) {ind=c(ind,rep(i,ninc))} if(ncomp != 1) {ind = c(ind,rep(ncomp,nreg-length(ind)))} else {ind=rep(1,nreg)} # #initialize delta # if (drawdelta){ olddelta = rep(0,nz*nvar) } else { #send placeholders to the _loop function if there is no Z matrix olddelta = 0 Z = matrix(0) deltabar = 0 Ad = matrix(0) } # # initialize probs # oldprob=rep(1/ncomp,ncomp) ################################################################### # Wayne Taylor # 09/19/2014 ################################################################### draws = rhierLinearMixture_rcpp_loop(regdata, Z, deltabar, Ad, mubar, Amu, nu, V, nu.e, ssq, R, keep, nprint, drawdelta, as.matrix(olddelta), a, oldprob, ind, tau) #################################################################### attributes(draws$taudraw)$class=c("bayesm.mat","mcmc") attributes(draws$taudraw)$mcpar=c(1,R,keep) if(drawdelta){ attributes(draws$Deltadraw)$class=c("bayesm.mat","mcmc") attributes(draws$Deltadraw)$mcpar=c(1,R,keep)} attributes(draws$betadraw)$class=c("bayesm.hcoef") attributes(draws$nmix)$class="bayesm.nmix" return(draws) }bayesm/R/llnhlogit.R0000755000176000001440000000213712524673066014123 0ustar ripleyusersllnhlogit=function(theta,choice,lnprices,Xexpend) { # function to evaluate non-homothetic logit likelihood # choice is a n x 1 vector with indicator of choice (1,...,m) # lnprices is n x m array of log-prices faced # Xexpend is n x d array of variables predicting expenditure # # non-homothetic model specifies ln(psi_i(u))= alpha_i - exp(k_i)u # # structure of theta vector: # alpha (m x 1) # k (m x 1) # gamma (k x 1) expenditure function coefficients # tau scaling of v # m=ncol(lnprices) n=length(choice) d=ncol(Xexpend) alpha=theta[1:m] k=theta[(m+1):(2*m)] gamma=theta[(2*m+1):(2*m+d)] tau=theta[length(theta)] iotam=c(rep(1,m)) c1=as.vector(Xexpend%*%gamma)%x%iotam-as.vector(t(lnprices))+alpha c2=c(rep(exp(k),n)) u=callroot(c1,c2,.0000001,20) v=alpha - u*exp(k)-as.vector(t(lnprices)) vmat=matrix(v,ncol=m,byrow=TRUE) vmat=tau*vmat ind=seq(1,n) vchosen=vmat[cbind(ind,choice)] lnprob=vchosen-log((exp(vmat))%*%iotam) return(sum(lnprob)) } bayesm/R/rmvpgibbs_rcpp.r0000644000176000001440000001074512566706215015206 0ustar ripleyusersrmvpGibbs=function(Data,Prior,Mcmc){ # # Revision History: # modified by rossi 12/18/04 to include error checking # 3/07 added classes # W. Taylor 4/15 - added nprint option to MCMC argument # # # purpose: Gibbs MVP model with full covariance matrix # # Arguments: # Data contains # p the number of alternatives (could be time or could be from pick j of p survey) # y -- a vector of length n*p of indicators (1 if "chosen" if not) # X -- np x k matrix of covariates (including intercepts) # each X_i is p x nvar # # Prior contains a list of (betabar, A, nu, V) # if elements of prior do not exist, defaults are used # # Mcmc is a list of (beta0,sigma0,R,keep) # beta0,sigma0 are intial values, if not supplied defaults are used # R is number of draws # keep is thinning parm, keep every keepth draw # nprint - print estimated time remaining on every nprint'th draw # # Output: a list of every keepth betadraw and sigmsdraw # # model: # w_i = X_ibeta + e e~N(0,Sigma) note w_i,e are p x 1 # y_ij = 1 if w_ij > 0 else y_ij = 0 # # priors: # beta ~ N(betabar,A^-1) in prior # Sigma ~ IW(nu,V) # # Check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of p, y, X")} if(is.null(Data$p)) {pandterm("Requires Data element p -- number of binary indicators")} p=Data$p if(is.null(Data$y)) {pandterm("Requires Data element y -- values of binary indicators")} y=Data$y if(is.null(Data$X)) {pandterm("Requires Data element X -- matrix of covariates")} X=Data$X # # check data for validity # levely=as.numeric(levels(as.factor(y))) bady=FALSE for (i in 0:1) { if(levely[i+1] != i) {bady=TRUE} } cat("Table of y values",fill=TRUE) print(table(y)) if (bady) {pandterm("Invalid y")} if (length(y)%%p !=0) {pandterm("length of y is not a multiple of p")} n=length(y)/p k=ncol(X) if(nrow(X) != (n*p)) {pandterm(paste("X has ",nrow(X)," rows; must be = p*n"))} # # check for prior elements # if(missing(Prior)) { betabar=rep(0,k) ; A=BayesmConstant.A*diag(k) ; nu=p+BayesmConstant.nuInc; V=nu*diag(p)} else {if(is.null(Prior$betabar)) {betabar=rep(0,k)} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=BayesmConstant.A*diag(k)} else {A=Prior$A} if(is.null(Prior$nu)) {nu=p+BayesmConstant.nuInc} else {nu=Prior$nu} if(is.null(Prior$V)) {V=nu*diag(p)} else {V=Prior$V}} if(length(betabar) != k) pandterm("length betabar ne k") if(sum(dim(A)==c(k,k)) != 2) pandterm("A is of incorrect dimension") if(nu < 1) pandterm("invalid nu value") if(sum(dim(V)==c(p,p)) != 2) pandterm("V is of incorrect dimension") # # check for Mcmc # if(missing(Mcmc)) pandterm("Requires Mcmc argument -- at least R must be included") if(is.null(Mcmc$R)) {pandterm("Requires element R of Mcmc")} else {R=Mcmc$R} if(is.null(Mcmc$beta0)) {beta0=rep(0,k)} else {beta0=Mcmc$beta0} if(is.null(Mcmc$sigma0)) {sigma0=diag(p)} else {sigma0=Mcmc$sigma0} if(length(beta0) != k) pandterm("beta0 is not of length k") if(sum(dim(sigma0) == c(p,p)) != 2) pandterm("sigma0 is of incorrect dimension") if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} # # print out problem # cat(" ",fill=TRUE) cat("Starting Gibbs Sampler for MVP",fill=TRUE) cat(" ",n," obs of ",p," binary indicators; ",k," indep vars (including intercepts)",fill=TRUE) cat(" ",fill=TRUE) cat("Prior Parms:",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat("A",fill=TRUE) print(A) cat("nu",fill=TRUE) print(nu) cat("V",fill=TRUE) print(V) cat(" ",fill=TRUE) cat("MCMC Parms:",fill=TRUE) cat(" ",R," reps; keeping every ",keep,"th draw"," nprint= ",nprint,fill=TRUE) cat("initial beta= ",beta0,fill=TRUE) cat("initial sigma= ",fill=TRUE) print(sigma0) cat(" ",fill=TRUE) ################################################################### # Wayne Taylor # 09/03/2014 ################################################################### loopout = rmvpGibbs_rcpp_loop(R,keep,nprint,p,y,X,beta0,sigma0,V,nu,betabar,A); ################################################################### attributes(loopout$betadraw)$class=c("bayesm.mat","mcmc") attributes(loopout$betadraw)$mcpar=c(1,R,keep) attributes(loopout$sigmadraw)$class=c("bayesm.var","bayesm.mat","mcmc") attributes(loopout$sigmadraw)$mcpar=c(1,R,keep) return(loopout) }bayesm/R/rhierBinLogit.R0000755000176000001440000001715413114117322014655 0ustar ripleyusers# # ----------------------------------------------------------------------------- # rhierBinLogit = function(Data,Prior,Mcmc){ .Deprecated(msg = "'rhierBinLogit' is depricated \nUse 'rhierMnlRwMixture' instead") # # revision history: # changed 5/12/05 by Rossi to add error checking # 1/07 removed init.rmultiregfp # 3/07 added classes # # purpose: run binary heterogeneous logit model # # Arguments: # Data contains a list of (lgtdata[[i]],Z) # lgtdata[[i]]=list(y,X) # y is index of brand chosen, y=1 is exp[X'beta]/(1+exp[X'beta]) # X is a matrix that is n_i x by nvar # Z is a matrix of demographic variables nlgt*nz that have been # mean centered so that the intercept is interpretable # Prior contains a list of (nu,V,Deltabar,ADelta) # beta_i ~ N(Z%*%Delta,Vbeta) # vec(Delta) ~ N(vec(Deltabar),Vbeta (x) ADelta^-1) # Vbeta ~ IW(nu,V) # Mcmc is a list of (sbeta,R,keep) # sbeta is scale factor for RW increment for beta_is # R is number of draws # keep every keepth draw # # Output: # a list of Deltadraw (R/keep x nvar x nz), Vbetadraw (R/keep x nvar**2), # llike (R/keep), betadraw is a nlgt x nvar x nz x R/keep array of draws of betas # nunits=length(lgtdata) # # define functions needed # # ------------------------------------------------------------------------ # loglike= function(y,X,beta) { # function computes log likelihood of data for binomial logit model # Pr(y=1) = 1 - Pr(y=0) = exp[X'beta]/(1+exp[X'beta]) prob = exp(X%*%beta)/(1+exp(X%*%beta)) prob = prob*y + (1-prob)*(1-y) sum(log(prob)) } # # # check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of m, lgtdata, and (possibly) Z")} if(is.null(Data$lgtdata)) {pandterm("Requires Data element lgtdata (list of data for each unit)")} lgtdata=Data$lgtdata nlgt=length(lgtdata) if(is.null(Data$Z)) { cat("Z not specified -- putting in iota",fill=TRUE); fsh() ; Z=matrix(rep(1,nlgt),ncol=1)} else {if (!is.matrix(Data$Z)) {pandterm("Z must be a matrix")} else {if (nrow(Data$Z) != nlgt) {pandterm(paste("nrow(Z) ",nrow(Z),"ne number logits ",nlgt))} else {Z=Data$Z}}} nz=ncol(Z) # # check lgtdata for validity # m=2 # set two choice alternatives for Greg's code ypooled=NULL Xpooled=NULL if(!is.null(lgtdata[[1]]$X & is.matrix(lgtdata[[1]]$X))) {oldncol=ncol(lgtdata[[1]]$X)} for (i in 1:nlgt) { if(is.null(lgtdata[[i]]$y)) {pandterm(paste0("Requires element y of lgtdata[[",i,"]]"))} if(is.null(lgtdata[[i]]$X)) {pandterm(paste0("Requires element X of lgtdata[[",i,"]]"))} if(!is.matrix(lgtdata[[i]]$X)) {pandterm(paste0("lgtdata[[",i,"]]$X must be a matrix"))} if(!is.vector(lgtdata[[i]]$y, mode = "numeric") & !is.vector(lgtdata[[i]]$y, mode = "logical") & !is.matrix(lgtdata[[i]]$y)) {pandterm(paste0("lgtdata[[",i,"]]$y must be a numeric or logical vector or matrix"))} if(is.matrix(lgtdata[[i]]$y) & ncol(lgtdata[[i]]$y)>1) {pandterm(paste0("lgtdata[[",i,"]]$y must be a vector or one-column matrix"))} ypooled=c(ypooled,lgtdata[[i]]$y) nrowX=nrow(lgtdata[[i]]$X) if((nrowX) !=length(lgtdata[[i]]$y)) {pandterm(paste("nrow(X) ne length(yi); exception at unit",i))} newncol=ncol(lgtdata[[i]]$X) if(newncol != oldncol) {pandterm(paste("All X elements must have same # of cols; exception at unit",i))} Xpooled=rbind(Xpooled,lgtdata[[i]]$X) oldncol=newncol } nvar=ncol(Xpooled) levely=as.numeric(levels(as.factor(ypooled))) if(length(levely) != m) {pandterm(paste("y takes on ",length(levely)," values -- must be = m"))} bady=FALSE for (i in 0:1 ) { if(levely[i+1] != i) bady=TRUE } cat("Table of Y values pooled over all units",fill=TRUE) print(table(ypooled)) if (bady) {pandterm("Invalid Y")} # # check on prior # if(missing(Prior)){ nu=nvar+3 V=nu*diag(nvar) Deltabar=matrix(rep(0,nz*nvar),ncol=nvar) ADelta=.01*diag(nz) } else { if(is.null(Prior$nu)) {nu=nvar+3} else {nu=Prior$nu} if(nu < 1) {pandterm("invalid nu value")} if(is.null(Prior$V)) {V=nu*diag(rep(1,nvar))} else {V=Prior$V} if(sum(dim(V)==c(nvar,nvar)) !=2) pandterm("Invalid V in prior") if(is.null(Prior$ADelta) ) {ADelta=.01*diag(nz)} else {ADelta=Prior$ADelta} if(ncol(ADelta) != nz | nrow(ADelta) != nz) {pandterm("ADelta must be nz x nz")} if(is.null(Prior$Deltabar) ) {Deltabar=matrix(rep(0,nz*nvar),ncol=nvar)} else {Deltabar=Prior$Deltabar} } # # check on Mcmc # if(missing(Mcmc)) {pandterm("Requires Mcmc list argument")} else { if(is.null(Mcmc$sbeta)) {sbeta=.2} else {sbeta=Mcmc$sbeta} if(is.null(Mcmc$keep)) {keep=1} else {keep=Mcmc$keep} if(is.null(Mcmc$R)) {pandterm("Requires R argument in Mcmc list")} else {R=Mcmc$R} } # # print out problem # cat(" ",fill=TRUE) cat("Attempting MCMC Inference for Hierarchical Binary Logit:",fill=TRUE) cat(paste(" ",nvar," variables in X"),fill=TRUE) cat(paste(" ",nz," variables in Z"),fill=TRUE) cat(paste(" for ",nlgt," cross-sectional units"),fill=TRUE) cat(" ",fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("nu =",nu,fill=TRUE) cat("V ",fill=TRUE) print(V) cat("Deltabar",fill=TRUE) print(Deltabar) cat("ADelta",fill=TRUE) print(ADelta) cat(" ",fill=TRUE) cat("MCMC Parms: ",fill=TRUE) cat(paste("sbeta=",round(sbeta,3)," R= ",R," keep= ",keep),fill=TRUE) cat("",fill=TRUE) nlgt=length(lgtdata) nvar=ncol(lgtdata[[1]]$X) nz=ncol(Z) # # initialize storage for draws # Vbetadraw=matrix(double(floor(R/keep)*nvar*nvar),ncol=nvar*nvar) betadraw=array(double(floor(R/keep)*nlgt*nvar),dim=c(nlgt,nvar,floor(R/keep))) Deltadraw=matrix(double(floor(R/keep)*nvar*nz),ncol=nvar*nz) oldbetas=matrix(double(nlgt*nvar),ncol=nvar) oldVbeta=diag(nvar) oldVbetai=diag(nvar) oldDelta=matrix(double(nvar*nz),ncol=nvar) betad = array(0,dim=c(nvar)) betan = array(0,dim=c(nvar)) reject = array(0,dim=c(R/keep)) llike=array(0,dim=c(R/keep)) itime=proc.time()[3] cat("MCMC Iteration (est time to end - min)",fill=TRUE) fsh() for (j in 1:R) { rej = 0 logl = 0 sV = sbeta*oldVbeta root=t(chol(sV)) # Draw B-h|B-bar, V for (i in 1:nlgt) { betad = oldbetas[i,] betan = betad + root%*%rnorm(nvar) # data lognew = loglike(lgtdata[[i]]$y,lgtdata[[i]]$X,betan) logold = loglike(lgtdata[[i]]$y,lgtdata[[i]]$X,betad) # heterogeneity logknew = -.5*(t(betan)-Z[i,]%*%oldDelta) %*% oldVbetai %*% (betan-t(Z[i,]%*%oldDelta)) logkold = -.5*(t(betad)-Z[i,]%*%oldDelta) %*% oldVbetai %*% (betad-t(Z[i,]%*%oldDelta)) # MH step alpha = exp(lognew + logknew - logold - logkold) if(alpha=="NaN") alpha=-1 u = runif(n=1,min=0, max=1) if(u < alpha) { oldbetas[i,] = betan logl = logl + lognew } else { logl = logl + logold rej = rej+1 } } # Draw B-bar and V as a multivariate regression out=rmultireg(oldbetas,Z,Deltabar,ADelta,nu,V) oldDelta=out$B oldVbeta=out$Sigma oldVbetai=chol2inv(chol(oldVbeta)) if((j%%100)==0) { ctime=proc.time()[3] timetoend=((ctime-itime)/j)*(R-j) cat(" ",j," (",round(timetoend/60,1),")",fill=TRUE) fsh() } mkeep=j/keep if(mkeep*keep == (floor(mkeep)*keep)) {Deltadraw[mkeep,]=as.vector(oldDelta) Vbetadraw[mkeep,]=as.vector(oldVbeta) betadraw[,,mkeep]=oldbetas llike[mkeep]=logl reject[mkeep]=rej/nlgt } } ctime=proc.time()[3] cat(" Total Time Elapsed: ",round((ctime-itime)/60,2),fill=TRUE) attributes(betadraw)$class=c("bayesm.hcoef") attributes(Deltadraw)$class=c("bayesm.mat","mcmc") attributes(Deltadraw)$mcpar=c(1,R,keep) attributes(Vbetadraw)$class=c("bayesm.var","bayesm.mat","mcmc") attributes(Vbetadraw)$mcpar=c(1,R,keep) return(list(betadraw=betadraw,Vbetadraw=Vbetadraw,Deltadraw=Deltadraw,llike=llike,reject=reject)) } bayesm/R/rscaleusage_rcpp.r0000644000176000001440000002323613117541521015476 0ustar ripleyusersrscaleUsage= function(Data,Prior,Mcmc) { # # purpose: run scale-usage mcmc # draws y,Sigma,mu,tau,sigma,Lambda,e # R. McCulloch 12/28/04 # added classes 3/07 # # arguments: # Data: # all components are required: # k: integer giving the scale of the responses, each observation is an integer from 1,2,...k # x: data, num rows=number of respondents, num columns = number of questions # Prior: # all components are optional # nu,V: Sigma ~ IW(nu,V) # mubar,Am: mu ~N(mubar,Am^{-1}) # gsigma: grid for sigma # gl11,gl22,gl12: grids for ij element of Lambda # Lambdanu,LambdaV: Lambda ~ IW(Lambdanu,LambdaV) # ge: grid for e # Mcmc: # all components are optional (but you would typically want to specify R= number of draws) # R: number of mcmc iterations # keep: frequency with which draw is kept # ndghk: number of draws for ghk # nprint - print estimated time remaining on every nprint'th draw # e,y,mu,Sigma,sigma,tau,Lambda: initial values for the state # doe, ...doLambda: indicates whether draw should be made # output: # List with draws of each of Sigma,mu,tau,sigma,Lambda,e # eg. result$Sigma is the draws of Sigma # Each component is a matrix expept e, which is a vector # for the matrices Sigma and Lambda each row transpose of the Vec # eg. result$Lambda has rows (Lambda11,Lambda21,Lambda12,Lambda22) # # define functions needed # # ----------------------------------------------------------------------------------- myin = function(i,ind) {i %in% ind} ispd = function(mat,d=nrow(mat)) { if(!is.matrix(mat)) { res = FALSE } else if(!((nrow(mat)==d) & (ncol(mat)==d))) { res = FALSE } else { diff = (t(mat)+mat)/2 - mat perdiff = sum(diff^2)/sum(mat^2) res = ((det(mat)>0) & (perdiff < 1e-10)) } res } #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ # print out components of inputs ---------------------------------------------- cat('\nIn function rscaleUsage\n\n') if(!missing(Data)) { cat(' Data has components: ') cat(paste(names(Data),collapse=' ')[1],'\n') } if(!missing(Prior)) { cat(' Prior has components: ') cat(paste(names(Prior),collapse=' ')[1],'\n') } if(!missing(Mcmc)) { cat(' Mcmc has components: ') cat(paste(names(Mcmc),collapse=' ')[1],'\n') } cat('\n') # ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ # process Data argument -------------------------- if(missing(Data)) {pandterm("Requires Data argument - list of k=question scale and x = data")} if(is.null(Data$k)) { pandterm("k not specified") } else { k = as.integer(Data$k) if(!((k>0) & (k<50))) {pandterm("Data$k must be integer between 1 and 50")} } if(is.null(Data$x)) { pandterm('x (the data), not specified') } else { if(!is.matrix(Data$x)) {pandterm('Data$x must be a matrix')} x = matrix(as.integer(Data$x),nrow=nrow(Data$x)) checkx = sum(sapply(as.vector(x),myin,1:k)) if(!(checkx == nrow(x)*ncol(x))) {pandterm('each element of Data$x must be in 1,2...k')} p = ncol(x) n = nrow(x) if((p<2) | (n<1)) {pandterm(paste('invalid dimensions for x: nrow,ncol: ',n,p))} } # ++++++++++++++++++++++++++++++++++++++++++++++++ # process Mcmc argument --------------------- #run mcmc R = 1000 keep = BayesmConstant.keep ndghk= 100 nprint = BayesmConstant.nprint if(!missing(Mcmc)) { if(!is.null(Mcmc$R)) { R = as.integer(Mcmc$R) } if(!is.null(Mcmc$keep)) { keep = as.integer(Mcmc$keep) } if(!is.null(Mcmc$ndghk)) { ndghk = as.integer(Mcmc$ndghk) } if(!is.null(Mcmc$nprint)) { nprint = as.integer(Mcmc$nprint) } } if(R<1) { pandterm('R must be positive')} if(keep<1) { pandterm('keep must be positive') } if(ndghk<1) { pandterm('ndghk must be positive') } if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} #state y = matrix(as.double(x),nrow=nrow(x)) mu = apply(y,2,mean) Sigma = var(y) tau = rep(0,n) sigma = rep(1,n) #Lambda = matrix(c(3.7,-.22,-.22,.32),ncol=2) #Lambda = matrix(c((k/4)^2,(k/4)*.5*(-.2),0,.25),nrow=2); Lambda[1,2]=Lambda[2,1] Lambda = matrix(c(4,0,0,.5),ncol=2) e=0 if(!missing(Mcmc)) { if(!is.null(Mcmc$y)) { y = Mcmc$y } if(!is.null(Mcmc$mu)) { mu = Mcmc$mu } if(!is.null(Mcmc$Sigma)) { Sigma = Mcmc$Sigma } if(!is.null(Mcmc$tau)) { tau = Mcmc$tau } if(!is.null(Mcmc$sigma)) { sigma = Mcmc$sigma } if(!is.null(Mcmc$Lambda)) { Lambda = Mcmc$Lambda } if(!is.null(Mcmc$e)) { e = Mcmc$e } } if(!ispd(Sigma,p)) { pandterm(paste('Sigma must be positive definite with dimension ',p)) } if(!ispd(Lambda,2)) { pandterm(paste('Lambda must be positive definite with dimension ',2)) } if(!is.vector(mu)) { pandterm('mu must be a vector') } if(length(mu) != p) { pandterm(paste('mu must have length ',p)) } if(length(tau) != n) { pandterm(paste('tau must have length ',n)) } if(!is.vector(sigma)) { pandterm('sigma must be a vector') } if(length(sigma) != n) { pandterm(paste('sigma must have length ',n)) } if(!is.matrix(y)) { pandterm('y must be a matrix') } if(nrow(y) != n) { pandterm(paste('y must have',n,'rows')) } if(ncol(y) != p) { pandterm(paste('y must have',p,'columns')) } #do draws domu=TRUE doSigma=TRUE dosigma=TRUE dotau=TRUE doLambda=TRUE doe=TRUE if(!missing(Mcmc)) { if(!is.null(Mcmc$domu)) { domu = Mcmc$domu } if(!is.null(Mcmc$doSigma)) { doSigma = Mcmc$doSigma } if(!is.null(Mcmc$dotau)) { dotau = Mcmc$dotau } if(!is.null(Mcmc$dosigma)) { dosigma = Mcmc$dosigma } if(!is.null(Mcmc$doLambda)) { doLambda = Mcmc$doLambda } if(!is.null(Mcmc$doe)) { doe = Mcmc$doe } } #++++++++++++++++++++++++++++++++++++++ #process Prior argument ---------------------------------- nu = p+BayesmConstant.nuInc V= nu*diag(p) mubar = matrix(rep(k/2,p),ncol=1) Am = BayesmConstant.A*diag(p) gs = 100 #changed from 200 to 100 by Dan Yavorsky (dyavorsky@gmail.com) Oct 2016 if(!missing(Prior)) { if(!is.null(Prior$gs)) { gs = Prior$gs } } #allow user to modify gs; Dan Yavorsky (dyavorsky@gmail.com) Oct 2016 gsigma = 6*(1:gs)/gs gl11 = .1 + 5.9*(1:gs)/gs gl22 = .1 + 2.0*(1:gs)/gs #gl12 = -.8 + 1.6*(1:gs)/gs gl12 = -2.0 + 4*(1:gs)/gs nuL=20 VL = (nuL-3)*Lambda ge = -.1+.2*(0:gs)/gs if(!missing(Prior)) { if(!is.null(Prior$nu)) { nu = Prior$nu; V = nu*diag(p) } if(!is.null(Prior$V)) { V = Prior$V } if(!is.null(Prior$mubar)) { mubar = matrix(Prior$mubar,ncol=1) } if(!is.null(Prior$Am)) { Am = Prior$Am } if(!is.null(Prior$gsigma)) { gsigma = Prior$gsigma } if(!is.null(Prior$gl11)) { gl11 = Prior$gl11 } if(!is.null(Prior$gl22)) { gl22 = Prior$gl22 } if(!is.null(Prior$gl12)) { gl12 = Prior$gl12 } if(!is.null(Prior$Lambdanu)) { nuL = Prior$Lambdanu; VL = (nuL-3)*Lambda } if(!is.null(Prior$LambdaV)) { VL = Prior$LambdaV } if(!is.null(Prior$ge)) { ge = Prior$ge } } if(!ispd(V,p)) { pandterm(paste('V must be positive definite with dimension ',p)) } if(!ispd(Am,p)) { pandterm(paste('Am must be positive definite with dimension ',p)) } if(!ispd(VL,2)) { pandterm(paste('VL must be positive definite with dimension ',2)) } if(nrow(mubar) != p) { pandterm(paste('mubar must have length',p)) } #++++++++++++++++++++++++++++++++++++++++ #print out run info ------------------------- # # note in the documentation and in BSM, m is used instead of p # for print-out purposes I'm using m P. Rossi 12/06 cat(' n,m,k: ', n,p,k,'\n') cat(' R,keep,ndghk,nprint: ', R,keep,ndghk,nprint,'\n') cat('\n') cat(' Data:\n') cat(' x[1,1],x[n,1],x[1,m],x[n,m]: ',x[1,1],x[n,1],x[1,p],x[n,p],'\n\n') cat(' Prior:\n') cat(' ','nu: ',nu,'\n') cat(' ','V[1,1]/nu,V[m,m]/nu: ',V[1,1]/nu,V[p,p]/nu,'\n') cat(' ','mubar[1],mubar[m]: ',mubar[1],mubar[p],'\n') cat(' ','Am[1,1],Am[m,m]: ',Am[1,1],Am[p,p],'\n') cat(' ','Lambdanu: ',nuL,'\n') cat(' ','LambdaV11,22/(Lambdanu-3): ',VL[1,1]/(nuL-3),VL[2,2]/(nuL-3),'\n') cat(' ','sigma grid, 1,',length(gsigma),': ',gsigma[1],', ',gsigma[length(gsigma)],'\n') cat(' ','Lambda11 grid, 1,',length(gl11),': ',gl11[1],', ',gl11[length(gl11)],'\n') cat(' ','Lambda12 grid, 1,',length(gl12),': ',gl12[1],', ',gl12[length(gl12)],'\n') cat(' ','Lambda22 grid, 1,',length(gl22),': ',gl22[1],', ',gl22[length(gl22)],'\n') cat(' ','e grid, 1,',length(ge),': ',ge[1],', ',ge[length(ge)],'\n') cat(' ','draw e: ',doe,'\n') cat(' ','draw Lambda: ',doLambda,'\n') #++++++++++++++++++++++++++++++++++++++++++++ ################################################################### # Wayne Taylor # 3/14/2015 ################################################################### out = rscaleUsage_rcpp_loop(k,x,p,n, R,keep,ndghk,nprint, y,mu,Sigma,tau,sigma,Lambda,e, domu,doSigma,dosigma,dotau,doLambda,doe, nu,V,mubar,Am, gsigma,gl11,gl22,gl12, nuL,VL,ge) R = out$ndpost ################################################################### attributes(out$drmu)$class=c("bayesm.mat","mcmc") attributes(out$drmu)$mcpar=c(1,R,keep) attributes(out$drtau)$class=c("bayesm.mat","mcmc") attributes(out$drtau)$mcpar=c(1,R,keep) attributes(out$drsigma)$class=c("bayesm.mat","mcmc") attributes(out$drsigma)$mcpar=c(1,R,keep) attributes(out$drLambda)$class=c("bayesm.mat","mcmc") attributes(out$drLambda)$mcpar=c(1,R,keep) attributes(out$dre)$class=c("bayesm.mat","mcmc") attributes(out$dre)$mcpar=c(1,R,keep) attributes(out$drSigma)$class=c("bayesm.var","bayesm.mat","mcmc") attributes(out$drSigma)$mcpar=c(1,R,keep) return(list(Sigmadraw=out$drSigma,mudraw=out$drmu,taudraw = out$drtau, sigmadraw=out$drsigma,Lambdadraw=out$drLambda,edraw=out$dre)) } bayesm/R/summary.bayesm.nmix.R0000755000176000001440000000261710647461730016055 0ustar ripleyuserssummary.bayesm.nmix=function(object,names,burnin=trunc(.1*nrow(probdraw)),...){ nmixlist=object if(mode(nmixlist) != "list") stop(" Argument must be a list \n") probdraw=nmixlist[[1]]; compdraw=nmixlist[[3]] if(!is.matrix(probdraw)) stop(" First Element of List (probdraw) must be a matrix \n") if(mode(compdraw) != "list") stop(" Third Element of List (compdraw) must be a list \n") ncomp=length(compdraw[[1]]) if(ncol(probdraw) != ncomp) stop(" Dim of First Element of List not compatible with Dim of Second \n") # # function to summarize draws of normal mixture components # R=nrow(probdraw) if(R < 100) {cat("fewer than 100 draws submitted \n"); return(invisible())} datad=length(compdraw[[1]][[1]]$mu) mumat=matrix(0,nrow=R,ncol=datad) sigmat=matrix(0,nrow=R,ncol=(datad*datad)) if(missing(names)) names=as.character(1:datad) for(i in (burnin+1):R){ if(i%%500 ==0) cat("processing draw ",i,"\n",sep="");fsh() out=momMix(probdraw[i,,drop=FALSE],compdraw[i]) mumat[i,]=out$mu sigmat[i,]=out$sigma } cat("\nNormal Mixture Moments\n Mean\n") attributes(mumat)$class="bayesm.mat" attributes(sigmat)$class="bayesm.var" summary(mumat,names,burnin=burnin,QUANTILES=FALSE,TRAILER=FALSE) cat(" \n") summary(sigmat,burnin=burnin) cat("note: 1st and 2nd Moments for a Normal Mixture \n") cat(" may not be interpretable, consider plots\n") invisible() } bayesm/R/rhierMnlDP_rcpp.r0000644000176000001440000003027413117541521015204 0ustar ripleyusersrhierMnlDP=function(Data,Prior,Mcmc){ # # created 3/08 by Rossi from rhierMnlRwMixture adding DP draw for to replace finite mixture of normals # # revision history: # changed 12/17/04 by rossi to fix bug in drawdelta when there is zero/one unit # in a mixture component # added loglike output, changed to reflect new argument order in llmnl, mnlHess 9/05 # changed weighting scheme to (1-w)logl_i + w*Lbar (normalized) 12/05 # 3/07 added classes # W. Taylor 4/15 - added nprint option to MCMC argument # # purpose: run hierarchical mnl logit model with mixture of normals # using RW and cov(RW inc) = (hess_i + Vbeta^-1)^-1 # uses normal approximation to pooled likelihood # # Arguments: # Data contains a list of (p,lgtdata, and possibly Z) # p is number of choice alternatives # lgtdata is a list of lists (one list per unit) # lgtdata[[i]]=list(y,X) # y is a vector indicating alternative chosen # integers 1:p indicate alternative # X is a length(y)*p x nvar matrix of values of # X vars including intercepts # Z is an length(lgtdata) x nz matrix of values of variables # note: Z should NOT contain an intercept # Prior contains a list of (deltabar,Ad,lambda_hyper,Prioralpha) # alpha: starting value # lambda_hyper: hyperparms of prior on lambda # Prioralpha: hyperparms of alpha prior; a list of (Istarmin,Istarmax,power) # if elements of the prior don't exist, defaults are assumed # Mcmc contains a list of (s,c,R,keep,nprint) # # Output: as list containing # Deltadraw R/keep x nz*nvar matrix of draws of Delta, first row is initial value # betadraw is nlgt x nvar x R/keep array of draws of betas # probdraw is R/keep x 1 matrix of draws of probs of mixture components # compdraw is a list of list of lists (length R/keep) # compdraw[[rep]] is the repth draw of components for mixtures # loglike log-likelikelhood at each kept draw # # Priors: # beta_i = D %*% z[i,] + u_i # vec(D)~N(deltabar) # u_i ~ N(theta_i) # theta_i~G # G|lambda,alpha ~ DP(G|G0(lambda),alpha) # # lambda: # G0 ~ N(mubar,Sigma (x) Amu^-1) # mubar=vec(mubar) # Sigma ~ IW(nu,nu*v*I) note: mode(Sigma)=nu/(nu+2)*v*I # mubar=0 # amu is uniform on grid specified by alim # nu is log uniform, nu=d-1+exp(Z) z is uniform on seq defined bvy nulim # v is uniform on sequence specificd by vlim # # Prioralpha: # alpha ~ (1-(alpha-alphamin)/(alphamax-alphamin))^power # alphamin=exp(digamma(Istarmin)-log(gamma+log(N))) # alphamax=exp(digamma(Istarmax)-log(gamma+log(N))) # gamma= .5772156649015328606 # # MCMC parameters # s is the scaling parameter for the RW inc covariance matrix; s^2 Var is inc cov # matrix # w is parameter for weighting function in fractional likelihood # w is the weight on the normalized pooled likelihood # R is number of draws # keep is thinning parameter, keep every keepth draw # nprint - print estimated time remaining on every nprint'th draw #-------------------------------------------------------------------------------------------------- llmnlFract= function(beta,y,X,betapooled,rootH,w,wgt){ z=as.vector(rootH%*%(beta-betapooled)) return((1-w)*llmnl(beta,y,X)+w*wgt*(-.5*(z%*%z))) } # # check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of p,lgtdata, and (possibly) Z")} if(is.null(Data$p)) {pandterm("Requires Data element p (# chce alternatives)") } p=Data$p if(is.null(Data$lgtdata)) {pandterm("Requires Data element lgtdata (list of data for each unit)")} lgtdata=Data$lgtdata nlgt=length(lgtdata) drawdelta=TRUE if(is.null(Data$Z)) { cat("Z not specified",fill=TRUE); fsh() ; drawdelta=FALSE} else {if (!is.matrix(Data$Z)) {pandterm("Z must be a matrix")} else {if (nrow(Data$Z) != nlgt) {pandterm(paste("Nrow(Z) ",nrow(Z),"ne number logits ",nlgt))} else {Z=Data$Z}}} if(drawdelta) { nz=ncol(Z) colmeans=apply(Z,2,mean) if(sum(colmeans) > .00001) {pandterm(paste("Z does not appear to be de-meaned: colmeans= ",colmeans))} } # # check lgtdata for validity # ypooled=NULL Xpooled=NULL if(!is.null(lgtdata[[1]]$X & is.matrix(lgtdata[[1]]$X))) {oldncol=ncol(lgtdata[[1]]$X)} for (i in 1:nlgt) { if(is.null(lgtdata[[i]]$y)) {pandterm(paste0("Requires element y of lgtdata[[",i,"]]"))} if(is.null(lgtdata[[i]]$X)) {pandterm(paste0("Requires element X of lgtdata[[",i,"]]"))} if(!is.matrix(lgtdata[[i]]$X)) {pandterm(paste0("lgtdata[[",i,"]]$X must be a matrix"))} if(!is.vector(lgtdata[[i]]$y, mode = "numeric") & !is.vector(lgtdata[[i]]$y, mode = "logical") & !is.matrix(lgtdata[[i]]$y)) {pandterm(paste0("lgtdata[[",i,"]]$y must be a numeric or logical vector or matrix"))} if(is.matrix(lgtdata[[i]]$y)){ if(ncol(lgtdata[[i]]$y)>1) {pandterm(paste0("lgtdata[[",i,"]]$y must be a vector or one-column matrix"))}} ypooled=c(ypooled,lgtdata[[i]]$y) nrowX=nrow(lgtdata[[i]]$X) if((nrowX/p) !=length(lgtdata[[i]]$y)) {pandterm(paste("nrow(X) ne p*length(yi); exception at unit",i))} newncol=ncol(lgtdata[[i]]$X) if(newncol != oldncol) {pandterm(paste("All X elements must have same # of cols; exception at unit",i))} Xpooled=rbind(Xpooled,lgtdata[[i]]$X) oldncol=newncol } nvar=ncol(Xpooled) levely=as.numeric(levels(as.factor(ypooled))) if(length(levely) != p) {pandterm(paste("y takes on ",length(levely)," values -- must be = p"))} bady=FALSE for (i in 1:p ) { if(levely[i] != i) bady=TRUE } cat("Table of Y values pooled over all units",fill=TRUE) print(table(ypooled)) if (bady) {pandterm("Invalid Y")} # # check on prior # alimdef=BayesmConstant.DPalimdef nulimdef=BayesmConstant.DPnulimdef vlimdef=BayesmConstant.DPvlimdef if(missing(Prior)) {Prior=NULL} if(is.null(Prior$lambda_hyper)) {lambda_hyper=list(alim=alimdef,nulim=nulimdef,vlim=vlimdef)} else {lambda_hyper=Prior$lambda_hyper; if(is.null(lambda_hyper$alim)) {lambda_hyper$alim=alimdef} if(is.null(lambda_hyper$nulim)) {lambda_hyper$nulim=nulimdef} if(is.null(lambda_hyper$vlim)) {lambda_hyper$vlim=vlimdef} } if(is.null(Prior$Prioralpha)) {Prioralpha=list(Istarmin=BayesmConstant.DPIstarmin,Istarmax=min(50,0.1*nlgt),power=BayesmConstant.DPpower)} else {Prioralpha=Prior$Prioralpha; if(is.null(Prioralpha$Istarmin)) {Prioralpha$Istarmin=BayesmConstant.DPIstarmin} else {Prioralpha$Istarmin=Prioralpha$Istarmin} if(is.null(Prioralpha$Istarmax)) {Prioralpha$Istarmax=min(50,0.1*nlgt)} else {Prioralpha$Istarmax=Prioralpha$Istarmax} if(is.null(Prioralpha$power)) {Prioralpha$power=BayesmConstant.DPpower} } gamma= BayesmConstant.gamma Prioralpha$alphamin=exp(digamma(Prioralpha$Istarmin)-log(gamma+log(nlgt))) Prioralpha$alphamax=exp(digamma(Prioralpha$Istarmax)-log(gamma+log(nlgt))) Prioralpha$n=nlgt # # check Prior arguments for valdity # if(lambda_hyper$alim[1]<0) {pandterm("alim[1] must be >0")} if(lambda_hyper$nulim[1]<0) {pandterm("nulim[1] must be >0")} if(lambda_hyper$vlim[1]<0) {pandterm("vlim[1] must be >0")} if(Prioralpha$Istarmin <1){pandterm("Prioralpha$Istarmin must be >= 1")} if(Prioralpha$Istarmax <= Prioralpha$Istarmin){pandterm("Prioralpha$Istarmin must be < Prioralpha$Istarmax")} if(is.null(Prior$Ad) & drawdelta) {Ad=BayesmConstant.A*diag(nvar*nz)} else {Ad=Prior$Ad} if(drawdelta) {if(ncol(Ad) != nvar*nz | nrow(Ad) != nvar*nz) {pandterm("Ad must be nvar*nz x nvar*nz")}} if(is.null(Prior$deltabar)& drawdelta) {deltabar=rep(0,nz*nvar)} else {deltabar=Prior$deltabar} if(drawdelta) {if(length(deltabar) != nz*nvar) {pandterm("deltabar must be of length nvar*nz")}} # # check on Mcmc # if(missing(Mcmc)) {pandterm("Requires Mcmc list argument")} else { if(is.null(Mcmc$s)) {s=BayesmConstant.RRScaling/sqrt(nvar)} else {s=Mcmc$s} if(is.null(Mcmc$w)) {w=BayesmConstant.w} else {w=Mcmc$w} if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} if(is.null(Mcmc$maxuniq)) {maxuniq=BayesmConstant.DPmaxuniq} else {keep=Mcmc$maxuniq} if(is.null(Mcmc$gridsize)) {gridsize=BayesmConstant.DPgridsize} else {gridsize=Mcmc$gridsize} if(is.null(Mcmc$R)) {pandterm("Requires R argument in Mcmc list")} else {R=Mcmc$R} } # # print out problem # cat(" ",fill=TRUE) cat("Starting MCMC Inference for Hierarchical Logit:",fill=TRUE) cat(" Dirichlet Process Prior",fill=TRUE) cat(paste(" ",p," alternatives; ",nvar," variables in X"),fill=TRUE) cat(paste(" for ",nlgt," cross-sectional units"),fill=TRUE) cat(" ",fill=TRUE) cat(" Prior Parms: ",fill=TRUE) cat(" G0 ~ N(mubar,Sigma (x) Amu^-1)",fill=TRUE) cat(" mubar = ",0,fill=TRUE) cat(" Sigma ~ IW(nu,nu*v*I)",fill=TRUE) cat(" Amu ~ uniform[",lambda_hyper$alim[1],",",lambda_hyper$alim[2],"]",fill=TRUE) cat(" nu ~ uniform on log grid [",nvar-1+exp(lambda_hyper$nulim[1]), ",",nvar-1+exp(lambda_hyper$nulim[2]),"]",fill=TRUE) cat(" v ~ uniform[",lambda_hyper$vlim[1],",",lambda_hyper$vlim[2],"]",fill=TRUE) cat(" ",fill=TRUE) cat(" alpha ~ (1-(alpha-alphamin)/(alphamax-alphamin))^power",fill=TRUE) cat(" Istarmin = ",Prioralpha$Istarmin,fill=TRUE) cat(" Istarmax = ",Prioralpha$Istarmax,fill=TRUE) cat(" alphamin = ",Prioralpha$alphamin,fill=TRUE) cat(" alphamax = ",Prioralpha$alphamax,fill=TRUE) cat(" power = ",Prioralpha$power,fill=TRUE) cat(" ",fill=TRUE) if(drawdelta) { cat("deltabar",fill=TRUE) print(deltabar) cat("Ad",fill=TRUE) print(Ad) } cat(" ",fill=TRUE) cat("MCMC Parms: ",fill=TRUE) cat(paste("s=",round(s,3)," w= ",w," R= ",R," keep= ",keep," nprint= ",nprint," maxuniq= ",maxuniq, " gridsize for lambda hyperparms= ",gridsize),fill=TRUE) cat("",fill=TRUE) # # allocate space for draws # oldbetas=matrix(double(nlgt*nvar),ncol=nvar) # # intialize compute quantities for Metropolis # cat("initializing Metropolis candidate densities for ",nlgt," units ...",fill=TRUE) fsh() # # now go thru and computed fraction likelihood estimates and hessians # # Lbar=log(pooled likelihood^(n_i/N)) # # fraction loglike = (1-w)*loglike_i + w*Lbar # betainit=c(rep(0,nvar)) # # compute pooled optimum # out=optim(betainit,llmnl,method="BFGS",control=list( fnscale=-1,trace=0,reltol=1e-6), X=Xpooled,y=ypooled) betapooled=out$par H=mnlHess(betapooled,ypooled,Xpooled) rootH=chol(H) # # initialize betas for all units # for (i in 1:nlgt) { wgt=length(lgtdata[[i]]$y)/length(ypooled) out=optim(betapooled,llmnlFract,method="BFGS",control=list( fnscale=-1,trace=0,reltol=1e-4), X=lgtdata[[i]]$X,y=lgtdata[[i]]$y,betapooled=betapooled,rootH=rootH,w=w,wgt=wgt) if(out$convergence == 0) { hess=mnlHess(out$par,lgtdata[[i]]$y,lgtdata[[i]]$X) lgtdata[[i]]=c(lgtdata[[i]],list(converge=1,betafmle=out$par,hess=hess)) } else { lgtdata[[i]]=c(lgtdata[[i]],list(converge=0,betafmle=c(rep(0,nvar)), hess=diag(nvar))) } oldbetas[i,]=lgtdata[[i]]$betafmle if(i%%50 ==0) cat(" completed unit #",i,fill=TRUE) fsh() } #Initialize placeholders when drawdelta == FALSE if (drawdelta==FALSE){ Z = matrix(0) deltabar = 0 Ad = matrix(0) } ################################################################### # Wayne Taylor # 2/21/2015 ################################################################### out = rhierMnlDP_rcpp_loop(R,keep,nprint, lgtdata,Z,deltabar,Ad,Prioralpha,lambda_hyper, drawdelta,nvar,oldbetas,s,maxuniq,gridsize, BayesmConstant.A,BayesmConstant.nuInc,BayesmConstant.DPalpha) ################################################################### if(drawdelta){ attributes(out$Deltadraw)$class=c("bayesm.mat","mcmc") attributes(out$Deltadraw)$mcpar=c(1,R,keep)} attributes(out$betadraw)$class=c("bayesm.hcoef") attributes(out$nmix)$class="bayesm.nmix" attributes(out$adraw)$class=c("bayesm.mat","mcmc") attributes(out$nudraw)$class=c("bayesm.mat","mcmc") attributes(out$vdraw)$class=c("bayesm.mat","mcmc") attributes(out$Istardraw)$class=c("bayesm.mat","mcmc") attributes(out$alphadraw)$class=c("bayesm.mat","mcmc") return(out) }bayesm/R/rhierMnlRwMixture_rcpp.r0000644000176000001440000003136413114117322016643 0ustar ripleyusersrhierMnlRwMixture=function(Data,Prior,Mcmc){ # # revision history: # 12/04 changed by rossi to fix bug in drawdelta when there is zero/one unit in a mixture component # 09/05 added loglike output, changed to reflect new argument order in llmnl, mnlHess # 12/05 changed weighting scheme to (1-w)logl_i + w*Lbar (normalized) # 03/07 added classes # 09/08 changed Dirichlet a check # 04/15 by Wayne Taylor: added nprint option to MCMC argument # 07/16 by Wayne Taylor: added sign restrictions # 10/10 by Dan Yavorsky: changed default priors when sign restrictions imposed # # purpose: run hierarchical mnl logit model with mixture of normals # using RW and cov(RW inc) = (hess_i + Vbeta^-1)^-1 # uses normal approximation to pooled likelihood # # Arguments: # Data contains a list of (p,lgtdata, and possibly Z) # p is number of choice alternatives # lgtdata is a list of lists (one list per unit) # lgtdata[[i]]=list(y,X) # y is a vector indicating alternative chosen # integers 1:p indicate alternative # X is a length(y)*p x nvar matrix of values of # X vars including intercepts # Z is an length(lgtdata) x nz matrix of values of variables # note: Z should NOT contain an intercept # Prior contains a list of (deltabar,Ad,mubar,Amu,nu,V,ncomp,SignRes) # ncomp is the number of components in normal mixture # if elements of Prior (other than ncomp) do not exist, defaults are used # SignRes is a vector of sign restrictions # Mcmc contains a list of (s,c,R,keep,nprint) # # Output: as list containing # Deltadraw R/keep x nz*nvar matrix of draws of Delta, first row is initial value # betadraw is nlgt x nvar x R/keep array of draws of betas # probdraw is R/keep x ncomp matrix of draws of probs of mixture components # compdraw is a list of list of lists (length R/keep) # compdraw[[rep]] is the repth draw of components for mixtures # loglike log-likelikelhood at each kept draw # # Priors: # beta_i = D %*% z[i,] + u_i # u_i ~ N(mu_ind[i],Sigma_ind[i]) # ind[i] ~multinomial(p) # p ~ dirichlet (a) # D is a k x nz array # delta= vec(D) ~ N(deltabar,A_d^-1) # mu_j ~ N(mubar,A_mu^-1(x)Sigma_j) # Sigma_j ~ IW(nu,V^-1) # ncomp is number of components # # MCMC parameters # s is the scaling parameter for the RW inc covariance matrix; s^2 Var is inc cov # matrix # w is parameter for weighting function in fractional likelihood # w is the weight on the normalized pooled likelihood # R is number of draws # keep is thinning parameter, keep every keepth draw # nprint - print estimated time remaining on every nprint'th draw # # check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of p,lgtdata, and (possibly) Z")} if(is.null(Data$p)) {pandterm("Requires Data element p (# choice alternatives)") } p=Data$p if(is.null(Data$lgtdata)) {pandterm("Requires Data element lgtdata (list of data for each unit)")} lgtdata=Data$lgtdata nlgt=length(lgtdata) drawdelta=TRUE if(is.null(Data$Z)) { cat("Z not specified",fill=TRUE); fsh() ; drawdelta=FALSE} else {if (!is.matrix(Data$Z)) {pandterm("Z must be a matrix")} else {if (nrow(Data$Z) != nlgt) {pandterm(paste("Nrow(Z) ",nrow(Z),"ne number logits ",nlgt))} else {Z=Data$Z}}} if(drawdelta) { nz=ncol(Z) colmeans=apply(Z,2,mean) if(sum(colmeans) > .00001) {pandterm(paste("Z does not appear to be de-meaned: colmeans= ",colmeans))} } # # check lgtdata for validity # ypooled=NULL Xpooled=NULL if(!is.null(lgtdata[[1]]$X & is.matrix(lgtdata[[1]]$X))) {oldncol=ncol(lgtdata[[1]]$X)} for (i in 1:nlgt) { if(is.null(lgtdata[[i]]$y)) {pandterm(paste0("Requires element y of lgtdata[[",i,"]]"))} if(is.null(lgtdata[[i]]$X)) {pandterm(paste0("Requires element X of lgtdata[[",i,"]]"))} if(!is.matrix(lgtdata[[i]]$X)) {pandterm(paste0("lgtdata[[",i,"]]$X must be a matrix"))} if(!is.vector(lgtdata[[i]]$y, mode = "numeric") & !is.vector(lgtdata[[i]]$y, mode = "logical") & !is.matrix(lgtdata[[i]]$y)) {pandterm(paste0("lgtdata[[",i,"]]$y must be a numeric or logical vector or matrix"))} if(is.matrix(lgtdata[[i]]$y)) { if(ncol(lgtdata[[i]]$y)>1) { pandterm(paste0("lgtdata[[",i,"]]$y must be a vector or one-column matrix")) } } ypooled=c(ypooled,lgtdata[[i]]$y) nrowX=nrow(lgtdata[[i]]$X) if((nrowX/p) !=length(lgtdata[[i]]$y)) {pandterm(paste("nrow(X) ne p*length(yi); exception at unit",i))} newncol=ncol(lgtdata[[i]]$X) if(newncol != oldncol) {pandterm(paste("All X elements must have same # of cols; exception at unit",i))} Xpooled=rbind(Xpooled,lgtdata[[i]]$X) oldncol=newncol } nvar=ncol(Xpooled) levely=as.numeric(levels(as.factor(ypooled))) if(length(levely) != p) {pandterm(paste("y takes on ",length(levely)," values -- must be = p"))} bady=FALSE for (i in 1:p ) { if(levely[i] != i) bady=TRUE } cat("Table of Y values pooled over all units",fill=TRUE) print(table(ypooled)) if (bady) {pandterm("Invalid Y")} # # check on prior # if(missing(Prior)) {pandterm("Requires Prior list argument (at least ncomp)")} if(is.null(Prior$ncomp)) {pandterm("Requires Prior element ncomp (num of mixture components)")} else {ncomp=Prior$ncomp} if(is.null(Prior$SignRes)) {SignRes=rep(0,nvar)} else {SignRes=Prior$SignRes} if(length(SignRes) != nvar) {pandterm("The length SignRes must be equal to the dimension of X")} if(sum(!(SignRes %in% c(-1,0,1))>0)) {pandterm("All elements of SignRes must be equal to -1, 0, or 1")} if(is.null(Prior$mubar) & sum(abs(SignRes))==0) { mubar=matrix(rep(0,nvar),nrow=1) } else { if(is.null(Prior$mubar) & sum(abs(SignRes)) >0) { mubar=matrix(rep(0,nvar)+2*abs(SignRes),nrow=1) } else { mubar=matrix(Prior$mubar,nrow=1) } } if(ncol(mubar) != nvar) {pandterm(paste("mubar must have ncomp cols, ncol(mubar)= ",ncol(mubar)))} if(is.null(Prior$Amu) & sum(abs(SignRes))==0) { Amu=matrix(BayesmConstant.A,ncol=1) } else { if(is.null(Prior$Amu) & sum(abs(SignRes)) >0) { Amu=matrix(BayesmConstant.A*10,ncol=1) } else {Amu=matrix(Prior$Amu,ncol=1) } } if(ncol(Amu) != 1 | nrow(Amu) != 1) {pandterm("Am must be a 1 x 1 array")} if(is.null(Prior$nu) & sum(abs(SignRes))==0) { nu=nvar+BayesmConstant.nuInc } else { if(is.null(Prior$nu) & sum(abs(SignRes)) >0) { nu=nvar+BayesmConstant.nuInc+12 } else { nu=Prior$nu } } if(nu < 1) {pandterm("invalid nu value")} if(is.null(Prior$V) & sum(abs(SignRes))==0) { V=nu*diag(nvar) } else { if(is.null(Prior$V) & sum(abs(SignRes)) >0) { V=nu*diag(abs(SignRes)*0.1+(!abs(SignRes))*4) } else { V=Prior$V } } if(sum(dim(V)==c(nvar,nvar)) !=2) pandterm("Invalid V in prior") if(is.null(Prior$Ad) & drawdelta) {Ad=BayesmConstant.A*diag(nvar*nz)} else {Ad=Prior$Ad} if(drawdelta) {if(ncol(Ad) != nvar*nz | nrow(Ad) != nvar*nz) {pandterm("Ad must be nvar*nz x nvar*nz")}} if(is.null(Prior$deltabar)& drawdelta) {deltabar=rep(0,nz*nvar)} else {deltabar=Prior$deltabar} if(drawdelta) {if(length(deltabar) != nz*nvar) {pandterm("deltabar must be of length nvar*nz")}} if(is.null(Prior$a)) { a=rep(BayesmConstant.a,ncomp)} else {a=Prior$a} if(length(a) != ncomp) {pandterm("Requires dim(a)= ncomp (no of components)")} bada=FALSE for(i in 1:ncomp) { if(a[i] < 0) bada=TRUE} if(bada) pandterm("invalid values in a vector") if(is.null(Prior$nu)&sum(abs(SignRes))>0) {nu = nvar+15} if(is.null(Prior$Amu)&sum(abs(SignRes))>0) {Amu = matrix(.1)} if(is.null(Prior$V)&sum(abs(SignRes))>0) {V = nu*(diag(nvar)-diag(abs(SignRes)>0)*.8)} # # check on Mcmc # if(missing(Mcmc)) {pandterm("Requires Mcmc list argument")} else { if(is.null(Mcmc$s)) {s=BayesmConstant.RRScaling/sqrt(nvar)} else {s=Mcmc$s} if(is.null(Mcmc$w)) {w=BayesmConstant.w} else {w=Mcmc$w} if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$R)) {pandterm("Requires R argument in Mcmc list")} else {R=Mcmc$R} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} } # # print out problem # cat(" ",fill=TRUE) cat("Starting MCMC Inference for Hierarchical Logit:",fill=TRUE) cat(" Normal Mixture with",ncomp,"components for first stage prior",fill=TRUE) cat(paste(" ",p," alternatives; ",nvar," variables in X"),fill=TRUE) cat(paste(" for ",nlgt," cross-sectional units"),fill=TRUE) cat(" ",fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("nu =",nu,fill=TRUE) cat("V ",fill=TRUE) print(V) cat("mubar ",fill=TRUE) print(mubar) cat("Amu ", fill=TRUE) print(Amu) cat("a ",fill=TRUE) print(a) if(drawdelta) { cat("deltabar",fill=TRUE) print(deltabar) cat("Ad",fill=TRUE) print(Ad) } cat(" ",fill=TRUE) cat("MCMC Parms: ",fill=TRUE) cat(paste("s=",round(s,3)," w= ",w," R= ",R," keep= ",keep," nprint= ",nprint),fill=TRUE) cat("",fill=TRUE) oldbetas = matrix(double(nlgt * nvar), ncol = nvar) #-------------------------------------------------------------------------------------------------- # # create functions needed # llmnlFract= function(beta,y,X,betapooled,rootH,w,wgt,SignRes = rep(0,ncol(X))){ z=as.vector(rootH%*%(beta-betapooled)) return((1-w)*llmnl_con(beta,y,X,SignRes)+w*wgt*(-.5*(z%*%z))) } mnlHess_con=function (betastar, y, X, SignRes = rep(0,ncol(X))) { #Reparameterize beta to betastar to allow for sign restrictions beta = betastar beta[SignRes!=0] = SignRes[SignRes!=0]*exp(beta[SignRes!=0]) n = length(y) j = nrow(X)/n k = ncol(X) Xbeta = X %*% beta Xbeta = matrix(Xbeta, byrow = T, ncol = j) Xbeta = exp(Xbeta) iota = c(rep(1, j)) denom = Xbeta %*% iota Prob = Xbeta/as.vector(denom) Hess = matrix(double(k * k), ncol = k) for (i in 1:n) { p = as.vector(Prob[i, ]) A = diag(p) - outer(p, p) Xt = X[(j * (i - 1) + 1):(j * i), ] Hess = Hess + crossprod(Xt, A) %*% Xt } return(Hess) } #------------------------------------------------------------------------------------------------------- # # intialize compute quantities for Metropolis # cat("initializing Metropolis candidate densities for ",nlgt," units ...",fill=TRUE) fsh() # # now go thru and computed fraction likelihood estimates and hessians # # Lbar=log(pooled likelihood^(n_i/N)) # # fraction loglike = (1-w)*loglike_i + w*Lbar # betainit=c(rep(0,nvar)) # # compute pooled optimum # out=optim(betainit,llmnl_con,method="BFGS",control=list( fnscale=-1,trace=0,reltol=1e-6), X=Xpooled,y=ypooled,SignRes=SignRes) betapooled=out$par H=mnlHess_con(betapooled,ypooled,Xpooled,SignRes) rootH=chol(H) for (i in 1:nlgt) { wgt=length(lgtdata[[i]]$y)/length(ypooled) out=optim(betapooled,llmnlFract,method="BFGS",control=list( fnscale=-1,trace=0,reltol=1e-4), X=lgtdata[[i]]$X,y=lgtdata[[i]]$y,betapooled=betapooled,rootH=rootH,w=w,wgt=wgt,SignRes=SignRes) if(out$convergence == 0) { hess=mnlHess_con(out$par,lgtdata[[i]]$y,lgtdata[[i]]$X,SignRes) lgtdata[[i]]=c(lgtdata[[i]],list(converge=1,betafmle=out$par,hess=hess)) } else { lgtdata[[i]]=c(lgtdata[[i]],list(converge=0,betafmle=c(rep(0,nvar)), hess=diag(nvar))) } oldbetas[i,]=lgtdata[[i]]$betafmle if(i%%50 ==0) cat(" completed unit #",i,fill=TRUE) fsh() } # # initialize values # # set initial values for the indicators # ind is of length(nlgt) and indicates which mixture component this obs # belongs to. # ind=NULL ninc=floor(nlgt/ncomp) for (i in 1:(ncomp-1)) {ind=c(ind,rep(i,ninc))} if(ncomp != 1) {ind = c(ind,rep(ncomp,nlgt-length(ind)))} else {ind=rep(1,nlgt)} # # initialize probs # oldprob=rep(1/ncomp,ncomp) # #initialize delta # if (drawdelta){ olddelta = rep(0,nz*nvar) } else { #send placeholders to the _loop function if there is no Z matrix olddelta = 0 Z = matrix(0) deltabar = 0 Ad = matrix(0) } ################################################################### # Wayne Taylor # 09/22/2014 ################################################################### draws = rhierMnlRwMixture_rcpp_loop(lgtdata, Z, deltabar, Ad, mubar, Amu, nu, V, s, R, keep, nprint, drawdelta, as.matrix(olddelta), a, oldprob, oldbetas, ind, SignRes) #################################################################### if(drawdelta){ attributes(draws$Deltadraw)$class=c("bayesm.mat","mcmc") attributes(draws$Deltadraw)$mcpar=c(1,R,keep)} attributes(draws$betadraw)$class=c("bayesm.hcoef") attributes(draws$nmix)$class="bayesm.nmix" return(draws) }bayesm/R/clusterMix_rcpp.R0000644000176000001440000000447112566706215015311 0ustar ripleyusersclusterMix=function(zdraw,cutoff=.9,SILENT=FALSE,nprint=BayesmConstant.nprint){ # # # revision history: # written by p. rossi 9/05 # # purpose: cluster observations based on draws of indicators of # normal mixture components # # arguments: # zdraw is a R x nobs matrix of draws of indicators (typically output from rnmixGibbs) # the rth row of zdraw contains rth draw of indicators for each observations # each element of zdraw takes on up to p values for up to p groups. The maximum # number of groups is nobs. Typically, however, the number of groups will be small # and equal to the number of components used in the normal mixture fit. # # cutoff is a cutoff used in determining one clustering scheme it must be # a number between .5 and 1. # # nprint - print every nprint'th draw # # output: # two clustering schemes each with a vector of length nobs which gives the assignment # of each observation to a cluster # # clustera (finds zdraw with similarity matrix closest to posterior mean of similarity) # clusterb (finds clustering scheme by assigning ones if posterior mean of similarity matrix # > cutoff and computing associated z ) # # define needed functions # # ------------------------------------------------------------------------------------------ # # check arguments # if(missing(zdraw)) {pandterm("Requires zdraw argument -- R x n matrix of indicator draws")} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} # # check validity of zdraw rows -- must be integers in the range 1:nobs # nobs=ncol(zdraw) R=nrow(zdraw) if(sum(zdraw %in% (1:nobs)) < ncol(zdraw)*nrow(zdraw)) {pandterm("Bad zdraw argument -- all elements must be integers in 1:nobs")} cat("Table of zdraw values pooled over all rows",fill=TRUE) print(table(zdraw)) # # check validity of cuttoff if(cutoff > 1 || cutoff < .5) {pandterm(paste("cutoff invalid, = ",cutoff))} ################################################################### # Keunwoo Kim # 10/06/2014 ################################################################### out=clusterMix_rcpp_loop(zdraw, cutoff, SILENT, nprint) ################################################################### return(list(clustera=as.vector(out$clustera),clusterb=as.vector(out$clusterb))) }bayesm/R/mnlHess.R0000755000176000001440000000136010316323040013512 0ustar ripleyusersmnlHess = function(beta,y,X) { # p.rossi 2004 # changed argument order 9/05 # # Purpose: compute mnl -Expected[Hessian] # # Arguments: # beta is k vector of coefs # y is n vector with element = 1,...,j indicating which alt chosen # X is nj x k matrix of xvalues for each of j alt on each of n occasions # # Output: -Hess evaluated at beta # n=length(y) j=nrow(X)/n k=ncol(X) Xbeta=X%*%beta Xbeta=matrix(Xbeta,byrow=T,ncol=j) Xbeta=exp(Xbeta) iota=c(rep(1,j)) denom=Xbeta%*%iota Prob=Xbeta/as.vector(denom) Hess=matrix(double(k*k),ncol=k) for (i in 1:n) { p=as.vector(Prob[i,]) A=diag(p)-outer(p,p) Xt=X[(j*(i-1)+1):(j*i),] Hess=Hess+crossprod(Xt,A)%*%Xt } return(Hess) } bayesm/R/rivDP_rcpp.R0000644000176000001440000002305213114116632014156 0ustar ripleyusersrivDP = function(Data,Prior,Mcmc) { # # revision history: # P. Rossi 1/06 # added draw of alpha 2/06 # added automatic scaling 2/06 # removed reqfun 7/07 -- now functions are in rthetaDP # fixed initialization of theta 3/09 # fixed error in assigning user defined prior parms # W. Taylor 4/15 - added nprint option to MCMC argument # W. Taylor 7/16 - corrected bug for colAllw.set_size(ncolw) (see email to Peter and Keunwoo on 11/30/15 for more details) # # purpose: # draw from posterior for linear I.V. model with DP process for errors # # Arguments: # Data -- list of z,w,x,y # y is vector of obs on lhs var in structural equation # x is "endogenous" var in structural eqn # w is matrix of obs on "exogenous" vars in the structural eqn # z is matrix of obs on instruments # Prior -- list of md,Ad,mbg,Abg,mubar,Amu,nuV # md is prior mean of delta # Ad is prior prec # mbg is prior mean vector for beta,gamma # Abg is prior prec of same # lamda is a list of prior parms for DP draw # mubar is prior mean of means for "errors" # Amu is scale precision parm for means # nu,V parms for IW on Sigma (idential priors for each normal comp # alpha prior parm for DP process (weight on base measure) # or starting value if there is a prior on alpha (requires element Prioralpha) # Prioralpha list of hyperparms for draw of alpha (alphamin,alphamax,power,n) # # Mcmc -- list of R,keep,starting values for delta,beta,gamma,theta # maxuniq is maximum number of unique theta values # R is number of draws # keep is thinning parameter # nprint - print estimated time remaining on every nprint'th draw # SCALE if scale data, def: TRUE # gridsize is the gridsize parm for alpha draws # # Output: # list of draws of delta,beta,gamma and thetaNp1 which is used for # predictive distribution of errors (density estimation) # # Model: # # x=z'delta + e1 # y=beta*x + w'gamma + e2 # e1,e2 ~ N(theta_i) # # Priors # delta ~ N(md,Ad^-1) # vec(beta,gamma) ~ N(mbg,Abg^-1) # theta ~ DPP(alpha|lambda) # # # extract data and check dimensios # if(missing(Data)) {pandterm("Requires Data argument -- list of z,w,x,y")} if(is.null(Data$w)) isgamma=FALSE else isgamma=TRUE if(isgamma) w = Data$w #matrix if(is.null(Data$z)) {pandterm("Requires Data element z")} z=Data$z if(is.null(Data$x)) {pandterm("Requires Data element x")} x=as.vector(Data$x) if(is.null(Data$y)) {pandterm("Requires Data element y")} y=as.vector(Data$y) # # check data for validity # n=length(y) if(isgamma) {if(!is.matrix(w)) {pandterm("w is not a matrix")} dimg=ncol(w) if(n != nrow(w) ) {pandterm("length(y) ne nrow(w)")}} if(!is.matrix(z)) {pandterm("z is not a matrix")} dimd=ncol(z) if(n != length(x) ) {pandterm("length(y) ne length(x)")} if(n != nrow(z) ) {pandterm("length(y) ne nrow(z)")} # # extract elements corresponding to the prior # alimdef=BayesmConstant.DPalimdef nulimdef=BayesmConstant.DPnulimdef vlimdef=BayesmConstant.DPvlimdef if(missing(Prior)) { md=c(rep(0,dimd)) Ad=diag(BayesmConstant.A,dimd) if(isgamma) dimbg=1+dimg else dimbg=1 mbg=c(rep(0,dimbg)) Abg=diag(BayesmConstant.A,dimbg) gamma= BayesmConstant.gamma Istarmin=BayesmConstant.DPIstarmin alphamin=exp(digamma(Istarmin)-log(gamma+log(n))) Istarmax=floor(.1*n) alphamax=exp(digamma(Istarmax)-log(gamma+log(n))) power=BayesmConstant.DPpower Prioralpha=list(n=n,alphamin=alphamin,alphamax=alphamax,power=power) lambda_hyper=list(alim=alimdef,nulim=nulimdef,vlim=vlimdef) } else { if(is.null(Prior$md)) md=c(rep(0,dimd)) else md=Prior$md if(is.null(Prior$Ad)) Ad=diag(BayesmConstant.A,dimd) else Ad=Prior$Ad if(isgamma) dimbg=1+dimg else dimbg=1 if(is.null(Prior$mbg)) mbg=c(rep(0,dimbg)) else mbg=Prior$mbg if(is.null(Prior$Abg)) Abg=diag(BayesmConstant.A,dimbg) else Abg=Prior$Abg if(!is.null(Prior$Prioralpha)) {Prioralpha=Prior$Prioralpha} else {gamma= BayesmConstant.gamma Istarmin=BayesmConstant.DPIstarmin alphamin=exp(digamma(Istarmin)-log(gamma+log(n))) Istarmax=floor(.1*n) alphamax=exp(digamma(Istarmax)-log(gamma+log(n))) power=BayesmConstant.DPpower Prioralpha=list(n=n,alphamin=alphamin,alphamax=alphamax,power=power)} if(is.null(Prior$lambda_hyper)) {lambda_hyper=Prior$lambda_hyper} else {lambda_hyper=Prior$lambda_hyper; if(is.null(lambda_hyper$alim)) {lambda_hyper$alim=alimdef} if(is.null(lambda_hyper$nulim)) {lambda_hyper$nulim=nulimdef} if(is.null(lambda_hyper$vlim)) {lambda_hyper$vlim=vlimdef} } } # # check Prior arguments for valdity # if(lambda_hyper$alim[1]<0) {pandterm("alim[1] must be >0")} if(lambda_hyper$nulim[1]<0) {pandterm("nulim[1] must be >0")} if(lambda_hyper$vlim[1]<0) {pandterm("vlim[1] must be >0")} # # obtain starting values for MCMC # # we draw need inital values of delta, theta and indic # if(missing(Mcmc)) {pandterm("requires Mcmc argument")} theta=NULL if(!is.null(Mcmc$delta)) {delta = Mcmc$delta} else {lmxz = lm(x~z,data.frame(x=x,z=z)) delta = lmxz$coef[2:(ncol(z)+1)]} if(!is.null(Mcmc$theta)) {theta=Mcmc$theta } else {onecomp=list(mu=c(0,0),rooti=diag(2)) theta=vector("list",length(y)) for(i in 1:n) {theta[[i]]=onecomp} } dimd = length(delta) if(is.null(Mcmc$maxuniq)) {maxuniq=BayesmConstant.DPmaxuniq} else {maxuniq=Mcmc$maxuniq} if(is.null(Mcmc$R)) {pandterm("requres Mcmc argument, R")} R = Mcmc$R if(is.null(Mcmc$keep)) {keep=BayesmConstant.keep} else {keep=Mcmc$keep} if(is.null(Mcmc$nprint)) {nprint=BayesmConstant.nprint} else {nprint=Mcmc$nprint} if(nprint<0) {pandterm('nprint must be an integer greater than or equal to 0')} if(is.null(Mcmc$gridsize)) {gridsize=BayesmConstant.DPgridsize} else {gridsize=Mcmc$gridsize} if(is.null(Mcmc$SCALE)) {SCALE=BayesmConstant.DPSCALE} else {SCALE=Mcmc$SCALE} # # scale and center # if(SCALE){ scaley=sqrt(var(y)) scalex=sqrt(var(x)) meany=mean(y) meanx=mean(x) meanz=apply(z,2,mean) y=(y-meany)/scaley; x=(x-meanx)/scalex z=scale(z,center=TRUE,scale=FALSE) if(isgamma) {meanw=apply(w,2,mean); w=scale(w,center=TRUE,scale=FALSE)} } # # print out model # cat(" ",fill=TRUE) cat("Starting Gibbs Sampler for Linear IV Model With DP Process Errors",fill=TRUE) cat(" ",fill=TRUE) cat(" nobs= ",n,"; ",ncol(z)," instruments",fill=TRUE) cat(" ",fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("mean of delta ",fill=TRUE) print(md) cat(" ",fill=TRUE) cat("Adelta",fill=TRUE) print(Ad) cat(" ",fill=TRUE) cat("mean of beta/gamma",fill=TRUE) print(mbg) cat(" ",fill=TRUE) cat("Abeta/gamma",fill=TRUE) print(Abg) cat(" ",fill=TRUE) cat("G0 ~ N(mubar,Sigma (x) Amu^-1)",fill=TRUE) cat(" mubar = ",0,fill=TRUE) cat(" Sigma ~ IW(nu,nu*v*I)",fill=TRUE) cat(" Amu ~ uniform[",lambda_hyper$alim[1],",",lambda_hyper$alim[2],"]",fill=TRUE) cat(" nu ~ uniform on log grid [",2-1+exp(lambda_hyper$nulim[1]), ",",2-1+exp(lambda_hyper$nulim[2]),"]",fill=TRUE) cat(" v ~ uniform[",lambda_hyper$vlim[1],",",lambda_hyper$vlim[2],"]",fill=TRUE) cat(" ",fill=TRUE) cat("Parameters of Prior on Dirichlet Process parm (alpha)",fill=TRUE) cat("alphamin= ",Prioralpha$alphamin," alphamax= ",Prioralpha$alphamax," power=", Prioralpha$power,fill=TRUE) cat("alpha values correspond to Istarmin = ",Istarmin," Istarmax = ",Istarmax,fill=TRUE) cat(" ",fill=TRUE) cat("MCMC parms: R= ",R," keep= ",keep," nprint= ",nprint,fill=TRUE) cat(" maximum number of unique thetas= ",maxuniq,fill=TRUE) cat(" gridsize for alpha draws= ",gridsize,fill=TRUE) cat(" SCALE data= ",SCALE,fill=TRUE) cat(" ",fill=TRUE) ################################################################### # Wayne Taylor # 3/14/2015 ################################################################### if(isgamma == FALSE) w=matrix() out = rivDP_rcpp_loop(R,keep,nprint,dimd,mbg,Abg,md,Ad,y,isgamma,z,x,w, delta,PrioralphaList=Prioralpha,gridsize,SCALE,maxuniq,scalex,scaley,lambda_hyper, BayesmConstant.A,BayesmConstant.nu) ################################################################### nmix=list(probdraw=matrix(c(rep(1,length(out$thetaNp1draw))),ncol=1),zdraw=NULL,compdraw=out$thetaNp1draw) # # densitymix is in the format to be used with the generic mixture of normals plotting # methods (plot.bayesm.nmix) # attributes(nmix)$class=c("bayesm.nmix") attributes(out$deltadraw)$class=c("bayesm.mat","mcmc") attributes(out$deltadraw)$mcpar=c(1,R,keep) attributes(out$betadraw)$class=c("bayesm.mat","mcmc") attributes(out$betadraw)$mcpar=c(1,R,keep) attributes(out$alphadraw)$class=c("bayesm.mat","mcmc") attributes(out$alphadraw)$mcpar=c(1,R,keep) attributes(out$Istardraw)$class=c("bayesm.mat","mcmc") attributes(out$Istardraw)$mcpar=c(1,R,keep) if(isgamma){ attributes(out$gammadraw)$class=c("bayesm.mat","mcmc") attributes(out$gammadraw)$mcpar=c(1,R,keep)} if(isgamma) { return(list(deltadraw=out$deltadraw,betadraw=out$betadraw,alphadraw=out$alphadraw,Istardraw=out$Istardraw, gammadraw=out$gammadraw,nmix=nmix))} else { return(list(deltadraw=out$deltadraw,betadraw=out$betadraw,alphadraw=out$alphadraw,Istardraw=out$Istardraw, nmix=nmix))} }bayesm/vignettes/0000755000176000001440000000000013123305446013573 5ustar ripleyusersbayesm/vignettes/Constrained_MNL_Vignette.Rmd0000644000176000001440000003260313117570164021073 0ustar ripleyusers--- title: "Hierarchical Multinomial Logit with Sign Constraints" output: rmarkdown::html_document: theme: spacelab highlight: pygments toc: true toc_float: true toc_depth: 3 number_sections: no fig_caption: yes vignette: > %\VignetteIndexEntry{Hierarchical Multinomial Logit with Sign Constraints} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r, echo = FALSE} library(bayesm) knitr::opts_chunk$set(fig.align = "center", fig.height = 3.5, warning = FALSE, error = FALSE, message = FALSE) ``` ***** # Introduction `bayesm`'s posterior sampling function `rhierMnlRwMixture` permits the imposition of sign constraints on the individual-specific parameters of a hierarchical multinomial logit model. This may be desired if, for example, the researcher believes there are heterogenous effects from, say, price, but that all responses should be negative (i.e., sign-constrained). This vignette provides exposition of the model, discussion of prior specification, and an example. # Model The model follows the hierarchical multinomial logit specification given in Example 3 of the "`bayesm` Overview" Vignette, but will be repeated here succinctly. Individuals are assumed to be rational economic agents that make utility-maximizing choices. Utility is modeled as the sum of deterministic and stochastic components, where the inverse-logit of the probability of chosing an alternative is linear in the parameters and the error is assumed to follow a Type I Extreme Value distribution: $$ U_{ij} = X_{ij}\beta_i + \varepsilon_{ij} \hspace{0.8em} \text{with} \hspace{0.8em} \varepsilon_{ij}\ \sim \text{ iid Type I EV} $$ These assumptions yield choice probabilities of: $$ \text{Pr}(y_i=j) = \frac{\exp \{x_{ij}'\beta_i\}}{\sum_{k=1}^p\exp\{x_{ik}'\beta_i\}} $$ $x_i$ is $n_i \times k$ and $i = 1, \ldots, N$. There are $p$ alternatives, $j = 1, \ldots, p$. An outside option, often denoted $j=0$ can be introduced by assigning $0$'s to that option's covariate ($x$) values. We impose sign constraints by defining a $k$-length constraint vector `SignRes` that takes values from the set $\{-1, 0, 1\}$ to define $\beta_{ik} = f(\beta_{ik}^*)$ where $f(\cdot)$ is as follows: $$ \beta_{ik} = f(\beta_{ik}^*) = \left\{ \begin{array}{lcl} \exp(\beta_{ik}^*) & \text{if} & \texttt{SignRes[k]} = 1 \\ \beta_{ik}^* & \text{if} & \texttt{SignRes[k]} = 0 \\ -\exp(\beta_{ik}^*) & \text{if} & \texttt{SignRes[k]} = -1 \\ \end{array} \right. $$ The "deep" individual-specific parameters ($\beta_i^*$) are assumed to be drawn from a mixture of $M$ normal distributions with mean values driven by cross-sectional unit characteristics $Z$. That is, $\beta_i^* = z_i' \Delta + u_i$ where $u_i$ has a mixture-of-normals distribution.^[As documented in the helpfile for this function (accessible by `?bayesm::rhierMnlRwMixture`), draws from the posterior of the constrained parameters ($\beta$) can be found in the output `$betadraw` while draws from the posterior of the unconstrained parameters ($\beta^*$) are available in `$nmix$compdraw`.] Considering $\beta_i^*$ a length-$k$ row vector, we will stack the $N$ $\beta_i^*$'s vertically and write: $$ B=Z\Delta + U $$ Thus we have $\beta_i$, $z_i$, and $u_i$ as the $i^\text{th}$ rows of $B$, $Z$, and $U$. $B$ is $N \times k$, $Z$ is $N \times M$, $\Delta$ is $M \times k$, and $U$ is $N \times k$ where the distribution on $U$ is such that: $$ \Pr(\beta_{ik}^*) = \sum_{m=1}^M \pi_m \phi(z_i' \Delta \vert \mu_j, \Sigma_j) $$ $\phi$ is the normal pdf. # Priors Natural conjugate priors are specified: $$ \pi \sim \text{Dirichlet}(a) $$ $$ \text{vec}(\Delta) = \delta \sim MVN(\bar{\delta}, A_\delta^{-1}) $$ $$ \mu_m \sim MVN(\bar{\mu}, \Sigma_m \otimes a_\mu^{-1}) $$ $$ \Sigma_m \sim IW(\nu, V) $$ This specification of priors assumes that $\mu_m$ is independent of $\Sigma_m$ and that, conditional on the hyperparameters, the $\beta_i$'s are _a priori_ independent. $a$ implements prior beliefs on the number of normal components in the mixture with a default of 5. $\nu$ is a "tightness" parameter of the inverted-Wishart distribution and $V$ is its location matrix. Without sign constraints, they default to $\nu=k+3$ and $V=\nu I$, which has the effect of centering the prior on $I$ and making it "barely proper". $a_\mu$ is a tightness parameter for the priors on $\mu$, and when no sign constraints are imposed it defaults to an extremely diffuse prior of 0.01. These defaults assume the logit coefficients ($\beta_{ik}$'s) are on the order of approximately 1 and, if so, are typically reasonable hyperprior values. However, when sign constraints are imposed, say, `SignRes[k]=-1` such that $\beta_{ik} = -\exp\{\beta_{ik}^*\}$, then these hyperprior defults pile up mass near zero --- a result that follows from the nature of the exponential function and the fact that the $\beta_{ik}^*$'s are on the log scale. Let's show this graphically. ```{r} # define function drawprior <- function (mubar_betak, nvar, ncomp, a, nu, Amu, V, ndraw) { betakstar <- double(ndraw) betak <- double(ndraw) otherbeta <- double(ndraw) mubar <- c(rep(0, nvar-1), mubar_betak) for(i in 1:ndraw) { comps=list() for(k in 1:ncomp) { Sigma <- rwishart(nu,chol2inv(chol(V)))$IW comps[[k]] <- list(mubar + t(chol(Sigma/Amu)) %*% rnorm(nvar), backsolve(chol(Sigma), diag(1,nvar)) ) } pvec <- rdirichlet(a) beta <- rmixture(1,pvec,comps)$x betakstar[i] <- beta[nvar] betak[i] <- -exp(beta[nvar]) otherbeta[i] <- beta[1] } return(list(betakstar=betakstar, betak=betak, otherbeta=otherbeta)) } set.seed(1234) ``` ```{r} # specify rhierMnlRwMixture defaults mubar_betak <- 0 nvar <- 10 ncomp <- 3 a <- rep(5, ncomp) nu <- nvar + 3 Amu <- 0.01 V <- nu*diag(c(rep(1,nvar-1),1)) ndraw <- 10000 defaultprior <- drawprior(mubar_betak, nvar, ncomp, a, nu, Amu, V, ndraw) ``` ```{r, fig.align='center', fig.height=3.5, results='hold'} # plot priors under defaults par(mfrow=c(1,3)) trimhist <- -20 hist(defaultprior$betakstar, breaks=40, col="magenta", main="Beta_k_star", xlab="", ylab="", yaxt="n") hist(defaultprior$betak[defaultprior$betak>trimhist], breaks=40, col="magenta", main="Beta_k", xlab="", ylab="", yaxt="n", xlim=c(trimhist,0)) hist(defaultprior$otherbeta, breaks=40, col="magenta", main="Other Beta", xlab="", ylab="", yaxt="n") ``` We see that the hyperprior values for constrained logit parameters are far from uninformative. As a result, `rhierMnlRwMixture` implements different default priors for parameters when sign constraints are imposed. In particular, $a_\mu=0.1$, $\nu = k + 15$, and $V = \nu*\text{diag}(d)$ where $d_i=4$ if $\beta_{ik}$ is unconstrained and $d_i=0.1$ if $\beta_{ik}$ is constrained. Additionally, $\bar{\mu}_m = 0$ if unconstrained and $\bar{\mu}_m = 2$ otherwise. As the following plots show, this yields substantially less informative hyperpriors on $\beta_{ik}^*$ without significantly affecting the hyperpriors on $\beta_{ik}$ or $\beta_{ij}$ ($j \ne k$). ```{r} # adjust priors for constraints mubar_betak <- 2 nvar <- 10 ncomp <- 3 a <- rep(5, ncomp) nu <- nvar + 15 Amu <- 0.1 V <- nu*diag(c(rep(4,nvar-1),0.1)) ndraw <- 10000 tightprior <- drawprior(mubar_betak, nvar, ncomp, a, nu, Amu, V, ndraw) ``` ```{r, fig.align='center', fig.height=3.5, results='hold'} # plot priors under adjusted values par(mfrow=c(1,3)) trimhist <- -20 hist(tightprior$betakstar, breaks=40, col="magenta", main="Beta_k_star", xlab="", ylab="", yaxt="n") hist(tightprior$betak[tightprior$betak>trimhist], breaks=40, col="magenta", main="Beta_k", xlab="", ylab="", yaxt="n", xlim=c(trimhist,0)) hist(tightprior$otherbeta, breaks=40, col="magenta", main="Other Beta", xlab="", ylab="", yaxt="n") ``` # Example Here we demonstrate the implementation of the hierarchical multinomial logit model with sign-constrained parameters. We return to the `camera` data used in Example 3 of the "`bayesm` Overview" Vignette. This dataset contains conjoint choice data for 332 respondents who evaluated digital cameras. The data are stored in a lists-of-lists format with one list per respondent, and each respondent's list having two elements: a vector of choices (`y`) and a matrix of covariates (`X`). Notice the dimensions: there is one value for each choice occasion in each individual's `y` vector but one row per alternative in each individual's `X` matrix, making `nrow(x)` = 5 $\times$ `length(y)` because there are 5 alternatives per choice occasion. ```{r} library(bayesm) data(camera) length(camera) str(camera[[1]]) ``` As shown next, the first 4 covariates are binary indicators for the brands Canon, Sony, Nikon, and Panasonic. These correspond to choice (`y`) values of 1, 2, 3, and 4. `y` can also take the value 5, indicating that the respondent chose "none". The data include binary indicators for two levels of pixel count, zoom strength, swivel video display capability, and wifi connectivity. The last covaritate is price, recorded in hundreds of U.S. dollars so that the magnitude of the expected price coefficient is such that the default prior settings in `rhierMnlRwMixture` do not need to be adjusted. ```{r} str(camera[[1]]$y) str(as.data.frame(camera[[1]]$X)) ``` Let's say we would like to estimate the part-worths of the various attributes of these digital cameras using a multinomial logit model. To incorporate individual-level heterogeneous effects, we elect to use a hierarchical (i.e., random coefficient) specification. Further, we believe that despite the heterogeneity, each consumer's estimate price response ($\beta_{i,\text{price}}$) should be negative, which we will impose with a sign constraint. Following the above discussion, we use the default priors, which "adjust" automatically when sign constraints are imposed. ```{r, echo = FALSE} nvar <- 10 mubar <- c(rep(0,nvar-1),2) Amu <- 0.1 ncomp <- 5 a <- rep(5, ncomp) nu <- 25 V <- nu*diag(c(rep(4,nvar-1),0.1)) ``` ```{r, eval = FALSE} SignRes <- c(rep(0,nvar-1),-1) data <- list(lgtdata=camera, p=5) prior <- list(mubar=mubar, Amu=Amu, ncomp=ncomp, a=a, nu=nu, V=V, SignRes=SignRes) mcmc <- list(R=1e4, nprint=0) out <- rhierMnlRwMixture(Data=data, Prior=prior, Mcmc=mcmc) ``` ```{r, echo = FALSE} temp <- capture.output( {SignRes <- c(rep(0,nvar-1),-1); data <- list(lgtdata = camera, p = 5); prior <- list(mubar=mubar, Amu=Amu, ncomp=ncomp, a=a, nu=nu, V=V, SignRes=SignRes); mcmc <- list(R = 1e4, nprint = 0); out <- rhierMnlRwMixture(Data = data, Prior = prior, Mcmc = mcmc)}, file = NULL) ``` While much can be done to analyze the output, we will focus here on the constrained parameters on price. We first plot the posterior distributions for the price parameter for individuals $i=1,2,3$. Notice that the posterior distributions for the selected individual's price parameters lie entirely below zero. \begin{center} \textbf{Posterior Distributions for beta\_price} \end{center} ```{r} par(mfrow=c(1,3)) ind_hist <- function(mod, i) { hist(mod$betadraw[i , 10, ], breaks = seq(-14,0,0.5), col = "dodgerblue3", border = "grey", yaxt = "n", xlim = c(-14,0), xlab = "", ylab = "", main = paste("Ind.",i)) } ind_hist(out,1) ind_hist(out,2) ind_hist(out,3) ``` Next we plot a histogram of the posterior means for the 332 individual price paramters ($\beta_{i,\text{price}}$): ```{r} par(mfrow=c(1,1)) hist(apply(out$betadraw[ , 10, ], 1, mean), xlim = c(-20,0), breaks = 20, col = "firebrick2", border = "gray", xlab = "", ylab = "", main = "Posterior Means for Ind. Price Params, With Sign Constraint") ``` As a point of comparison, we re-run the model without the sign constraint using the default priors (output omitted) and provide the same set of plots. Note now that the right tail of the posterior distribution of $\beta_2^\text{price}$ extends to the right of zero. ```{r} data0 <- list(lgtdata = camera, p = 5) prior0 <- list(ncomp = 5) mcmc0 <- list(R = 1e4, nprint = 0) ``` ```{r, eval = FALSE} out0 <- rhierMnlRwMixture(Data = data0, Prior = prior0, Mcmc = mcmc0) ``` ```{r, echo = FALSE} temp <- capture.output( {out0 <- rhierMnlRwMixture(Data = data0, Prior = prior0, Mcmc = mcmc0)}, file = NULL) ``` ```{r} par(mfrow=c(1,3)) ind_hist <- function(mod, i) { hist(mod$betadraw[i , 10, ], breaks = seq(-12,2,0.5), col = "dodgerblue4", border = "grey", yaxt = "n", xlim = c(-12,2), xlab = "", ylab = "", main = paste("Ind.",i)) } ind_hist(out0,1) ind_hist(out0,2) ind_hist(out0,3) ``` ```{r} par(mfrow=c(1,1)) hist(apply(out0$betadraw[ , 10, ], 1, mean), xlim = c(-15,5), breaks = 20, col = "firebrick3", border = "gray", xlab = "", ylab = "", main = "Posterior Means for Ind. Price Params, No Sign Constraint") ``` ***** _Authored by [Dan Yavorsky](dyavorsky@gmail.com) and [Peter Rossi](perossichi@gmail.com). Last updated June 2017._ bayesm/vignettes/bayesm_Overview_Vignette.Rmd0000644000176000001440000015530213117606056021264 0ustar ripleyusers--- title: "bayesm Overview" output: rmarkdown::html_document : theme: spacelab highlight: pygments toc: true toc_float: true toc_depth: 3 number_sections: yes fig_caption: yes vignette: > %\VignetteIndexEntry{bayesm Overview} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r, echo = FALSE} library(bayesm) knitr::opts_chunk$set(fig.align = "center", fig.height = 3.5, warning = FALSE, error = FALSE, message = FALSE) ``` ***** # Introduction `bayesm` is an R package that facilitates statistical analysis using Bayesian methods. The package provides a set of functions for commonly used models in applied microeconomics and quantitative marketing. The goal of this vignette is to make it easier for users to adopt `bayesm` by providing a comprehensive overview of the package's contents and detailed examples of certain functions. We begin with the overview, followed by a discussion of how to work with `bayesm`. The discussion covers the structure of function arguments, the required input data formats, and the various output formats. The final section provides detailed examples to demonstrate Bayesian inference with the linear normal, multinomial logit, and hierarchical multinomial logit regression models. # Package Contents For ease of exposition, we have grouped the package contents into: - Posterior sampling functions - Utility functions - S3 methods^[For example, calling the generic function `summary(x)` on an object `x` with class `bayesm.mat` actually dispatches the method `summary.bayesm.mat` on `x`, which is equivalent to calling `summary.bayes.mat(x)`. For a nice introduction, see _Advanced R_ by Hadley Wickham, available [online](http://adv-r.had.co.nz/OO-essentials.html).] - Datasets Because the first two groups contain many functions, we organize them into subgroups by purpose. Below, we display each group of functions in a table with one column per subgroup. ----------------------------------------------------------------------------- Linear Models Limited Dependent Hierarchical Models Density Estimation \ Variable Models \ \ --------------- -------------------- -------------------- ------------------- `runireg`* `rbprobitGibbs`** `rhierLinearModel` `rnmixGibbs`* `runiregGibbs` `rmnpGibbs` `rhierLinearMixture` `rDPGibbs` `rsurGibbs`* `rmvpGibbs` `rhierMnlRwMixture`* \ `rivGibbs` `rmnlIndepMetrop` `rhierMnlDP` \ `rivDP` `rscaleUsage` `rbayesBLP` \ \ `rnegbinRw` `rhierNegbinRw` \ \ `rordprobitGibbs` ----------------------------------------------------------------------------- Table: Posterior Sampling Functions *`bayesm` offers the utility function `breg` with a related but limited set of capabilities as `runireg` --- similarly with `rmultireg` for `rsurGibbs`, `rmixGibbs` for `rnmixGibbs`, and `rhierBinLogit` for `rhierMnlRwMixture`. **`rbiNormGibbs` provides a tutorial-like example of Gibbs Sampling from a bivariate normal distribution. ------------------------------------------------------------------------------------ Log-Likelihood\ \ Log Density Random Draws Mixture-of-Normals Miscellaneous (data vector) (univariate) \ \ \ ------------------ --------------- ------------- ------------------- --------------- `llmnl` `lndIChisq` `rdirichlet` `clusterMix` `cgetC` `llmnp` `lndIWishart` `rmixture` `eMixMargDen` `condMom` `llnhlogit` `lndMvn` `rmvst` `mixDen` `createX` \ `lndMvst` `rtrun` `mixDenBi` `ghkvec` \ \ `rwishart` `momMix` `logMargDenNR` \ \ \ \ `mnlHess` \ \ \ \ `mnpProb` \ \ \ \ `nmat` \ \ \ \ `numEff` \ \ \ \ `simnhlogit` ------------------------------------------------------------------------------------ Table: Utility Functions ------------------------------------------- Plot Methods Summary Methods -------------------- ---------------------- `plot.bayesm.mat` `summary.bayesm.mat` `plot.bayesm.nmix` `summary.bayesm.nmix` `plot.bayesm.hcoef` `summary.bayesm.var` ------------------------------------------- Table: S3 Methods --------------------------------------- \ \ \ --------- -------------- -------------- `bank` `customerSat` `orangeJuice` `camera` `detailing` `Scotch` `cheese` `margarine` `tuna` --------------------------------------- Table: Datasets Some discussion of the naming conventions may be warranted. All functions use CamelCase but begin lowercase. Posterior sampling functions begin with `r` to match R's style of naming random number generation functions since these functions all draw from (posterior) distributions. Common abbreviations include _DP_ for Dirichlet Process, _IV_ for instrumental variables, _MNL_ and _MNP_ for multinomial logit and probit, _SUR_ for seemingly unrelated regression, and _hier_ for hierarchical. Utility functions that begin with `ll` calculate the log-likelihood of a data vector, while those that begin with `lnd` provide the log-density. Other abbreviations should be straighforward; please see the help file for a specific function if its name is unclear. # Working with `bayesm` We expect most users of the package to interact primarily with the posterior sampling functions. These functions take a consistent set of arguments as inputs (`Data`, `Prior`, and `Mcmc` --- each is a list) and they return output in a consistent format (always a list). `summary` and `plot` generic functions can then be used to facilitate analysis of the output because of the classes and methods defined in `bayesm`. The following subsections describe the format of the standardized function arguments as well as the required format of the data inputs and the format of the output from `bayesm`'s posterior sampling functions. ## Input: Function Arguments The posterior sampling functions take three arguments: `Data`, `Prior`, and `Mcmc`. Each argument is a **list**. As a minimal example, assume you'd like to perform a linear regression and that you have in your work space `y` (a vector of length $n$) and `X` (a matrix of dimension $n \times p$). For this example, we utilize the default values for `Prior` and so we do not specify the `Prior` argument. These components (`Data`, `Prior`, and `Mcmc` as well as their arguments including `R` and `nprint`) are discussed in the subsections that follow. Then the `bayesm` syntax is simply: ```{r, eval = FALSE} mydata <- list(y = y, X = X) mymcmc <- list(R = 1e6, nprint = 0) out <- runireg(Data = mydata, Mcmc = mymcmc) ``` The list elements of `Data`, `Prior`, and `Mcmc` must be named. For example, you could not use the following code because the `Data` argument `mydata2` has unnamed elements. ```{r, eval=FALSE} mydata2 <- list(y, X) out <- runireg(Data = mydata2, Mcmc = mymcmc) ``` ### `Data` Argument `bayesm`'s posterior sampling functions do not accept data stored in dataframes; data must be stored as vectors or matrices. For **non-hierarchical** models, the list of input data simply contains the approprate data vectors or matrices from the set \{`y`, `X`, `w`, `z`\}^[Functions such as `rivGibbs` only permit one endogenous variable and so the function argument is lowercase: `x`.] and possibly a scalar (length one vector) from the set \{`k`, `p`\}. - For functions that require only a single data argument (such as the two density estimation functions, `rnmixGibbs` and `rDPGibbs`), `y` is that argument. More typically, `y` is used for LHS^[LHS and RHS stand for left-hand side and right-hand side.] variable(s) and `X` for RHS variables. For estimation using instrumental variables, variables in the structural equation are separated into "exogenous" variables `w` and an "edogenous" variable `x`; `z` is a matrix of instruments. - For the scalars, `p` indicates the number of choice alternatives in discrete choice models and `k` is used as the maximum ordinate in models for ordinal data (e.g., `rordprobitGibbs`). For **hierarchical** models, the input data has up to 3 components. We'll discuss these components using the mixed logit model (`rhierMnlRwMixture`) as an example. For `rhierMnlRwMixture`, the `Data` argument is `list(lgtdata, Z, p)`. 1. The first component for all hierarchical models is required. It is a list of lists named either `regdata` or `lgtdata`, depending on the function. In `rhierMnlRwMixture`, `lgtdata` is a list of lists, with each interior list containing a vector or one-column matrix of multinomial outcomes `y` and a design matrix of covariates `X`. In Example 3 below, we show how to convert data from a data frame to this required list-of-lists format. 1. The second component, `Z`, is present but optional for all hierarchical models. `Z` is a matrix of cross-sectional unit characteristics that drive the mean responses; that is, a matrix of covariates for the individual parameters (e.g. $\beta_i$'s). For example, the model (omitting the priors) for `rhierMnlRwMixture` is: $$ y_i \sim \text{MNL}(X_i'\beta_i) \hspace{1em} \text{with} \hspace{1em} \beta_i = Z \Delta_i + u_i \hspace{1em} \text{and} \hspace{1em} u_i \sim N(\mu_j, \Sigma_j) $$ where $i$ indexes individuals and $j$ indexes cross-sectional unit characteristics. 1. The third component (if accepted) is a scalar, such as `p` or `k`, and like the arguments by the same names in the non-hierarchical models, is used to indicate the size of the choice set or the maximum value of a scale or count variable. In `rhierMnlRwMixture`, the argument is `p`, which is used to indicate the number of choice alternatives. Note that `rbayesBLP` (the hierarchical logit model with _aggregate_ data as in Berry, Levinsohn, and Pakes (1995) and Jiang, Manchanda, and Rossi (2009)) deviates slightly from the standard data input. `rbayesBLP` uses `j` instead of `p` to be consistent with the literature and calls the LHS variable `share` rather than `y` to emphasize that aggregate (market share instead of individual choice) data are required. ### `Prior` Argument Specification of prior distributions is model-specific, so our discussion here is brief. All posterior sampling functions offer default values for parameters of prior distributions. These defaults were selected to yield proper yet reasonably-diffuse prior distributions (assuming the data are in approximately unit scale). In addition, these defaults are consistent across functions. For example, normal priors have default values of mean 0 with value 0.01 for the scaling factor of the prior precision matrix. Specification of the prior is important. Significantly more detail can be found in chapters 2--5 of BSM[^BSM] and the help files for the posterior sampling functions. We strongly recommend you consult them before accepting the default values. [^BSM]: Rossi, Peter, Greg Allenby and Robert McCulloch, _Bayesian Statistics and Marketing_, John Wiley \& Sons, 2005. [Website](http://www.perossi.org/home/bsm-1). ### `Mcmc` Argument {#mcmcarg} The `Mcmc` argument controls parameters of the sampling algorithm. The most common components of this list include: - `R`: the number of MCMC draws - `keep`: a thinning parameter indicating that every `keep`$^\text{th}$ draw should be retained - `nprint`: an option to print the estimated time remaining to the console after each `nprint`$^\text{th}$ draw MCMC methods are non-iid. As a result, a large simulation size may be required to get reliable results. We recommend setting `R` large enough to yield an adequate effective sample size and letting `keep` default to the value 1 unless doing so imposes memory constraints. A careful reader of the `bayesm` help files will notice that many of the examples set `R` equal to 1000 or less. This low number of draws was chosen for speed, as the examples are meant to demonstrate _how_ to run the code and do not necessarily suggest best practices for a proper statistical analysis. `nprint` defaults to 100, but for large `R`, you may want to increase the `nprint` option. Alternatively, you can set `nprint=0`, in which case the priors will still be printed to the console, but the estimated time remaining will not. Additional components of the `Mcmc` argument are function-specific, but typically include starting values for the algorithm. For example, the `Mcmc` argument for `runiregGibbs` takes `sigmasq` as a scalar element of the list. The Gibbs Sampler for `runiregGibbs` first draws $\beta | \sigma^2$, then draws $\sigma^2 | \beta$, and then repeats. For the first draw of $\beta$ in the MCMC chain, a value of $\sigma^2$ is required. The user can specify a value using `Mcmc$sigmasq`, or the user can omit the argument and the function will use its default (`sigmasq = var(Data$y)`). ## Output: Returned Results `bayesm` posterior sampling functions return a consistent set of results and output to the user. At a minimum, this output includes draws from the posterior distribution. `bayesm` provides a set of `summary` and `plot` methods to facilitate analysis of this output, but the user is free to analyze the results as he or she sees fit. ### Output Formats All `bayesm` posterior sampling functions return a list. The elements of that list include a set of vectors, matrices, and/or arrays (and possibly a list), the exact set of which depend on the function. - Vectors are returned for draws of parameters with no natural grouping. For example, `runireg` implements and iid sampler to draw from the posterior of a homoskedastic univariate regression with a conjugate prior (i.e., a Bayesian analog to OLS regression). One output list element is `sigmasqdraw`, a length `R/keep` vector for the scalar parameter $\sigma^2$. - Matrices are returned for draws of parameters with a natural grouping. Again using `runireg` as the example, the output list includes `betadraw`, an `R/keep` $\times$ `ncol(X)` matrix for the vector of $\beta$ parameters. Contrary to the next bullet, draws for the parameters in a variance-covariance matrix are returned in matrix form. For example, `rmnpGibbs` implements a Gibbs Sampler for a multinomial probit model where one set of parameters is the $(p-1) \times (p-1)$ matrix $\Sigma$. The output list for `rmnpGibbs` includes the list element `sigmadraw`, which is a matrix of dimension `R/keep`$\times (p-1)*(p-1)$ with each row containing a draw (in vector form) for all the elements of the matrix $\Sigma$. `bayesm`'s `summary` and `plot` methods (see below) are designed to handle this format. - Arrays are used when parameters have a natural matrix-grouping, such that the MCMC algorithm returns `R/keep` draws of the matrix. For example, `rsurGibbs` returns a list that includes `Sigmadraw`, an $m \times m \times$`R/keep` array, where $m$ is the number of regression equations. As a second example, `rhierLinearModel` estimates a hierarchical linear regression model with a normal prior, and returns a list that includes `betadraw`, an $n \times k \times$`R/keep` array, where $n$ signifies the number of individuals (each with their own $\beta_i$) and $k$ signifies the number of covariates (`ncol(X)` = $k$). - For functions that use a mixture-of-normals or Dirichlet Process prior, the output list includes a list (`nmix`) pertaining to that prior. `nmix` is itself a list with 3 components: `probdraw`, `zdraw`, and `compdraw`. `probdraw` reports the probability that each draw came from a particular normal component; `zdraw` indicates which mixture-of-normals component each draw is assigned to; and `compdraw` provides draws for the mixture-of-normals components (i.e., mean vectors and Cholesky roots of covariance matrices). Note that if you specify a "mixture" with only one normal component, there will be no useful information in `probdraw`. Also note that `zdraw` is not relevant for density estimation and will be null except in `rnmixGibbs` and `rDPGibbs`. ### Classes and Methods In R generally, objects can be assigned a _class_ and then a _generic_ function can be used to run a _method_ on an object with that class. The list elements in the output from `bayesm` posterior sampling functions are assigned special `bayesm` classes. The `bayesm` package includes `summary` and `plot` methods for use with these classes (see the table in Section 2 above). This means you can call the generic function (e.g., `summary`) on individual list elements of `bayesm` output and it will return specially-formatted summary results, including the effective sample size. To see this, the code below provides an example using `runireg`. Here the generic function `summary` dispatches the method `summary.bayesm.mat` because the `betadraw` element of `runireg`'s output has class `bayesm.mat`. This example also shows the information about the prior that is printed to the console during the call to a posterior sampling function. Notice, however, that no remaining time is printed because `nprint` is set to zero. ```{r} set.seed(66) R <- 2000 n <- 200 X <- cbind(rep(1,n), runif(n)) beta <- c(1,2) sigsq <- 0.25 y <- X %*% beta + rnorm(n, sd = sqrt(sigsq)) out <- runireg(Data = list(y = y, X = X), Mcmc = list(R = R, nprint = 0)) summary(out$betadraw, tvalues = beta) ``` ## Access to Code `bayesm` was originally created as a companion to BSM, at which time most functions were written in R. The package has since been expanded to include additional functionality and most code has been converted to C++ via `Rcpp` for faster performance. However, for users interested in obtaining the original implementation of a posterior sampling function (in R instead of C++), you may still access the last version (2.2-5) of `bayesm` prior to the C++/`Rcpp` conversion from the [package archive](https://cran.r-project.org/src/contrib/Archive/bayesm/) on CRAN. To access the `R` code in the current version of `bayesm`, the user can simply call a function without parenthesis. For example, `bayesm::runireg`. However, most posterior sampling functions only perform basic checks in `R` and then call an unexported C++ function to do the heavy lifting (i.e., the MCMC draws). This C++ source code is not available to the user via the installed `bayesm` package because C++ code is compiled upon package installation on Linux machines and pre-compiled by CRAN for Mac and Windows. To access this source code, the user must download the "package source" from CRAN. This can be accomplished by clicking on the appropriate link at the `bayesm` [package archive](https://cran.r-project.org/src/contrib/Archive/bayesm/) or by executing the `R` command `download.packages(pkgs="bayesm", destdir=".", type="source")`. Either of these methods will provide you with a compressed file "bayesm_version.tar.gz" that can be uncompressed. The C++ code can then be found in the "src" subdirectory. # Examples We begin with a brief introduction to regression and Bayesian estimation. This will help set the notation and provide background for the examples that follow. We do not claim that this will be a sufficient introduction to the reader for which these ideas are new. We refer that reader to excellent texts on regression analysis by Cameron \& Trivedi, Davidson \& MacKinnon, Goldberger, Greene, Wasserman, and Wooldridge.[^1] For Bayesian methods, we recommend Gelman et al., Jackman, Marin \& Robert, Rossi et al., and Zellner.[^2] [^1]: Cameron, Colin and Pravin Trivedi, _Microeconometrics: Methods and Applications_, Cambridge University Press, 2005. Davidson, Russell and James MacKinnon, _Estimation and Inference in Econometrics_, Oxford University Press, 1993. Goldberger, Arthur, _A Course in Econometrics_, Harvard University Press, 1991. Greene, William, _Econometric Analysis_, Prentice Hall, 2012 (7th edition). Wasserman, Larry, _All of Statistics: A Concise Course in Statistical Inferece_, Springer, 2004. Wooldridge, Jeffrey, _Econometric Analysis of Cross Section and Panel Data_, MIT Press, 2010 (2nd edition). [^2]: Gelman, Andrew, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin, _Bayesian Data Analysis_, CRC Press, 2013 (3rd edition). Jackman, Simon, _Bayesian Analysis for the Social Sciences_, Wiley, 2009. Marin, Jean-Michel and Christian Robert, _Bayesian Essentials with R_, Springer, 2014 (2nd edition). Rossi, Peter, Greg Allenby, and Robert McCulloch, _Bayesian Statistics and Marketing_, Wiley, 2005. Zellner, Arnold, _An Introduction to Bayesian Inference in Economics_, Wiley, 1971. ## What is Regression Suppose you believe a variable $y$ varies with (or is caused by) a set of variables $x_1, x_2, \ldots, x_k$. For notational convenience, we'll collect the set of $x$ variables into $X$. These variables $y$ and $X$ have a joint distribution $f(y, X)$. Typically, interest will not fall on this joint distribution, but rather on the conditional distribution of the "outcome" variable $y$ given the "explanatory" variables (or "covariates") $x_1, x_2, \ldots, x_k$; this conditional distribution being $f(y|X)$. To carry out inference on the relationship between $y$ and $X$, the researcher then often focuses attention on one aspect of the conditional distribution, most commonly its expected value. This conditional mean is assumed to be a function $g$ of the covariates such that $\mathbb{E}[y|X] = g(X, \beta)$ where $\beta$ is a vector of parameters. A function for the conditional mean is known as a "regression" function. The canonical introductory regression model is the normal linear regression model, which assumes that $y \sim N(X\beta, \sigma^2)$. Most students of regression will have first encountered this model as a combination of deterministic and stochastic components. There, the stochastic component is defined as deviations from the conditional mean, $\varepsilon = y - \mathbb{E}[y|X]$, such that $y = \mathbb{E}[y|X] + \varepsilon$ or that $y = g(X, \beta) + \varepsilon$. The model is then augmented with the assumptions that $g(X, \beta) = X \beta$ and $\varepsilon \sim N(0,\sigma^2)$ so that the normal linear regression model is: $$ y = X \beta + \varepsilon \text{ with } \varepsilon \sim N(0,\sigma^2) \hspace{1em} \text{or} \hspace{1em} y \sim N(X\beta, \sigma^2) $$ When taken to data, additional assumptions are made which include a full-rank condition on $X$ and often that $\varepsilon_i$ for $i=1,\ldots,n$ are independent and identically distributed. Our first example will demonstrate how to estimate the parameters of the normal linear regression model using Bayesian methods made available by the posterior sampling function `runireg`. We then provide an example to estimate the parameters of a model when $y$ is a categorical variable. This second example is called a multinomial logit model and uses the logistic "link" function $g(X, \beta) = [1 + exp(-X\beta)]^{-1}$. Our third and final example will extend the multinomial logit model to permit individual-level parameters. This is known as a hierarchical model and requires panel data to perform the estimation. Before launching into the examples, we briefly introduce Bayesian methodology and contrast it with classical methods. ## What is Bayesian Inference Under classical econometric methods, $\beta$ is most commonly estimated by minimizing the sum of squared residuals, maximizing the likelihood, or matching sample moments to population moments. The distribution of the estimators (e.g., $\hat{\beta}$) and test statistics derived from these methods rely on asymptotic concepts and are based on imaginary samples not observed. In contrast, Bayesian inference provides the benefits of (a) exact sample results, (b) integration of descision-making, estimation, testing, and model selection, and (c) a full accounting of uncertainty. These benefits from Bayesian inference rely heavily on probability theory and, in particular, distributional theory, some elements of which we now briefly review. Recall the relationship between the joint and conditional densities for random variables $W$ and $Z$: $$ P_{A|B}(A=a|B=b) = \frac{P_{A,B}(A=a, B=b)}{P_B(B=b)} $$ This relationship can be used to derive Bayes' Theorem, which we write with $D$ for "data" and $\theta$ as the parameters (and with implied subscripts): $$ P(\theta|D) = \frac{P(D|\theta)P(\theta)}{P(D)} $$ Noticing that $P(D)$ does not contain the parameters of interest ($\theta$) and is therefore simply a normalizing constant, we can instead write: $$ P(\theta|D) \propto P(D|\theta)P(\theta) $$ Introducing Bayesian terminology, we have that the "Posterior" is proportional to the Likelihood times the Prior. Thus, given (1) a dataset ($D$), (2) an assumption on the data generating process (the likelihood, $P(D|\theta)$), and (3) a specification of the prior distribution of the parameters ($P(\theta)$), we can find the _exact_ (posterior) distribution of the parameters given the observed data. This is in stark contrast to classical econometric methods, which typically only provide the _asymptotic_ distributions of estimators. However, for any problem of practical interest, the posterior distribution is a high-dimensional object. Additionally, it may not be possible to analytically calculate the posterior or its features (e.g., marginal distributions or moments such as the mean). To handle these issues, the modern approach to Bayesian inference relies on simulation methods to sample from the (high-dimensional) posterior distribution and then construct marginal distributions (or their features) from the sampled draws of the posterior. As a result, simulation and summaries of the posterior play important roles in modern Bayesian statistics. `bayesm`'s posterior sampling functions (as their name suggests) sample from posterior distributions. `bayesm`'s `summary` and `plot` methods can be used to analyze those draws. Unlike most classical econometric methods, the MCMC methods implemented in `bayesm`'s posterior sampling functions provide an estimate of the entire posterior distribution, not just a few moments. Given this "rich" result from Bayesian methods, it is best to summarize posterior distributions using histograms or quantiles. We advise that you resist the temptation to simply report the posterior mean and standard deviation; for non-normal distributions, those moments may have little meaning. In the examples that follow, we will describe the data we use, present the model, demonstrate how to estimate it using the appropriate posterior sampling function, and provide various ways to summarize the output. ## Example 1: Linear Normal Regression ### Data For our first example, we will use the `cheese` dataset, which provides `r data(cheese); format(nrow(cheese), big.mark=",")` observations of weekly sales volume for a package of Borden sliced cheese, as well as a measure of promotional display activity and price. The data are aggregated to the "key" account (i.e., retailer-market) level. ```{r} data(cheese) names(cheese) <- tolower(names(cheese)) str(cheese) ``` Suppose we want to assess the relationship between sales volume and price and promotional display activity. For this example, we will abstract from whether these relationships vary by retailer or whether prices are set endogenously. Simple statistics show a negative correlation between volume and price, and a positive correlation between volume and promotional activity, as we would expect. ```{r} options(digits=3) cor(cheese$volume, cheese$price) cor(cheese$volume, cheese$disp) ``` ### Model We model the expected log sales volume as a linear function of log(price) and promotional activity. Specifically, we assume $y_i$ to be iid with $p(y_i|x_i,\beta)$ normally distributed with a mean linear in $x$ and a variance of $\sigma^2$. We will denote observations with the index $i = 1, \ldots, n$ and covariates with the index $j = 1, \ldots, k$. The model can be written as: $$ y_i = \sum_{j=1}^k \beta_j x_{ij} + \varepsilon_i = x_i'\beta + \varepsilon_i \hspace{1em} \text{with} \hspace{1em} \varepsilon_i \sim iid\ N(0,\sigma^2) $$ or equivalently but more compactly as: $$ y \sim MVN(X\beta,\ \sigma^2I_n) $$ Here, the notation $N(0, \sigma^2)$ indicates a univariate normal distribution with mean $0$ and variance $\sigma^2$, while $MVN(X\beta,\ \sigma^2I_n)$ indicates a multivariate normal distribution with mean vector $X\beta$ and variance-covariance matrix $\sigma^2I_n$. In addition, $y_i$, $x_{ij}$, $\varepsilon_i$, and $\sigma^2$ are scalars while $x_i$ and $\beta$ are $k \times 1$ dimensional vectors. In the more compact notation, $y$ is an $n \times 1$ dimensional vector, $X$ is an $n \times k$ dimensional matrix with row $x_i$, and $I_n$ is an $n \times n$ dimensional identity matrix. With regard to the `cheese` dataset, $k = 2$ and $n = 5,555$. When employing Bayesian methods, the model is incomplete until the prior is specified. For our example, we elect to use natural conjugate priors, meaning the family of distributions for the prior is chosen such that, when combined with the likelihood, the posterior will be of the same distributional family. Specifically, we first factor the joint prior into marginal and conditional prior distributions: $$ p(\beta,\sigma^2) = p(\beta|\sigma^2)p(\sigma^2) $$ We then specify the prior for $\sigma^2$ as inverse-gamma (written in terms of a chi-squared random variable) and the prior for $\beta|\sigma^2$ as multivariate normal: $$ \sigma^2 \sim \frac{\nu s^2}{\chi^2_{\nu}} \hspace{1em} \text{and} \hspace{1em} \beta|\sigma^2 \sim MVN(\bar{\beta},\sigma^2A^{-1}) $$ Other than convenience, we have little reason to specify priors from these distributional families; however, we will select diffuse priors so as not to impose restrictions on the model. To do so, we must pick values for $\nu$ and $s^2$ (the degrees of freedom and scale parameters for the inverted chi-squared prior on $\sigma^2$) as well as $\bar{\beta}$ and $A^{-1}$ (the mean vector and variance-covariance matrix for the multivariate normal prior on the $\beta$ vector). The `bayesm` posterior sampling function for this model, `runireg`, defaults to the following values: - $\nu = 3$ - $s^2 =$ `var(y)` - $\bar{\beta} = 0$ - $A = 0.01*I$ We will use these defaults, as they are chosen to be diffuse for data with a unit scale. Thus, for each $\beta_j | \sigma^2$ we have specified a normal prior with mean 0 and variance $100\sigma^2$, and for $\sigma^2$ we have specified an inverse-gamma prior with $\nu = 3$ and $s^2 = \text{var}(y)$. We graph these prior distributions below. ```{r fig.show = "hold"} par(mfrow = c(1,2)) curve(dnorm(x,0,10), xlab = "", ylab = "", xlim = c(-30,30), main = expression(paste("Prior for ", beta[j])), col = "dodgerblue4") nu <- 3 ssq <- var(log(cheese$volume)) curve(nu*ssq/dchisq(x,nu), xlab = "", ylab = "", xlim = c(0,1), main = expression(paste("Prior for ", sigma^2)), col = "darkred") par(mfrow = c(1,1)) ``` ### Bayesian Estimation Although this model involves nontrivial natural conjugate priors, the posterior is available in closed form: $$ p(\beta, \sigma^2 | y, X) \propto (\sigma^2)^{-k/2} \exp \left\{ -\frac{1}{2\sigma^2}(\beta - \bar{\beta})'(X'X+A)(\beta - \bar{\beta}) \right\} \times (\sigma^2)^{-((n+\nu_0)/2+1)} \exp \left\{ -\frac{\nu_0s_0^2 + ns^2}{2\sigma^2} \right\} $$ or \begin{align*} \beta | \sigma^2, y, X &\sim N(\bar{\beta}, \sigma^2(X'X+A)^{-1}) \\ \\ \sigma^2 | y, X &\sim \frac{\nu_1s_1^2}{\chi^2_{\nu_1}}, \hspace{3em} \text{with} \> \nu_1 = \nu_0+n \hspace{1em} \text{and} \hspace{1em} s_1^2 = \frac{\nu_0s_0^2 + ns^2}{\nu_0+n} \end{align*} The latter representation suggests a simulation strategy for making draws from the posterior. We draw a value of $\sigma^2$ from its marginal posterior distribution, insert this value into the expression for the covariance matrix of the conditional normal distribution of $\beta|\{\sigma^2,y\}$ and draw from this multivariate normal. This simulation strategy is implemented by `runireg`, using the defaults for `Prior` specified above. The code is quite simple. ```{r, eval = FALSE} dat <- list(y = log(cheese$volume), X = model.matrix( ~ price + disp, data = cheese)) out <- runireg(Data = dat, Mcmc = list(R=1e4, nprint=1e3)) ``` ```{r, echo = FALSE} temp <- capture.output( {set.seed(1234); dat <- list(y = log(cheese$volume), X = model.matrix( ~ price + disp, data = cheese)); out <- runireg(Data = dat, Mcmc = list(R=1e4, nprint=1e3))}, file = NULL) ``` Note that `bayesm` posterior sampling functions print out information about the prior and about MCMC progress during the function call (unless `nprint` is set to 0), but for presentation purposes we suppressed that output here. `runireg` returns a list that we have saved in `out`. The list contains two elements, `betadraw` and `sigmasqdraw`, which you can verify by running `str(out)`. `betadraw` is an `R/keep` $\times$ `ncol(X)` ($10,000 \times 3$ with a column for each of the intercept, price, and display) dimension matrix with class `bayesm.mat`. We can analyze or summarize the marginal posterior distributions for any $\beta$ parameter or the $\sigma^2$ parameter. For example, we can plot histograms of the price coefficient (even though it is known to follow a t-distrbution, see BSM Ch. 2.8) and for $\sigma^2$. Notice how concentrated the posterior distributions are compared to their priors above. ```{r, fig.show = "hold"} B <- 1000+1 #burn in draws to discard R <- 10000 par(mfrow = c(1,2)) hist(out$betadraw[B:R,2], breaks = 30, main = "Posterior Dist. of Price Coef.", yaxt = "n", yaxs="i", xlab = "", ylab = "", col = "dodgerblue4", border = "gray") hist(out$sigmasqdraw[B:R], breaks = 30, main = "Posterior Dist. of Sigma2", yaxt = "n", yaxs="i", xlab = "", ylab = "", col = "darkred", border = "gray") par(mfrow = c(1,1)) ``` Additionally, we can compute features of these posterior distributions. For example, the posterior means price and display are: ```{r} apply(out$betadraw[B:R,2:3], 2, mean) ``` Conveniently, `bayesm` offers this functionality (and more) with its `summary` and `plot` methods. Notice that `bayesm`'s methods use a default burn-in length, calculated as `trunc(0.1*nrow(X))`. You can override the default by specifying the `burnin` argument. We see that the means for the first few retail fixed effects in the summary information below match those calculated "by hand" above. ```{r} summary(out$betadraw) ``` The same can be done with the `plot` generic function. However, we reference the method directly (`plot.bayesm.mat`) to plot a subset of the `bayesm` output -- specifically we plot the price coefficient. In the histogram, note that the green bars delimit a 95\% Bayesian credibility interval, yellow bars shows +/- 2 numerical standard errors for the posterior mean, and the red bar indicates the posterior mean. Also notice that this pink histogram of the posterior distribution on price, which was created by calling the `plot` generic, matches the blue one we created "by hand" above. The `plot` generic function also provides a trace plot and and ACF plot. In many applications (although not in this simple model), we cannot be certain that our draws from the posterior distribution adequately represent all areas of the posterior with nontrivial mass. This may occur, for instance, when using a "slow mixing" Markov Chain Monte Carlo (MCMC) algorithm to draw from the posterior. In such a case, we might see patterns in the trace plot and non-zero autocorrelations in the ACF plot; these will coincide with values for the Effective Sample Size less than `R`. (Effective Sample Size prints out with the `summary` generic function, as above.) Here, however, we are able to sample from the posterior distribution by taking iid draws, and so we see large Effective Sample Sizes in the `summary` output above, good mixing the trace plot below, and virtually no autocorrelation between draws in the ACF plot below. ```{r} plot.bayesm.mat(out$betadraw[,2]) ``` ## Example 2: Multinomial Logistic Regression ### Data Linear regression models like the one in the previous example are best suited for continuous outcome variables. Different models (known as limited dependent variable models) have been developed for binary or multinomial outcome variables, the most popular of which --- the multinomial logit --- will be the subject of this section. For this example, we analyze the `margarine` dataset, which provides panel data on purchases of margarine. The data are stored in two dataframes. The first, `choicePrice`, lists the outcome of `r data(margarine); format(nrow(margarine$choicePrice), big.mark=",")` choice occasions as well as the choosing household and the prices of the `r max(margarine$choicePrice[,2])` choice alternatives. The second, `demos`, provides demographic information about the choosing households, such as their income and family size. We begin by merging the information from these two dataframes: ```{r, results = "hold"} data(margarine) str(margarine) marg <- merge(margarine$choicePrice, margarine$demos, by = "hhid") ``` Compared to the standard $n \times k$ rectangular format for data to be used in a linear regression model, choice data may be stored in various formats, including a rectangular format where the $p$ choice alternatives are allocated across columns or rows, or a list-of-lists format as used in `bayesm`'s hierarchical models, which we demonstrate in Example 3 below. For all functions --- and notably those that implement multinomial logit and probit models --- the data must be in the format expected by the function, and `bayesm`'s posterior sampling funtions are no exception. In this example, we will implement a multinomial logit model using `rmnlIndepMetrop`. This posterior sampling function requires `y` to be a length-$n$ vector (or an $n \times 1$ matrix) of multinomial outcomes ($1, \dots, p$). That is, each element of `y` corresponds to a choice occasion $i$ with the value of the element $y_i$ indicating the choice that was made. So if the fourth alternative was chosen on the seventh choice occasion, then $y_7 = 4$. The `margarine` data are stored in that format, and so we easily specify `y` with the following code: ```{r} y <- marg[,2] ``` `rmnlIndepMetrop` requires `X` to be an $np \times k$ matrix. That is, each alternative is listed on its own row, with a group of $p$ rows together corresponding to the alternatives available on one choice occasion. However, the `margarine` data are stored with the various choice alternatives in columns rather than rows, so reformatting is necessary. `bayesm` provides the utility function `createX` to assist with the conversion. `createX` requires the user to specify the number of choice alternatives `p` as well as the number of alternative-specific variables `na` and an $n \times$ `na` matrix of alternative-specific data `Xa` ("a" for alternative-specific). Here, we have $p=10$ choice alternatives with `na` $=1$ alternative-specific variable (price). If we were only interested in using price as a covariate, we would code: ```{r} X1 <- createX(p=10, na=1, Xa=marg[,3:12], nd=NULL, Xd=NULL, base=1) colnames(X1) <- c(names(marg[,3:11]), "price") head(X1, n=10) ``` Notice that `createX` uses $p-1$ dummy variables to distinguish the $p$ choice alternatives. As with factor variables in linear regression, one factor must be the base; the coefficients on the other factors report deviations from the base. The user may specify the base alternative using the `base` argument (as we have done above), or let it default to the alternative with the highest index. For our example, we might also like to include some "demographic" variables. These are variables that do not vary with the choice alternatives. For example, with the `margarine` data we might want to include family size. Here again we turn to `createX`, this time specifying the `nd` and `Xd` arguments ("d" for demographic): ```{r, results = "hold"} X2 <- createX(p=10, na=NULL, Xa=NULL, nd=2, Xd=as.matrix(marg[,c(13,16)]), base=1) print(X2[1:10,1:9]); cat("\n") print(X2[1:10,10:18]) ``` Notice that `createX` again uses $p-1$ dummy variables to distinguish the $p$ choice alternatives. However, for demographic variables, the value of the demographic variable is spread across $p-1$ columns and $p-1$ rows. ### Model The logit specification was originally derived by Luce (1959) from assumptions on characteristics of choice probabilities. McFadden (1974) tied the model to rational economic theory by showing how the multinomial logit specification models choices made by a utility-maximizing consumer, assuming that the unobserved utility component is distributed Type I Extreme Value. We motivate use of this model following McFadden by assuming the decision maker chooses the alternative providing him with the highest utility, where the utility $U_{ij}$ from the choice $y_{ij}$ made by a decision maker in choice situation $i$ for product $j = 1, \ldots, p$ is modeled as the sum of a deterministic and a stochastic component: \[ U_{ij} = V_{ij} + \varepsilon_{ij} \hspace{2em} \text{with } \varepsilon_{ij}\ \sim \text{ iid T1EV} \] Regressors (both demographic and alternative-specific) are included in the model by assuming $V_{ij} = x_{ij}'\beta$. These assumptions result in choice probabilities of: $$ \text{Pr}(y_i=j) = \frac{\exp \{x_{ij}'\beta\}}{\sum_{k=1}^p\exp\{x_{ik}'\beta\}} $$ Independent priors for the components of the `beta` vector are specified as normal distributions. Using notation for the multivariate normal distribution, we have: $$ \beta \sim MVN(\bar{\beta},\ A^{-1}) $$ We use `bayesm`'s default values for the parameters of the priors: $\bar{\beta} = 0$ and $A = 0.01I$. ### Bayesian Estimation Experience with the MNL likelihood is that the asymptotic normal approximation is excellent. `rmnlIndepMetrop` implements an independent Metropolis algorithm to sample from the normal approximation to the posterior distribution of $\beta$: $$ p(\beta | X, y) \overset{\cdot}{\propto} |H|^{1/2} \exp \left\{ \frac{1}{2}(\beta - \hat{\beta})'H(\beta - \hat{\beta}) \right\} $$ where $\hat{\beta}$ is the MLE, $H = \sum_i x_i A_i x_i'$, and the candidate distribution used in the Metropolis algorithm is the multivariate student t. For more detail, see Section 11 of BSM Chapter 3. We sample from the normal approximation to the posterior as follows: ```{r, eval = FALSE} X <- cbind(X1, X2[,10:ncol(X2)]) out <- rmnlIndepMetrop(Data = list(y=y, X=X, p=10), Mcmc = list(R=1e4, nprint=1e3)) ``` ```{r, echo = FALSE} temp <- capture.output( {set.seed(1234); X <- cbind(X1, X2[,10:ncol(X2)]); out <- rmnlIndepMetrop(Data = list(y=y, X=X, p=10), Mcmc = list(R=1e4, nprint=1e3))}, file = NULL) ``` `rmnlIndepMetrop` returns a list that we have saved in `out`. The list contains 3 elements, `betadraw`, `loglike`, and `acceptr`, which you can verify by running `str(out)`. `betadraw` is a $10,000 \times 28$ dimension matrix with class `bayesm.mat`. As with the linear regression of Example 1 above, we can plot or summarize features of the the posterior distribution in many ways. For information on each marginal posterior distribution, call `summary(out)` or `plot(out)`. Because we have 28 covariates (intercepts and demographic variables make up 9 columns each and there is one column for the price variable) we omit the full set of results to save space and instead, we only present summary statistics for the marginal posterior distribution for $\beta_\text{price}$: ```{r} summary.bayesm.mat(out$betadraw[,10], names = "Price") ``` In addition to summary information for a marginal posterior distribution, we can plot it. We use `bayesm`'s `plot` generic function (calling `plot(out$betadraw)` would provide the same plots for all 28 $X$ variables). In the histogram, the green bars delimit a 95\% Bayesian credibility interval, yellow bars shows +/- 2 numerical standard errors for the posterior mean, and the red bar indicates the posterior mean. The subsequent two plots are a trace plot and and ACF plot. ```{r} plot.bayesm.mat(out$betadraw[,10], names = "Price") ``` We see that the posterior is approximately normally distributed with a mean of `r format(round(mean(out$betadraw[,10]),1), big.mark=",")` and a standard deviation of `r round(sd(out$betadraw[,10]), 2)`. The trace plot shows good mixing. The ACF plot shows a fair amount of correlation such that, even though the algorithm took `R = 10,000` draws, the Effective Sample Size (as reported in the summary stats above) is only `r format(round(summary.bayesm.mat(out$betadraw[,10])[1,5],0), big.mark = ",")`. Because of the nonlinearity in this model, interpreting the results is more difficult than with linear regression models. We do not elaborate further on the interpretation of coefficients and methods of displaying results from multinomial logit models, but for the uninitiated reader, we refer you to excellent sources for this information authored by Kenneth Train and Gary King.[^3] [^3]: Train, Kenneth, _Discrete Choice Models with Simulation_ Cambridge University Press, 2009. King, Gary _Unifying Political Methodlogy: The Likelihood Theory of Statistical Inference_, University of Michigan Press (1998) p. 108. King, Gary, Michael Tomz, and Jason Wittenberg, "Making the Most of Statistical Analyses: Improving Interpretation and Presentation" American Journal of Political Science, Vol. 44 (April 2000) pp. 347--361 at p. 355. ## Example 3: Hierarchical Logit ### Data While we could add individual-specific parameters to the previous model and use the same dataset, we elect to provide the reader with greater variety. For this example, we use the `camera` dataset in `bayesm`, which contains conjoint choice data for 332 respondents who evaluated digital cameras. These data have already been processed to exclude respondents that always answered "none", always picked the same brand, always selected the highest priced offering, or who appeared to be answering randomly. ```{r} data(camera) length(camera) str(camera[[1]]) colnames(camera[[1]]$X) ``` The `camera` data is stored in a list-of-lists format, which is the format required by `bayesm`'s posterior sampling functions for hierarchical models. This format has one list per individual with each list containing a vector `y` of choice outcomes and a matrix `X` of covariates. As with the multinomial logit model of the last example, `y` is a length-$n_i$ vector (or one-column matrix) and `X` has dimensions $n_ij \times k$ where $n_i$ is the number of choice occasions faced by individual $i$, $j$ is the number of choice alternatives, and $k$ is the number of covariates. For the `camera` data, $N=332$, $n_i=16$ for all $i$, $j=5$, and $k=10$. If your data were not in this format, it could be easily converted with a `for` loop and `createX`. For example, we can format `margarine` data from Example 2 above into a list-of-lists format with the following code, which simply loops over individuals, extracting and storing their `y` and `X` data one individual at a time: ```{r, eval = FALSE} data(margarine) chpr <- margarine$choicePrice chpr$hhid <- as.factor(chpr$hhid) N <- nlevels(chpr$hhid) dat <- vector(mode = "list", length = N) for (i in 1:N) { dat[[i]]$y <- chpr[chpr$hhid==levels(chpr$hhid)[i], "choice"] dat[[i]]$X <- createX(p=10, na=1, Xa=chpr[chpr$hhid==levels(chpr$hhid)[i],3:12], nd=NULL, Xd=NULL) } ``` Returning to the `camera` data, the first 4 covariates are binary indicators for the brands Canon, Sony, Nikon, and Panasonic. These correspond to choice (`y`) values of 1, 2, 3, and 4. `y` can also take the value 5, indicating that the respondent chose "none". The data include binary indicators for two levels of pixel count, zoom strength, swivel video display capability, and wifi connectivity. The last covaritate is price, recorded in hundreds of U.S. dollars (we leave price in these units so that we do not need to adjust the default prior settings). When we look at overall choice outcomes, we see that the brands and the outside alternative ("none") are chosen roughly in fifths, with specific implied market shares ranging from 17\%--25\%: ```{r} N <- length(camera) dat <- matrix(NA, N*16, 2) for (i in 1:length(camera)) { Ni <- length(camera[[i]]$y) dat[((i-1)*Ni+1):(i*Ni),1] <- i dat[((i-1)*Ni+1):(i*Ni),2] <- camera[[i]]$y } round(prop.table(table(dat[,2])), 3) ``` However, when we look at a few individuals' choices, we see much greater variability: ```{r} round(prop.table(table(dat[,1], dat[,2])[41:50,], 1), 3) ``` It is this heterogeneity in individual choice that motivates us to employ a hierarchical model. ### Model Hierarchical (also known as multi-level, random-coefficient, or mixed) models allow each respondent to have his or her own coefficients. Different people have different preferences, and models that estimate individual-level coefficients can fit data better and make more accurate predictions than single-level models. These models are quite popular in marketing, as they allow, for example, promotions to be targeted to individuals with high promotional part worths --- meaning those inviduals who are most likely to respond to the promotion. For more information, see Rossi et al. (1996).^[Rossi, McCulloch, and Allenby "The Value of Purchase History Data in Target Marketing" Marketing Science (1996).] The model follows the multinomial logit specification given in Example 2 above where individuals are assumed to be rational economic agents that make utility-maximizing choices. Now, however, the model includes individual-level parameters ($\beta_i$) assumed to be drawn from a normal distribution and with mean values driven by cross-sectional unit characteristics $Z$: $$ y_i \sim \text{MNL}(x_i'\beta_i) \hspace{1em} \text{with} \hspace{1em} \beta_i = z_i' \Delta + u_i \hspace{1em} \text{and} \hspace{1em} u_i \sim MVN(\mu, \Sigma) $$ $x_i$ is $n_i \times k$ and $i = 1, \ldots, N$. We can alternatively write the middle equation as $B=Z\Delta + U$ where $\beta_i$, $z_i$, and $u_i$ are the $i^\text{th}$ rows of $B$, $Z$, and $U$. $B$ is $N \times k$, $Z$ is $N \times m$, $\Delta$ is $m \times k$, and $U$ is $N \times k$. Note that we do not have any cross-sectional unit characteristics in the `camera` dataset and thus $Z$ will be omitted. The priors are: $$ \text{vec}(\Delta) = \delta \sim MVN(\bar{\delta}, A_\delta^{-1}) \hspace{2em} \mu \sim MVN(\bar{\mu}, \Sigma \otimes a^{-1}) \hspace{2em} \Sigma \sim IW(\nu, V) $$ This specification of priors assumes that, conditional on the hyperparameters (that is, the parameters of the prior distribution), the $\beta$'s are _a priori_ independent. This means that inference for each unit can be conducted independently of all other units, conditional on the hyperparameters, which is the Bayesian analogue of the fixed effects approach in classical statistics. Note also that we have assumed a normal "first-stage" prior distribution over the $\beta$'s. `rhierMnlRwMixture` permits a more-flexible mixture-of-normals first-stage prior (hence the "mixture" in the function name). However, for our example, we will not include this added flexibility (`Prior$ncomp = 1` below). ### Bayesian Estimation Although the model is more complex than the models used in the two previous examples, the increased programming difficulty for the researcher is minimal. As before, we specify `Data`, `Prior`, and `Mcmc` arguments, and call the posterior sampling function: ```{r} data <- list(lgtdata = camera, p = 5) prior <- list(ncomp = 1) mcmc <- list(R = 1e4, nprint = 0) out <- rhierMnlRwMixture(Data = data, Prior = prior, Mcmc = mcmc) ``` We store the results in `out`, which is a list of length 4. The list elements are `betadraw`, `nmix`, `loglike`, and `SignRes`. - `betadraw` is a $332 \times 10 \times 10,000$ array. These dimensions correspond to the number of individuals, the number of covariates, and the number of MCMC draws. - `nmix` is a list with elements `probdraw`, `zdraw`, and `compdraw`. - `probdraw` tells us the probability that each draw came from a particular normal component. This is relevant when there is a mixture-of-normals first-stage prior. However, since our specified prior over the $\beta$ vector is one normal distribution, `probdraw` is a $10,000 \times 1$ vector of all 1's. - `zdraw` is `NULL` as it is not relevant for this function. - `compdraw` provides draws for the mixture-of-normals components. Here, `compdraw` is a list of 10,000 lists. The $r^\text{th}$ of the 10,000 lists contains the $r^\text{th}$ draw of the $\mu$ vector (dim $1 \times 10$) and the Cholesky root of the $r^\text{th}$ draw for the $10 \times 10$ covariance matrix. - `loglike` is a $10,000 \times 1$ vector that provides the log-likelihood of each draw. - `SignRes` relates to whether any sign restrictions were placed on the model. This is discussed in detail in a separate vignette detailing a contrainsted hierarchical multinomial logit model; it is not relevant here. We can summarize results as before. `plot(out$betadraw)` provides plots for each variable that summarize the distributions of the individual parameters. For brevity, we provide just a histogram of posterior means for the 332 individual coefficients on wifi capability. ```{r} hist(apply(out$betadraw, 1:2, mean)[,9], col = "dodgerblue4", xlab = "", ylab = "", yaxt="n", xlim = c(-4,6), breaks = 20, main = "Histogram of Posterior Means For Individual Wifi Coefs") ``` We see that the distribution of individual posterior means is skewed, suggesting that our assumption of a normal first-stage prior may be incorrect. We could improve this model by using the more flexible mixture-of-normals prior or, if we believe all consumers value wifi connectivity positively, we could impose a sign constraint on that set of parameters --- both of which are demonstrated in the vignette for sign-constrained hierarchical multinomial logit. # Conclusion We hope that this vignette has provided the reader with a thorough introduction to the `bayesm` package and is sufficient to enable immediate use of its posterior sampling functions for bayesian estimation. Comments or edits can be sent to the vignette authors at the email addresses below. ***** _Authored by [Dan Yavorsky](dyavorsky@gmail.com) and [Peter Rossi](perossichi@gmail.com). 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{…|AŸüÇÜT¦ˆo%¶×õB’JWöæ—¯Þuɰƒ<ôæÞ“sÏ9éǘ1vÂ’”jBm2¡2¤ïªÃS6¢óæ¾ÖÖÊ|ñ4Ïßq¥Á9È–ª œO±«òç5˜5BÓçôõîŒ0E……|ñ#êZ!õóz…Ž7è*þJûü`ì¬ß½Üûðàs$}Z9%)šµ#õ¯ãŒøÓévÒií5Ù¿3‚§;là•OµP`ýåЃé %ºüLg¾„lgSø]†¿wþ›¦64÷F¦n²`v±KöK¥mÛíq¢B p\ '²/Cû4mÿ*àÙRTbayesm/DESCRIPTION0000644000176000001440000000371013134414120013262 0ustar ripleyusersPackage: bayesm Version: 3.1-0.1 Type: Package Title: Bayesian Inference for Marketing/Micro-Econometrics Depends: R (>= 3.2.0) Date: 2017-06-23 Author: Peter Rossi Maintainer: Peter Rossi License: GPL (>= 2) Imports: Rcpp (>= 0.12.0), utils, stats, graphics, grDevices LinkingTo: Rcpp, RcppArmadillo Suggests: knitr, rmarkdown VignetteBuilder: knitr URL: http://www.perossi.org/home/bsm-1 Description: Covers many important models used in marketing and micro-econometrics applications. The package includes: Bayes Regression (univariate or multivariate dep var), Bayes Seemingly Unrelated Regression (SUR), Binary and Ordinal Probit, Multinomial Logit (MNL) and Multinomial Probit (MNP), Multivariate Probit, Negative Binomial (Poisson) Regression, Multivariate Mixtures of Normals (including clustering), Dirichlet Process Prior Density Estimation with normal base, Hierarchical Linear Models with normal prior and covariates, Hierarchical Linear Models with a mixture of normals prior and covariates, Hierarchical Multinomial Logits with a mixture of normals prior and covariates, Hierarchical Multinomial Logits with a Dirichlet Process prior and covariates, Hierarchical Negative Binomial Regression Models, Bayesian analysis of choice-based conjoint data, Bayesian treatment of linear instrumental variables models, Analysis of Multivariate Ordinal survey data with scale usage heterogeneity (as in Rossi et al, JASA (01)), Bayesian Analysis of Aggregate Random Coefficient Logit Models as in BLP (see Jiang, Manchanda, Rossi 2009) For further reference, consult our book, Bayesian Statistics and Marketing by Rossi, Allenby and McCulloch (Wiley 2005) and Bayesian Non- and Semi-Parametric Methods and Applications (Princeton U Press 2014). RoxygenNote: 6.0.1 NeedsCompilation: yes Packaged: 2017-07-21 14:37:52 UTC; ripley Repository: CRAN Date/Publication: 2017-07-21 15:05:52 UTC bayesm/man/0000755000176000001440000000000013123305446012336 5ustar ripleyusersbayesm/man/simnhlogit.Rd0000755000176000001440000000265213117541521015011 0ustar ripleyusers\name{simnhlogit} \alias{simnhlogit} \concept{logit} \concept{non-homothetic} \title{Simulate from Non-homothetic Logit Model} \description{\code{simnhlogit} simulates from the non-homothetic logit model.} \usage{simnhlogit(theta, lnprices, Xexpend)} \arguments{ \item{theta }{ coefficient vector } \item{lnprices }{ \eqn{n x p} array of prices } \item{Xexpend }{ \eqn{n x k} array of values of expenditure variables} } \details{For details on parameterization, see \code{llnhlogit}.} \value{ A list containing: \item{y }{\eqn{n x 1} vector of multinomial outcomes (\eqn{1,\ldots,p})} \item{Xexpend }{ expenditure variables} \item{lnprices }{ price array } \item{theta }{ coefficients} \item{prob }{ \eqn{n x p} array of choice probabilities} } \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 4, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{llnhlogit}} } \examples{ N = 1000 p = 3 k = 1 theta = c(rep(1,p), seq(from=-1,to=1,length=p), rep(2,k), 0.5) lnprices = matrix(runif(N*p), ncol=p) Xexpend = matrix(runif(N*k), ncol=k) simdata = simnhlogit(theta, lnprices, Xexpend) } \keyword{models} bayesm/man/rmnlIndepMetrop.Rd0000644000176000001440000000624613117541521015753 0ustar ripleyusers\name{rmnlIndepMetrop} \alias{rmnlIndepMetrop} \concept{MCMC} \concept{multinomial logit} \concept{Metropolis algorithm} \concept{bayes} \title{MCMC Algorithm for Multinomial Logit Model} \description{ \code{rmnlIndepMetrop} implements Independence Metropolis algorithm for the multinomial logit (MNL) model. } \usage{rmnlIndepMetrop(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(y, X, p)} \item{Prior}{list(A, betabar)} \item{Mcmc }{list(R, keep, nprint, nu)} } \details{ \subsection{Model and Priors}{ y \eqn{\sim}{~} MNL(X, \eqn{\beta}) \cr \eqn{Pr(y=j) = exp(x_j'\beta)/\sum_k{e^{x_k'\beta}}} \eqn{\beta} \eqn{\sim}{~} \eqn{N(betabar, A^{-1})} } \subsection{Argument Details}{ \emph{\code{Data = list(y, X, p)}} \tabular{ll}{ \code{y: } \tab \eqn{n x 1} vector of multinomial outcomes (1, \ldots, p) \cr \code{X: } \tab \eqn{n*p x k} matrix \cr \code{p: } \tab number of alternatives } \emph{\code{Prior = list(A, betabar)} [optional]} \tabular{ll}{ \code{A: } \tab \eqn{k x k} prior precision matrix (def: 0.01*I) \cr \code{betabar: } \tab \eqn{k x 1} prior mean (def: 0) } \emph{\code{Mcmc = list(R, keep, nprint, nu)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) \cr \code{nu: } \tab d.f. parameter for independent t density (def: 6) } } } \value{ A list containing: \item{betadraw }{\eqn{R/keep x k} matrix of beta draws} \item{loglike }{\eqn{R/keep x 1} vector of log-likelihood values evaluated at each draw} \item{acceptr }{acceptance rate of Metropolis draws} } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rhierMnlRwMixture}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) simmnl = function(p, n, beta) { ## note: create X array with 2 alt.spec vars k = length(beta) X1 = matrix(runif(n*p,min=-1,max=1), ncol=p) X2 = matrix(runif(n*p,min=-1,max=1), ncol=p) X = createX(p, na=2, nd=NULL, Xd=NULL, Xa=cbind(X1,X2), base=1) Xbeta = X\%*\%beta ## now do probs p = nrow(Xbeta) / n Xbeta = matrix(Xbeta, byrow=TRUE, ncol=p) Prob = exp(Xbeta) iota = c(rep(1,p)) denom = Prob\%*\%iota Prob = Prob / as.vector(denom) ## draw y y = vector("double",n) ind = 1:p for (i in 1:n) { yvec = rmultinom(1, 1, Prob[i,]) y[i] = ind\%*\%yvec } return(list(y=y, X=X, beta=beta, prob=Prob)) } n = 200 p = 3 beta = c(1, -1, 1.5, 0.5) simout = simmnl(p,n,beta) Data1 = list(y=simout$y, X=simout$X, p=p) Mcmc1 = list(R=R, keep=1) out = rmnlIndepMetrop(Data=Data1, Mcmc=Mcmc1) cat("Summary of beta draws", fill=TRUE) summary(out$betadraw, tvalues=beta) ## plotting examples if(0){plot(out$betadraw)} } \keyword{models} bayesm/man/summary.bayesm.mat.Rd0000644000176000001440000000365713117541521016373 0ustar ripleyusers\name{summary.bayesm.mat} \alias{summary.bayesm.mat} \title{Summarize Mcmc Parameter Draws } \description{ \code{summary.bayesm.mat} is an S3 method to summarize marginal distributions given an array of draws } \usage{ \method{summary}{bayesm.mat}(object, names, burnin = trunc(0.1 * nrow(X)), tvalues, QUANTILES = TRUE, TRAILER = TRUE,...) } \arguments{ \item{object }{ \code{object} (hereafter \code{X}) is an array of draws, usually an object of class \code{bayesm.mat}} \item{names }{ optional character vector of names for the columns of \code{X}} \item{burnin }{ number of draws to burn-in (def: \eqn{0.1*nrow(X)})} \item{tvalues }{ optional vector of "true" values for use in simulation examples } \item{QUANTILES }{ logical for should quantiles be displayed (def: \code{TRUE})} \item{TRAILER }{ logical for should a trailer be displayed (def: \code{TRUE})} \item{... }{ optional arguments for generic function} } \details{ Typically, \code{summary.bayesm.nmix} will be invoked by a call to the generic summary function as in \code{summary(object)} where object is of class \code{bayesm.mat}. Mean, Std Dev, Numerical Standard error (of estimate of posterior mean), relative numerical efficiency (see \code{numEff}), and effective sample size are displayed. If \code{QUANTILES=TRUE}, quantiles of marginal distirbutions in the columns of \eqn{X} are displayed.\cr \code{summary.bayesm.mat} is also exported for direct use as a standard function, as in \code{summary.bayesm.mat(matrix)}.\cr \code{summary.bayesm.mat(matrix)} returns (invisibly) the array of the various summary statistics for further use. To assess this array use\code{stats=summary(Drawmat)}. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \seealso{ \code{\link{summary.bayesm.var}}, \code{\link{summary.bayesm.nmix}}} \examples{ \dontrun{out=rmnpGibbs(Data,Prior,Mcmc); summary(out$betadraw)} } \keyword{univar} bayesm/man/ghkvec.Rd0000755000176000001440000000606313117541521014103 0ustar ripleyusers\name{ghkvec} \alias{ghkvec} \concept{multivariate normal distribution} \concept{GHK method} \concept{integral} \title{Compute GHK approximation to Multivariate Normal Integrals} \description{ \code{ghkvec} computes the GHK approximation to the integral of a multivariate normal density over a half plane defined by a set of truncation points. } \usage{ghkvec(L, trunpt, above, r, HALTON=TRUE, pn)} \arguments{ \item{L }{ lower triangular Cholesky root of covariance matrix } \item{trunpt}{ vector of truncation points} \item{above }{ vector of indicators for truncation above(1) or below(0) } \item{r }{ number of draws to use in GHK } \item{HALTON}{ if \code{TRUE}, uses Halton sequence. If \code{FALSE}, uses \code{R::runif} random number generator (def: \code{TRUE})} \item{pn }{ prime number used for Halton sequence (def: the smallest prime numbers, i.e. 2, 3, 5, ...)} } \value{Approximation to integral} \note{ \code{ghkvec} can accept a vector of truncations and compute more than one integral. That is, \code{length(trunpt)/length(above)} number of different integrals, each with the same variance and mean 0 but different truncation points. See 'examples' below for an example with two integrals at different truncation points. The user can choose between two random number generators for the numerical integration: psuedo-random numbers by \code{R::runif} or quasi-random numbers by a Halton sequence. Generally, the quasi-random (Halton) sequence is more uniformly distributed within domain, so it shows lower error and improved convergence than the psuedo-random (\code{runif}) sequence (Morokoff and Caflisch, 1995). For the prime numbers generating Halton sequence, we suggest to use the first smallest prime numbers. Halton (1960) and Kocis and Whiten (1997) prove that their discrepancy measures (how uniformly the sample points are distributed) have the upper bounds, which decrease as the generating prime number decreases. Note: For a high dimensional integration (10 or more dimension), we suggest use of the psuedo-random number generator (\code{R::runif}) because, according to Kocis and Whiten (1997), Halton sequences may be highly correlated when the dimension is 10 or more. } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.\cr Keunwoo Kim, Anderson School, UCLA, \email{keunwoo.kim@gmail.com}. } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch, Chapter 2. \cr \url{http://www.perossi.org/home/bsm-1} For Halton sequence, see Halton (1960, Numerische Mathematik), Morokoff and Caflisch (1995, Journal of Computational Physics), and Kocis and Whiten (1997, ACM Transactions on Mathematical Software). } \examples{ Sigma = matrix(c(1, 0.5, 0.5, 1), ncol=2) L = t(chol(Sigma)) trunpt = c(0,0,1,1) above = c(1,1) # drawn by Halton sequence ghkvec(L, trunpt, above, r=100) # use prime number 11 and 13 ghkvec(L, trunpt, above, r=100, HALTON=TRUE, pn=c(11,13)) # drawn by R::runif ghkvec(L, trunpt, above, r=100, HALTON=FALSE) } \keyword{distribution} bayesm/man/clusterMix.Rd0000644000176000001440000000534013117541521014765 0ustar ripleyusers\name{clusterMix} \alias{clusterMix} \concept{normal mixture} \concept{clustering} \title{Cluster Observations Based on Indicator MCMC Draws} \description{ \code{clusterMix} uses MCMC draws of indicator variables from a normal component mixture model to cluster observations based on a similarity matrix. } \usage{clusterMix(zdraw, cutoff=0.9, SILENT=FALSE, nprint=BayesmConstant.nprint)} \arguments{ \item{zdraw}{ \eqn{R x nobs} array of draws of indicators} \item{cutoff}{ cutoff probability for similarity (def: \code{0.9})} \item{SILENT}{ logical flag for silent operation (def: \code{FALSE})} \item{nprint}{ print every nprint'th draw (def: \code{100})} } \details{ Define a similarity matrix, \eqn{Sim} with \code{Sim[i,j]=1} if observations \eqn{i} and \eqn{j} are in same component. Compute the posterior mean of Sim over indicator draws. Clustering is achieved by two means: Method A: Find the indicator draw whose similarity matrix minimizes \eqn{loss(E[Sim]-Sim(z))}, where loss is absolute deviation. Method B: Define a Similarity matrix by setting any element of \eqn{E[Sim] = 1} if \eqn{E[Sim] > cutoff}. Compute the clustering scheme associated with this "windsorized" Similarity matrix. } \value{ A list containing: \item{clustera:}{indicator function for clustering based on method A above} \item{clusterb:}{indicator function for clustering based on method B above} } \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch Chapter 3. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rnmixGibbs}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) { ## simulate data from mixture of normals n = 500 pvec = c(.5,.5) mu1 = c(2,2) mu2 = c(-2,-2) Sigma1 = matrix(c(1,0.5,0.5,1), ncol=2) Sigma2 = matrix(c(1,0.5,0.5,1), ncol=2) comps = NULL comps[[1]] = list(mu1, backsolve(chol(Sigma1),diag(2))) comps[[2]] = list(mu2, backsolve(chol(Sigma2),diag(2))) dm = rmixture(n, pvec, comps) ## run MCMC on normal mixture Data = list(y=dm$x) ncomp = 2 Prior = list(ncomp=ncomp, a=c(rep(100,ncomp))) R = 2000 Mcmc = list(R=R, keep=1) out = rnmixGibbs(Data=Data, Prior=Prior, Mcmc=Mcmc) ## find clusters begin = 500 end = R outclusterMix = clusterMix(out$nmix$zdraw[begin:end,]) ## check on clustering versus "truth" ## note: there could be switched labels table(outclusterMix$clustera, dm$z) table(outclusterMix$clusterb, dm$z) } } \keyword{models} \keyword{multivariate} bayesm/man/mixDenBi.Rd0000644000176000001440000000301613117541521014323 0ustar ripleyusers\name{mixDenBi} \alias{mixDenBi} \concept{normal mixture} \concept{marginal distribution} \concept{density} \title{Compute Bivariate Marginal Density for a Normal Mixture} \description{ \code{mixDenBi} computes the implied bivariate marginal density from a mixture of normals with specified mixture probabilities and component parameters. } \usage{mixDenBi(i, j, xi, xj, pvec, comps)} \arguments{ \item{i}{ index of first variable } \item{j}{ index of second variable } \item{xi}{ grid of values of first variable } \item{xj}{ grid of values of second variable } \item{pvec}{ normal mixture probabilities } \item{comps}{ list of lists of components } } \details{ \tabular{ll}{ \code{length(comps) } \tab is the number of mixture components \cr \code{comps[[j]] } \tab is a list of parameters of the \eqn{j}th component \cr \code{comps[[j]]$mu } \tab is mean vector \cr \code{comps[[j]]$rooti} \tab is the UL decomp of \eqn{\Sigma^{-1}} } } \value{An array (\code{length(xi)=length(xj) x 2}) with density value} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rnmixGibbs}}, \code{\link{mixDen}} } \keyword{models} \keyword{multivariate} bayesm/man/rbayesBLP.Rd0000644000176000001440000002422513117541521014454 0ustar ripleyusers\name{rbayesBLP} \alias{rbayesBLP} \concept{bayes} \concept{random coefficient logit} \concept{BLP} \concept{Metropolis Hasting} \title{Bayesian Analysis of Random Coefficient Logit Models Using Aggregate Data} \description{ \code{rbayesBLP} implements a hybrid MCMC algorithm for aggregate level sales data in a market with differentiated products. bayesm version 3.1-0 and prior verions contain an error when using instruments with this function; this will be fixed in a future version. } \usage{rbayesBLP(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(X, share, J, Z)} \item{Prior}{list(sigmasqR, theta_hat, A, deltabar, Ad, nu0, s0_sq, VOmega)} \item{Mcmc }{list(R, keep, nprint, H, initial_theta_bar, initial_r, initial_tau_sq, initial_Omega, initial_delta, s, cand_cov, tol)} } \value{ A list containing: \item{thetabardraw }{\eqn{K x R/keep} matrix of random coefficient mean draws} \item{Sigmadraw }{\eqn{K*K x R/keep} matrix of random coefficient variance draws} \item{rdraw }{\eqn{K*K x R/keep} matrix of \eqn{r} draws (same information as in \code{Sigmadraw})} \item{tausqdraw }{\eqn{R/keep x 1} vector of aggregate demand shock variance draws} \item{Omegadraw }{\eqn{2*2 x R/keep} matrix of correlated endogenous shock variance draws} \item{deltadraw }{\eqn{I x R/keep} matrix of endogenous structural equation coefficient draws} \item{acceptrate }{scalor of acceptance rate of Metropolis-Hasting} \item{s }{scale parameter used for Metropolis-Hasting} \item{cand_cov }{var-cov matrix used for Metropolis-Hasting} } \section{Argument Details}{ \emph{\code{Data = list(X, share, J, Z)}} [\code{Z} optional] \tabular{ll}{ \code{J: } \tab number of alternatives, excluding an outside option \cr \code{X: } \tab \eqn{J*T x K} matrix (no outside option, which is normalized to 0). \cr \code{ } \tab If IV is used, the last column of \code{X} is the endogeneous variable. \cr \code{share: } \tab \eqn{J*T} vector (no outside option). \cr \code{ } \tab Note that both the \code{share} vector and the \code{X} matrix are organized by the \eqn{jt} index. \cr \code{ } \tab \eqn{j} varies faster than \eqn{t}, i.e. \eqn{(j=1,t=1), (j=2,t=1), ..., (j=J,T=1), ..., (j=J,t=T)} \cr \code{Z: } \tab \eqn{J*T x I} matrix of instrumental variables (optional) } \emph{\code{Prior = list(sigmasqR, theta_hat, A, deltabar, Ad, nu0, s0_sq, VOmega)} [optional]} \tabular{ll}{ \code{sigmasqR: } \tab \eqn{K*(K+1)/2} vector for \eqn{r} prior variance (def: diffuse prior for \eqn{\Sigma}) \cr \code{theta_hat: } \tab \eqn{K} vector for \eqn{\theta_bar} prior mean (def: 0 vector) \cr \code{A: } \tab \eqn{K x K} matrix for \eqn{\theta_bar} prior precision (def: \code{0.01*diag(K)}) \cr \code{deltabar: } \tab \eqn{I} vector for \eqn{\delta} prior mean (def: 0 vector) \cr \code{Ad: } \tab \eqn{I x I} matrix for \eqn{\delta} prior precision (def: \code{0.01*diag(I)}) \cr \code{nu0: } \tab d.f. parameter for \eqn{\tau_sq} and \eqn{\Omega} prior (def: K+1) \cr \code{s0_sq: } \tab scale parameter for \eqn{\tau_sq} prior (def: 1) \cr \code{VOmega: } \tab \eqn{2 x 2} matrix parameter for \eqn{\Omega} prior (def: \code{matrix(c(1,0.5,0.5,1),2,2)}) } \emph{\code{Mcmc = list(R, keep, nprint, H, initial_theta_bar, initial_r, initial_tau_sq, initial_Omega, initial_delta, s, cand_cov, tol)} [only \code{R} and \code{H} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) \cr \code{H: } \tab number of random draws used for Monte-Carlo integration \cr \code{initial_theta_bar: } \tab initial value of \eqn{\theta_bar} (def: 0 vector) \cr \code{initial_r: } \tab initial value of \eqn{r} (def: 0 vector) \cr \code{initial_tau_sq: } \tab initial value of \eqn{\tau_sq} (def: 0.1) \cr \code{initial_Omega: } \tab initial value of \eqn{\Omega} (def: \code{diag(2)}) \cr \code{initial_delta: } \tab initial value of \eqn{\delta} (def: 0 vector) \cr \code{s: } \tab scale parameter of Metropolis-Hasting increment (def: automatically tuned) \cr \code{cand_cov: } \tab var-cov matrix of Metropolis-Hasting increment (def: automatically tuned) \cr \code{tol: } \tab convergence tolerance for the contraction mapping (def: 1e-6) } } \section{Model Details}{ \subsection{Model and Priors (without IV):}{ \eqn{u_ijt = X_jt \theta_i + \eta_jt + e_ijt}\cr \eqn{e_ijt} \eqn{\sim}{~} type I Extreme Value (logit)\cr \eqn{\theta_i} \eqn{\sim}{~} \eqn{N(\theta_bar, \Sigma)}\cr \eqn{\eta_jt} \eqn{\sim}{~} \eqn{N(0, \tau_sq)}\cr This structure implies a logit model for each consumer (\eqn{\theta}). Aggregate shares (\code{share}) are produced by integrating this consumer level logit model over the assumed normal distribution of \eqn{\theta}. \eqn{r} \eqn{\sim}{~} \eqn{N(0, diag(sigmasqR))}\cr \eqn{\theta_bar} \eqn{\sim}{~} \eqn{N(\theta_hat, A^-1)}\cr \eqn{\tau_sq} \eqn{\sim}{~} \eqn{nu0*s0_sq / \chi^2 (nu0)}\cr Note: we observe the aggregate level market share, not individual level choices.\cr Note: \eqn{r} is the vector of nonzero elements of cholesky root of \eqn{\Sigma}. Instead of \eqn{\Sigma} we draw \eqn{r}, which is one-to-one correspondence with the positive-definite \eqn{\Sigma}. } \subsection{Model and Priors (with IV):}{ \eqn{u_ijt = X_jt \theta_i + \eta_jt + e_ijt}\cr \eqn{e_ijt} \eqn{\sim}{~} type I Extreme Value (logit)\cr \eqn{\theta_i} \eqn{\sim}{~} \eqn{N(\theta_bar, \Sigma)}\cr \eqn{X_jt = [X_exo_jt, X_endo_jt]}\cr \eqn{X_endo_jt = Z_jt \delta_jt + \zeta_jt}\cr \eqn{vec(\zeta_jt, \eta_jt)} \eqn{\sim}{~} \eqn{N(0, \Omega)}\cr \eqn{r} \eqn{\sim}{~} \eqn{N(0, diag(sigmasqR))}\cr \eqn{\theta_bar} \eqn{\sim}{~} \eqn{N(\theta_hat, A^-1)}\cr \eqn{\delta} \eqn{\sim}{~} \eqn{N(deltabar, Ad^-1)}\cr \eqn{\Omega} \eqn{\sim}{~} \eqn{IW(nu0, VOmega)}\cr } } \section{MCMC and Tuning Details:}{ \subsection{MCMC Algorithm:}{ Step 1 (\eqn{\Sigma}):\cr Given \eqn{\theta_bar} and \eqn{\tau_sq}, draw \eqn{r} via Metropolis-Hasting.\cr Covert the drawn \eqn{r} to \eqn{\Sigma}.\cr Note: if user does not specify the Metropolis-Hasting increment parameters (\code{s} and \code{cand_cov}), \code{rbayesBLP} automatically tunes the parameters. Step 2 without IV (\eqn{\theta_bar}, \eqn{\tau_sq}):\cr Given \eqn{\Sigma}, draw \eqn{\theta_bar} and \eqn{\tau_sq} via Gibbs sampler.\cr Step 2 with IV (\eqn{\theta_bar}, \eqn{\delta}, \eqn{\Omega}):\cr Given \eqn{\Sigma}, draw \eqn{\theta_bar}, \eqn{\delta}, and \eqn{\Omega} via IV Gibbs sampler.\cr } \subsection{Tuning Metropolis-Hastings algorithm:}{ r_cand = r_old + s*N(0,cand_cov)\cr Fix the candidate covariance matrix as cand_cov0 = diag(rep(0.1, K), rep(1, K*(K-1)/2)).\cr Start from s0 = 2.38/sqrt(dim(r))\cr Repeat\{\cr Run 500 MCMC chain.\cr If acceptance rate < 30\% => update s1 = s0/5.\cr If acceptance rate > 50\% => update s1 = s0*3.\cr (Store r draws if acceptance rate is 20~80\%.)\cr s0 = s1\cr \} until acceptance rate is 30~50\% Scale matrix C = s1*sqrt(cand_cov0)\cr Correlation matrix R = Corr(r draws)\cr Use C*R*C as s^2*cand_cov. } } \references{For further discussion, see \emph{Bayesian Analysis of Random Coefficient Logit Models Using Aggregate Data} by Jiang, Manchanda, and Rossi, \emph{Journal of Econometrics}, 2009. \cr \url{http://www.sciencedirect.com/science/article/pii/S0304407608002297} } \author{Keunwoo Kim, Anderson School, UCLA, \email{keunwoo.kim@gmail.com}.} \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) { ## Simulate aggregate level data simulData <- function(para, others, Hbatch) { # Hbatch does the integration for computing market shares # in batches of size Hbatch ## parameters theta_bar <- para$theta_bar Sigma <- para$Sigma tau_sq <- para$tau_sq T <- others$T J <- others$J p <- others$p H <- others$H K <- J + p ## build X X <- matrix(runif(T*J*p), T*J, p) inter <- NULL for (t in 1:T) { inter <- rbind(inter, diag(J)) } X <- cbind(inter, X) ## draw eta ~ N(0, tau_sq) eta <- rnorm(T*J)*sqrt(tau_sq) X <- cbind(X, eta) share <- rep(0, J*T) for (HH in 1:(H/Hbatch)){ ## draw theta ~ N(theta_bar, Sigma) cho <- chol(Sigma) theta <- matrix(rnorm(K*Hbatch), nrow=K, ncol=Hbatch) theta <- t(cho)\%*\%theta + theta_bar ## utility V <- X\%*\%rbind(theta, 1) expV <- exp(V) expSum <- matrix(colSums(matrix(expV, J, T*Hbatch)), T, Hbatch) expSum <- expSum \%x\% matrix(1, J, 1) choiceProb <- expV / (1 + expSum) share <- share + rowSums(choiceProb) / H } ## the last K+1'th column is eta, which is unobservable. X <- X[,c(1:K)] return (list(X=X, share=share)) } ## true parameter theta_bar_true <- c(-2, -3, -4, -5) Sigma_true <- rbind(c(3,2,1.5,1), c(2,4,-1,1.5), c(1.5,-1,4,-0.5), c(1,1.5,-0.5,3)) cho <- chol(Sigma_true) r_true <- c(log(diag(cho)), cho[1,2:4], cho[2,3:4], cho[3,4]) tau_sq_true <- 1 ## simulate data set.seed(66) T <- 300 J <- 3 p <- 1 K <- 4 H <- 1000000 Hbatch <- 5000 dat <- simulData(para=list(theta_bar=theta_bar_true, Sigma=Sigma_true, tau_sq=tau_sq_true), others=list(T=T, J=J, p=p, H=H), Hbatch) X <- dat$X share <- dat$share ## Mcmc run R <- 2000 H <- 50 Data1 <- list(X=X, share=share, J=J) Mcmc1 <- list(R=R, H=H, nprint=0) set.seed(66) out <- rbayesBLP(Data=Data1, Mcmc=Mcmc1) ## acceptance rate out$acceptrate ## summary of draws summary(out$thetabardraw) summary(out$Sigmadraw) summary(out$tausqdraw) ### plotting draws plot(out$thetabardraw) plot(out$Sigmadraw) plot(out$tausqdraw) } } \keyword{models}bayesm/man/rnegbinRw.Rd0000644000176000001440000001014213117541521014557 0ustar ripleyusers\name{rnegbinRw} \alias{rnegbinRw} \concept{MCMC} \concept{NBD regression} \concept{Negative Binomial regression} \concept{Poisson regression} \concept{Metropolis algorithm} \concept{bayes} \title{MCMC Algorithm for Negative Binomial Regression} \description{ \code{rnegbinRw} implements a Random Walk Metropolis Algorithm for the Negative Binomial (NBD) regression model where \eqn{\beta|\alpha} and \eqn{\alpha|\beta} are drawn with two different random walks. } \usage{rnegbinRw(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(y, X)} \item{Prior}{list(betabar, A, a, b)} \item{Mcmc }{list(R, keep, nprint, s_beta, s_alpha, beta0, alpha)} } \details{ \subsection{Model and Priors}{ \eqn{y} \eqn{\sim}{~} \eqn{NBD(mean=\lambda, over-dispersion=alpha)} \cr \eqn{\lambda = exp(x'\beta)} \eqn{\beta} \eqn{\sim}{~} \eqn{N(betabar, A^{-1})} \cr \eqn{alpha} \eqn{\sim}{~} \eqn{Gamma(a, b)} (unless \code{Mcmc$alpha} specified) \cr Note: prior mean of \eqn{alpha = a/b}, \eqn{variance = a/(b^2)} } \subsection{Argument Details}{ \emph{\code{Data = list(y, X)}} \tabular{ll}{ \code{y: } \tab \eqn{n x 1} vector of counts (\eqn{0,1,2,\ldots}) \cr \code{X: } \tab \eqn{n x k} design matrix } \emph{\code{Prior = list(betabar, A, a, b)} [optional]} \tabular{ll}{ \code{betabar: } \tab \eqn{k x 1} prior mean (def: 0) \cr \code{A: } \tab \eqn{k x k} PDS prior precision matrix (def: 0.01*I) \cr \code{a: } \tab Gamma prior parameter (not used if \code{Mcmc$alpha} specified) (def: 0.5) \cr \code{b: } \tab Gamma prior parameter (not used if \code{Mcmc$alpha} specified) (def: 0.1) } \emph{\code{Mcmc = list(R, keep, nprint, s_beta, s_alpha, beta0, alpha)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) \cr \code{s_beta: } \tab scaling for beta | alpha RW inc cov matrix (def: 2.93/\code{sqrt(k)}) \cr \code{s_alpha: } \tab scaling for alpha | beta RW inc cov matrix (def: 2.93) \cr \code{alpha: } \tab over-dispersion parameter (def: alpha ~ Gamma(a,b)) } } } \value{ A list containing: \item{betadraw }{\eqn{R/keep x k} matrix of beta draws} \item{alphadraw }{\eqn{R/keep x 1} vector of alpha draws} \item{llike }{\eqn{R/keep x 1} vector of log-likelihood values evaluated at each draw} \item{acceptrbeta }{acceptance rate of the beta draws} \item{acceptralpha }{acceptance rate of the alpha draws} } \note{ The NBD regression encompasses Poisson regression in the sense that as alpha goes to infinity the NBD distribution tends toward the Poisson. For "small" values of alpha, the dependent variable can be extremely variable so that a large number of observations may be required to obtain precise inferences. } \author{Sridhar Narayanan (Stanford GSB) and Peter Rossi (Anderson School, UCLA), \email{perossichi@gmail.com}.} \references{For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rhierNegbinRw}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=1000} else {R=10} set.seed(66) simnegbin = function(X, beta, alpha) { # Simulate from the Negative Binomial Regression lambda = exp(X\%*\%beta) y = NULL for (j in 1:length(lambda)) { y = c(y, rnbinom(1, mu=lambda[j], size=alpha)) } return(y) } nobs = 500 nvar = 2 # Number of X variables alpha = 5 Vbeta = diag(nvar)*0.01 # Construct the regdata (containing X) simnegbindata = NULL beta = c(0.6, 0.2) X = cbind(rep(1,nobs), rnorm(nobs,mean=2,sd=0.5)) simnegbindata = list(y=simnegbin(X,beta,alpha), X=X, beta=beta) Data1 = simnegbindata Mcmc1 = list(R=R) out = rnegbinRw(Data=Data1, Mcmc=list(R=R)) cat("Summary of alpha/beta draw", fill=TRUE) summary(out$alphadraw, tvalues=alpha) summary(out$betadraw, tvalues=beta) ## plotting examples if(0){plot(out$betadraw)} } \keyword{models} bayesm/man/rhierNegbinRw.Rd0000644000176000001440000001353713117541521015402 0ustar ripleyusers\name{rhierNegbinRw} \alias{rhierNegbinRw} \concept{MCMC} \concept{hierarchical NBD regression} \concept{Negative Binomial regression} \concept{Poisson regression} \concept{Metropolis algorithm} \concept{bayes} \title{MCMC Algorithm for Hierarchical Negative Binomial Regression} \description{ \code{rhierNegbinRw} implements an MCMC algorithm for the hierarchical Negative Binomial (NBD) regression model. Metropolis steps for each unit-level set of regression parameters are automatically tuned by optimization. Over-dispersion parameter (alpha) is common across units. } \usage{rhierNegbinRw(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(regdata, Z)} \item{Prior}{list(Deltabar, Adelta, nu, V, a, b)} \item{Mcmc }{list(R, keep, nprint, s_beta, s_alpha, alpha, c, Vbeta0, Delta0)} } \details{ \subsection{Model and Priors}{ \eqn{y_i} \eqn{\sim}{~} NBD(mean=\eqn{\lambda}, over-dispersion=alpha) \cr \eqn{\lambda = exp(X_i\beta_i)} \eqn{\beta_i} \eqn{\sim}{~} \eqn{N(\Delta'z_i,Vbeta)} \eqn{vec(\Delta|Vbeta)} \eqn{\sim}{~} \eqn{N(vec(Deltabar), Vbeta (x) Adelta)} \cr \eqn{Vbeta} \eqn{\sim}{~} \eqn{IW(nu, V)} \cr \eqn{alpha} \eqn{\sim}{~} \eqn{Gamma(a, b)} (unless \code{Mcmc$alpha} specified) \cr Note: prior mean of \eqn{alpha = a/b}, variance \eqn{= a/(b^2)} } \subsection{Argument Details}{ \emph{\code{Data = list(regdata, Z)} [\code{Z} optional]} \tabular{ll}{ \code{regdata: } \tab list of lists with data on each of \code{nreg} units \cr \code{regdata[[i]]$X: } \tab \eqn{nobs_i x nvar} matrix of \eqn{X} variables \cr \code{regdata[[i]]$y: } \tab \eqn{nobs_i x 1} vector of count responses \cr \code{Z: } \tab \eqn{nreg x nz} matrix of unit characteristics (def: vector of ones) } \emph{\code{Prior = list(Deltabar, Adelta, nu, V, a, b)} [optional]} \tabular{ll}{ \code{Deltabar: } \tab \eqn{nz x nvar} prior mean matrix (def: 0) \cr \code{Adelta: } \tab \eqn{nz x nz} PDS prior precision matrix (def: 0.01*I) \cr \code{nu: } \tab d.f. parameter for Inverted Wishart prior (def: nvar+3) \cr \code{V: } \tab location matrix of Inverted Wishart prior (def: nu*I) \cr \code{a: } \tab Gamma prior parameter (def: 0.5) \cr \code{b: } \tab Gamma prior parameter (def: 0.1) } \emph{\code{Mcmc = list(R, keep, nprint, s_beta, s_alpha, alpha, c, Vbeta0, Delta0)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) \cr \code{s_beta: } \tab scaling for beta | alpha RW inc cov (def: 2.93/\code{sqrt(nvar)}) \cr \code{s_alpha: } \tab scaling for alpha | beta RW inc cov (def: 2.93) \cr \code{alpha: } \tab over-dispersion parameter (def: alpha ~ Gamma(a,b)) \cr \code{c: } \tab fractional likelihood weighting parm (def: 2) \cr \code{Vbeta0: } \tab starting value for Vbeta (def: I) \cr \code{Delta0: } \tab starting value for Delta (def: 0) } } } \value{ A list containing: \item{llike }{ \eqn{R/keep x 1} vector of values of log-likelihood} \item{betadraw }{ \eqn{nreg x nvar x R/keep} array of beta draws} \item{alphadraw }{ \eqn{R/keep x 1} vector of alpha draws} \item{acceptrbeta }{ acceptance rate of the beta draws} \item{acceptralpha }{ acceptance rate of the alpha draws} } \note{ The NBD regression encompasses Poisson regression in the sense that as alpha goes to infinity the NBD distribution tends to the Poisson. For "small" values of alpha, the dependent variable can be extremely variable so that a large number of observations may be required to obtain precise inferences. For ease of interpretation, we recommend demeaning \eqn{Z} variables. } \seealso{ \code{\link{rnegbinRw}} } \author{Sridhar Narayanan (Stanford GSB) and Peter Rossi (Anderson School, UCLA), \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 5, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) # Simulate from the Negative Binomial Regression simnegbin = function(X, beta, alpha) { lambda = exp(X\%*\%beta) y = NULL for (j in 1:length(lambda)) {y = c(y, rnbinom(1, mu=lambda[j], size=alpha)) } return(y) } nreg = 100 # Number of cross sectional units T = 50 # Number of observations per unit nobs = nreg*T nvar = 2 # Number of X variables nz = 2 # Number of Z variables ## Construct the Z matrix Z = cbind(rep(1,nreg), rnorm(nreg,mean=1,sd=0.125)) Delta = cbind(c(4,2), c(0.1,-1)) alpha = 5 Vbeta = rbind(c(2,1), c(1,2)) ## Construct the regdata (containing X) simnegbindata = NULL for (i in 1:nreg) { betai = as.vector(Z[i,]\%*\%Delta) + chol(Vbeta)\%*\%rnorm(nvar) X = cbind(rep(1,T),rnorm(T,mean=2,sd=0.25)) simnegbindata[[i]] = list(y=simnegbin(X,betai,alpha), X=X, beta=betai) } Beta = NULL for (i in 1:nreg) {Beta = rbind(Beta,matrix(simnegbindata[[i]]$beta,nrow=1))} Data1 = list(regdata=simnegbindata, Z=Z) Mcmc1 = list(R=R) out = rhierNegbinRw(Data=Data1, Mcmc=Mcmc1) cat("Summary of Delta draws", fill=TRUE) summary(out$Deltadraw, tvalues=as.vector(Delta)) cat("Summary of Vbeta draws", fill=TRUE) summary(out$Vbetadraw, tvalues=as.vector(Vbeta[upper.tri(Vbeta,diag=TRUE)])) cat("Summary of alpha draws", fill=TRUE) summary(out$alpha, tvalues=alpha) ## plotting examples if(0){ plot(out$betadraw) plot(out$alpha,tvalues=alpha) plot(out$Deltadraw,tvalues=as.vector(Delta)) } } \keyword{models} bayesm/man/rhierLinearModel.Rd0000644000176000001440000001130313117541521016047 0ustar ripleyusers\name{rhierLinearModel} \alias{rhierLinearModel} \concept{bayes} \concept{MCMC} \concept{Gibbs Sampling} \concept{hierarchical models} \concept{linear model} \title{Gibbs Sampler for Hierarchical Linear Model with Normal Heterogeneity} \description{ \code{rhierLinearModel} implements a Gibbs Sampler for hierarchical linear models with a normal prior. } \usage{rhierLinearModel(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(regdata, Z)} \item{Prior}{list(Deltabar, A, nu.e, ssq, nu, V)} \item{Mcmc }{list(R, keep, nprint)} } \details{ \subsection{Model and Priors}{ \code{nreg} regression equations with \eqn{nvar} \eqn{X} variables in each equation \cr \eqn{y_i = X_i\beta_i + e_i} with \eqn{e_i} \eqn{\sim}{~} \eqn{N(0, \tau_i)} \eqn{\tau_i} \eqn{\sim}{~} nu.e*\eqn{ssq_i/\chi^2_{nu.e}} where \eqn{\tau_i} is the variance of \eqn{e_i}\cr \eqn{\beta_i} \eqn{\sim}{~} N(Z\eqn{\Delta}[i,], \eqn{V_{\beta}}) \cr Note: Z\eqn{\Delta} is the matrix \eqn{Z * \Delta} and [i,] refers to \eqn{i}th row of this product\cr \eqn{vec(\Delta)} given \eqn{V_{\beta}} \eqn{\sim}{~} \eqn{N(vec(Deltabar), V_{\beta}(x) A^{-1})}\cr \eqn{V_{\beta}} \eqn{\sim}{~} \eqn{IW(nu,V)} \cr \eqn{Delta, Deltabar} are \eqn{nz x nvar}; \eqn{A} is \eqn{nz x nz}; \eqn{V_{\beta}} is \eqn{nvar x nvar}. Note: if you don't have any \eqn{Z} variables, omit \eqn{Z} in the \code{Data} argument and a vector of ones will be inserted; the matrix \eqn{\Delta} will be \eqn{1 x nvar} and should be interpreted as the mean of all unit \eqn{\beta}s. } \subsection{Argument Details}{ \emph{\code{Data = list(regdata, Z)} [\code{Z} optional]} \tabular{ll}{ \code{regdata: } \tab list of lists with \eqn{X} and \eqn{y} matrices for each of \code{nreg=length(regdata)} regressions \cr \code{regdata[[i]]$X: } \tab \eqn{n_i x nvar} design matrix for equation \eqn{i} \cr \code{regdata[[i]]$y: } \tab \eqn{n_i x 1} vector of observations for equation \eqn{i} \cr \code{Z: } \tab \eqn{nreg x nz} matrix of unit characteristics (def: vector of ones) } \emph{\code{Prior = list(Deltabar, A, nu.e, ssq, nu, V)} [optional]} \tabular{ll}{ \code{Deltabar: } \tab \eqn{nz x nvar} matrix of prior means (def: 0) \cr \code{A: } \tab \eqn{nz x nz} matrix for prior precision (def: 0.01I) \cr \code{nu.e: } \tab d.f. parameter for regression error variance prior (def: 3) \cr \code{ssq: } \tab scale parameter for regression error var prior (def: \code{var(y_i)}) \cr \code{nu: } \tab d.f. parameter for Vbeta prior (def: nvar+3) \cr \code{V: } \tab Scale location matrix for Vbeta prior (def: nu*I) } \emph{\code{Mcmc = list(R, keep, nprint)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parm -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) } } } \value{ A list containing: \item{betadraw }{\eqn{nreg x nvar x R/keep} array of individual regression coef draws} \item{taudraw }{\eqn{R/keep x nreg} matrix of error variance draws} \item{Deltadraw }{\eqn{R/keep x nz*nvar} matrix of Deltadraws} \item{Vbetadraw }{\eqn{R/keep x nvar*nvar} matrix of Vbeta draws} } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rhierLinearMixture}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) nreg = 100 nobs = 100 nvar = 3 Vbeta = matrix(c(1, 0.5, 0, 0.5, 2, 0.7, 0, 0.7, 1), ncol=3) Z = cbind(c(rep(1,nreg)), 3*runif(nreg)) Z[,2] = Z[,2] - mean(Z[,2]) nz = ncol(Z) Delta = matrix(c(1,-1,2,0,1,0), ncol=2) Delta = t(Delta) # first row of Delta is means of betas Beta = matrix(rnorm(nreg*nvar),nrow=nreg)\%*\%chol(Vbeta) + Z\%*\%Delta tau = 0.1 iota = c(rep(1,nobs)) regdata = NULL for (reg in 1:nreg) { X = cbind(iota, matrix(runif(nobs*(nvar-1)),ncol=(nvar-1))) y = X\%*\%Beta[reg,] + sqrt(tau)*rnorm(nobs) regdata[[reg]] = list(y=y, X=X) } Data1 = list(regdata=regdata, Z=Z) Mcmc1 = list(R=R, keep=1) out = rhierLinearModel(Data=Data1, Mcmc=Mcmc1) cat("Summary of Delta draws", fill=TRUE) summary(out$Deltadraw, tvalues=as.vector(Delta)) cat("Summary of Vbeta draws", fill=TRUE) summary(out$Vbetadraw, tvalues=as.vector(Vbeta[upper.tri(Vbeta,diag=TRUE)])) ## plotting examples if(0){ plot(out$betadraw) plot(out$Deltadraw) } } \keyword{regression} bayesm/man/llnhlogit.Rd0000644000176000001440000000402113117541521014615 0ustar ripleyusers\name{llnhlogit} \alias{llnhlogit} \concept{multinomial logit} \concept{non-homothetic utility} \title{Evaluate Log Likelihood for non-homothetic Logit Model} \description{ \code{llnhlogit} evaluates log-likelihood for the Non-homothetic Logit model. } \usage{llnhlogit(theta, choice, lnprices, Xexpend)} \arguments{ \item{theta }{ parameter vector (see details section) } \item{choice }{ \eqn{n x 1} vector of choice (1,\ldots,p) } \item{lnprices}{ \eqn{n x p} array of log-prices} \item{Xexpend }{ \eqn{n x d} array of vars predicting expenditure } } \details{ Non-homothetic logit model, \eqn{Pr(i) = exp(tau v_i) / sum_j exp(tau v_j)} \cr \eqn{v_i = alpha_i - e^{kappaStar_i}u^i - lnp_i} \cr tau is the scale parameter of extreme value error distribution.\cr \eqn{u^i} solves \eqn{u^i = psi_i(u^i)E/p_i}.\cr \eqn{ln(psi_i(U)) = alpha_i - e^{kappaStar_i}U}. \cr \eqn{ln(E) = gamma'Xexpend}.\cr Structure of theta vector: \cr alpha: \eqn{p x 1} vector of utility intercepts.\cr kappaStar: \eqn{p x 1} vector of utility rotation parms expressed on natural log scale. \cr gamma: \eqn{k x 1} -- expenditure variable coefs.\cr tau: \eqn{1 x 1} -- logit scale parameter.\cr } \value{Value of log-likelihood (sum of log prob of observed multinomial outcomes).} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 4, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{\code{\link{simnhlogit}}} \examples{ N=1000; p=3; k=1 theta = c(rep(1,p), seq(from=-1,to=1,length=p), rep(2,k), 0.5) lnprices = matrix(runif(N*p), ncol=p) Xexpend = matrix(runif(N*k), ncol=k) simdata = simnhlogit(theta, lnprices, Xexpend) ## evaluate likelihood at true theta llstar = llnhlogit(theta, simdata$y, simdata$lnprices, simdata$Xexpend) } \keyword{models}bayesm/man/rbprobitGibbs.Rd0000644000176000001440000000455613117541521015430 0ustar ripleyusers\name{rbprobitGibbs} \alias{rbprobitGibbs} \concept{bayes} \concept{MCMC} \concept{probit} \concept{Gibbs Sampling} \title{Gibbs Sampler (Albert and Chib) for Binary Probit} \description{ \code{rbprobitGibbs} implements the Albert and Chib Gibbs Sampler for the binary probit model. } \usage{rbprobitGibbs(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(y, X)} \item{Prior}{list(betabar, A)} \item{Mcmc }{list(R, keep, nprint)} } \details{ \subsection{Model and Priors}{ \eqn{z = X\beta + e} with \eqn{e} \eqn{\sim}{~} \eqn{N(0, I)} \cr \eqn{y = 1} if \eqn{z > 0} \eqn{\beta} \eqn{\sim}{~} \eqn{N(betabar, A^{-1})} } \subsection{Argument Details}{ \emph{\code{Data = list(y, X)}} \tabular{ll}{ \code{y: } \tab \eqn{n x 1} vector of 0/1 outcomes \cr \code{X: } \tab \eqn{n x k} design matrix } \emph{\code{Prior = list(betabar, A)} [optional]} \tabular{ll}{ \code{betabar: } \tab \eqn{k x 1} prior mean (def: 0) \cr \code{A: } \tab \eqn{k x k} prior precision matrix (def: 0.01*I) } \emph{\code{Mcmc = list(R, keep, nprint)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) } } } \value{ A list containing: \item{betadraw }{ \eqn{R/keep x k} matrix of betadraws} } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rmnpGibbs}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) ## function to simulate from binary probit including x variable simbprobit = function(X, beta) { y = ifelse((X\%*\%beta + rnorm(nrow(X)))<0, 0, 1) list(X=X, y=y, beta=beta) } nobs = 200 X = cbind(rep(1,nobs), runif(nobs), runif(nobs)) beta = c(0,1,-1) nvar = ncol(X) simout = simbprobit(X, beta) Data1 = list(X=simout$X, y=simout$y) Mcmc1 = list(R=R, keep=1) out = rbprobitGibbs(Data=Data1, Mcmc=Mcmc1) summary(out$betadraw, tvalues=beta) ## plotting example if(0){plot(out$betadraw, tvalues=beta)} } \keyword{models} bayesm/man/rmvst.Rd0000755000176000001440000000170513117541521014005 0ustar ripleyusers\name{rmvst} \alias{rmvst} \concept{multivariate t distribution} \concept{student-t} \concept{simulation} \title{ Draw from Multivariate Student-t } \description{ \code{rmvst} draws from a multivariate student-t distribution. } \usage{rmvst(nu, mu, root)} \arguments{ \item{nu}{ d.f. parameter } \item{mu}{ mean vector } \item{root}{ Upper Tri Cholesky Root of Sigma } } \value{length(mu) draw vector} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{lndMvst}}} \examples{ set.seed(66) rmvst(nu=5, mu=c(rep(0,2)), root=chol(matrix(c(2,1,1,2), ncol=2))) } \keyword{multivariate} \keyword{distribution} bayesm/man/rmultireg.Rd0000644000176000001440000000507213117541521014642 0ustar ripleyusers\name{rmultireg} \alias{rmultireg} \concept{bayes} \concept{multivariate regression} \concept{simulation} \title{Draw from the Posterior of a Multivariate Regression} \description{ \code{ rmultireg} draws from the posterior of a Multivariate Regression model with a natural conjugate prior. } \usage{rmultireg(Y, X, Bbar, A, nu, V)} \arguments{ \item{Y }{ \eqn{n x m} matrix of observations on m dep vars } \item{X }{ \eqn{n x k} matrix of observations on indep vars (supply intercept) } \item{Bbar }{ \eqn{k x m} matrix of prior mean of regression coefficients } \item{A }{ \eqn{k x k} Prior precision matrix } \item{nu }{ d.f. parameter for Sigma } \item{V }{ \eqn{m x m} pdf location parameter for prior on Sigma } } \details{ Model: \cr \eqn{Y = XB + U} with \eqn{cov(u_i) = \Sigma} \cr \eqn{B} is \eqn{k x m} matrix of coefficients; \eqn{\Sigma} is \eqn{m x m} covariance matrix. Priors: \cr \eqn{\beta} | \eqn{\Sigma} \eqn{\sim}{~} \eqn{N(betabar, \Sigma(x) A^{-1})} \cr \eqn{betabar = vec(Bbar)}; \eqn{\beta = vec(B)} \cr \eqn{\Sigma} \eqn{\sim}{~} IW(nu, V) } \value{ A list of the components of a draw from the posterior \item{B }{ draw of regression coefficient matrix } \item{Sigma }{ draw of Sigma } } \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 2, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) n =200 m = 2 X = cbind(rep(1,n),runif(n)) k = ncol(X) B = matrix(c(1,2,-1,3), ncol=m) Sigma = matrix(c(1, 0.5, 0.5, 1), ncol=m) RSigma = chol(Sigma) Y = X\%*\%B + matrix(rnorm(m*n),ncol=m)\%*\%RSigma betabar = rep(0,k*m) Bbar = matrix(betabar, ncol=m) A = diag(rep(0.01,k)) nu = 3 V = nu*diag(m) betadraw = matrix(double(R*k*m), ncol=k*m) Sigmadraw = matrix(double(R*m*m), ncol=m*m) for (rep in 1:R) { out = rmultireg(Y, X, Bbar, A, nu, V) betadraw[rep,] = out$B Sigmadraw[rep,] = out$Sigma } cat(" Betadraws ", fill=TRUE) mat = apply(betadraw, 2, quantile, probs=c(0.01, 0.05, 0.5, 0.95, 0.99)) mat = rbind(as.vector(B),mat) rownames(mat)[1] = "beta" print(mat) cat(" Sigma draws", fill=TRUE) mat = apply(Sigmadraw, 2 ,quantile, probs=c(0.01, 0.05, 0.5, 0.95, 0.99)) mat = rbind(as.vector(Sigma),mat); rownames(mat)[1]="Sigma" print(mat) } \keyword{regression} bayesm/man/runireg.Rd0000644000176000001440000000472713117541521014311 0ustar ripleyusers\name{runireg} \alias{runireg} \concept{bayes} \concept{regression} \title{IID Sampler for Univariate Regression} \description{ \code{runireg} implements an iid sampler to draw from the posterior of a univariate regression with a conjugate prior. } \usage{runireg(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(y, X)} \item{Prior}{list(betabar, A, nu, ssq)} \item{Mcmc }{list(R, keep, nprint)} } \details{ \subsection{Model and Priors}{ \eqn{y = X\beta + e} with \eqn{e} \eqn{\sim}{~} \eqn{N(0, \sigma^2)} \eqn{\beta} \eqn{\sim}{~} \eqn{N(betabar, \sigma^2*A^{-1})} \cr \eqn{\sigma^2} \eqn{\sim}{~} \eqn{(nu*ssq)/\chi^2_{nu}} } \subsection{Argument Details}{ \emph{\code{Data = list(y, X)}} \tabular{ll}{ \code{y: } \tab \eqn{n x 1} vector of observations \cr \code{X: } \tab \eqn{n x k} design matrix } \emph{\code{Prior = list(betabar, A, nu, ssq)} [optional]} \tabular{ll}{ \code{betabar: } \tab \eqn{k x 1} prior mean (def: 0) \cr \code{A: } \tab \eqn{k x k} prior precision matrix (def: 0.01*I) \cr \code{nu: } \tab d.f. parameter for Inverted Chi-square prior (def: 3) \cr \code{ssq: } \tab scale parameter for Inverted Chi-square prior (def: \code{var(y)}) } \emph{\code{Mcmc = list(R, keep, nprint)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of draws \cr \code{keep: } \tab thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) } } } \value{ A list containing: \item{betadraw }{ \eqn{R x k} matrix of betadraws } \item{sigmasqdraw }{ \eqn{R x 1} vector of sigma-sq draws} } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 2, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{runiregGibbs}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) n = 200 X = cbind(rep(1,n), runif(n)) beta = c(1,2) sigsq = 0.25 y = X\%*\%beta + rnorm(n,sd=sqrt(sigsq)) out = runireg(Data=list(y=y,X=X), Mcmc=list(R=R)) cat("Summary of beta and Sigmasq draws", fill=TRUE) summary(out$betadraw, tvalues=beta) summary(out$sigmasqdraw, tvalues=sigsq) ## plotting examples if(0){plot(out$betadraw)} } \keyword{regression} bayesm/man/cgetC.Rd0000644000176000001440000000176413117541521013661 0ustar ripleyusers\name{cgetC} \alias{cgetC} \title{Obtain A List of Cut-offs for Scale Usage Problems} \description{ \code{cgetC} obtains a list of censoring points, or cut-offs, used in the ordinal multivariate probit model of Rossi et al (2001). This approach uses a quadratic parameterization of the cut-offs. The model is useful for modeling correlated ordinal data on a scale from \eqn{1} to \eqn{k} with different scale usage patterns. } \usage{cgetC(e, k)} \arguments{ \item{e}{ quadratic parameter (\eqn{0 <} \code{e} \eqn{< 1}) } \item{k}{ items are on a scale from \eqn{1,\ldots, k} } } \section{Warning}{This is a utility function which implements \strong{no} error-checking.} \value{A vector of \eqn{k+1} cut-offs.} \author{Rob McCulloch and Peter Rossi, Anderson School, UCLA. \email{perossichi@gmail.com}.} \references{Rossi et al (2001), \dQuote{Overcoming Scale Usage Heterogeneity,} \emph{JASA} 96, 20--31.} \seealso{ \code{\link{rscaleUsage}} } \examples{ cgetC(0.1, 10) } \keyword{ utilities } bayesm/man/lndMvn.Rd0000644000176000001440000000205113117541521014060 0ustar ripleyusers\name{lndMvn} \alias{lndMvn} \concept{multivariate normal distribution} \concept{density} \title{ Compute Log of Multivariate Normal Density } \description{ \code{lndMvn} computes the log of a Multivariate Normal Density. } \usage{lndMvn(x, mu, rooti)} \arguments{ \item{x }{ density ordinate } \item{mu }{ mu vector } \item{rooti}{ inv of upper triangular Cholesky root of \eqn{\Sigma} } } \details{ \eqn{z} \eqn{\sim}{~} \eqn{N(mu,\Sigma)} } \value{Log density value} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 2, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{lndMvst}} } \examples{ Sigma = matrix(c(1, 0.5, 0.5, 1), ncol=2) lndMvn(x=c(rep(0,2)), mu=c(rep(0,2)), rooti=backsolve(chol(Sigma),diag(2))) } \keyword{distribution} bayesm/man/mixDen.Rd0000644000176000001440000000261313117541521014052 0ustar ripleyusers\name{mixDen} \alias{mixDen} \concept{normal mixture} \concept{marginal distribution} \concept{density} \title{Compute Marginal Density for Multivariate Normal Mixture} \description{ \code{mixDen} computes the marginal density for each dimension of a normal mixture at each of the points on a user-specifed grid.} \usage{mixDen(x, pvec, comps)} \arguments{ \item{x}{ array where \eqn{i}th column gives grid points for \eqn{i}th variable } \item{pvec}{ vector of mixture component probabilites } \item{comps}{ list of lists of components for normal mixture } } \details{ \tabular{ll}{ \code{length(comps) } \tab is the number of mixture components \cr \code{comps[[j]] } \tab is a list of parameters of the \eqn{j}th component \cr \code{comps[[j]]$mu } \tab is mean vector \cr \code{comps[[j]]$rooti} \tab is the UL decomp of \eqn{\Sigma^{-1}} } } \value{An array of the same dimension as grid with density values} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rnmixGibbs}} } \keyword{models} \keyword{multivariate} bayesm/man/lndIWishart.Rd0000755000176000001440000000223013117541521015054 0ustar ripleyusers\name{lndIWishart} \alias{lndIWishart} \concept{Inverted Wishart distribution} \concept{density} \title{Compute Log of Inverted Wishart Density} \description{ \code{lndIWishart} computes the log of an Inverted Wishart density. } \usage{lndIWishart(nu, V, IW)} \arguments{ \item{nu }{ d.f. parameter } \item{V }{ "location" parameter } \item{IW }{ ordinate for density evaluation } } \details{ \eqn{Z} \eqn{\sim}{~} Inverted Wishart(nu,V). \cr In this parameterization, \eqn{E[Z] = 1/(nu-k-1) V}, where \eqn{V} is a \eqn{k x k} matrix \cr \code{lndIWishart} computes the complete log-density, including normalizing constants. } \value{Log density value} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 2, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rwishart}} } \examples{ lndIWishart(5, diag(3), diag(3)+0.5) } \keyword{ distribution } bayesm/man/lndMvst.Rd0000644000176000001440000000227213117541521014256 0ustar ripleyusers\name{lndMvst} \alias{lndMvst} \concept{multivariate t distribution} \concept{student-t distribution} \concept{density} \title{Compute Log of Multivariate Student-t Density} \description{ \code{lndMvst} computes the log of a Multivariate Student-t Density. } \usage{lndMvst(x, nu, mu, rooti, NORMC)} \arguments{ \item{x }{ density ordinate } \item{nu }{ d.f. parameter } \item{mu }{ mu vector } \item{rooti}{ inv of Cholesky root of \eqn{\Sigma} } \item{NORMC}{ include normalizing constant (def: \code{FALSE}) } } \details{ \eqn{z} \eqn{\sim}{~} \eqn{MVst(mu, nu, \Sigma)} } \value{Log density value} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 2, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{lndMvn}} } \examples{ Sigma = matrix(c(1, 0.5, 0.5, 1), ncol=2) lndMvst(x=c(rep(0,2)), nu=4,mu=c(rep(0,2)), rooti=backsolve(chol(Sigma),diag(2))) } \keyword{distribution} bayesm/man/lndIChisq.Rd0000644000176000001440000000213613117541521014504 0ustar ripleyusers\name{lndIChisq} \alias{lndIChisq} \concept{Inverted Chi-squared Distribution} \concept{density} \title{Compute Log of Inverted Chi-Squared Density} \description{ \code{lndIChisq} computes the log of an Inverted Chi-Squared Density. } \usage{lndIChisq(nu, ssq, X)} \arguments{ \item{nu }{ d.f. parameter } \item{ssq }{ scale parameter } \item{X }{ ordinate for density evaluation (this must be a matrix)} } \details{ \eqn{Z = nu*ssq / \chi^2_{nu}} with \eqn{Z} \eqn{\sim}{~} Inverted Chi-Squared. \cr \code{lndIChisq} computes the complete log-density, including normalizing constants. } \value{Log density value} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 2, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{dchisq}} } \examples{ lndIChisq(3, 1, matrix(2)) } \keyword{distribution} bayesm/man/rmnpGibbs.Rd0000644000176000001440000001011213117541521014542 0ustar ripleyusers\name{rmnpGibbs} \alias{rmnpGibbs} \concept{bayes} \concept{multinomial probit} \concept{MCMC} \concept{Gibbs Sampling} \title{Gibbs Sampler for Multinomial Probit} \description{ \code{rmnpGibbs} implements the McCulloch/Rossi Gibbs Sampler for the multinomial probit model. } \usage{rmnpGibbs(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(y, X, p)} \item{Prior}{list(betabar, A, nu, V)} \item{Mcmc }{list(R, keep, nprint, beta0, sigma0)} } \details{ \subsection{Model and Priors}{ \eqn{w_i = X_i\beta + e} with \eqn{e} \eqn{\sim}{~} \eqn{N(0, \Sigma)}. Note: \eqn{w_i} and \eqn{e} are \eqn{(p-1) x 1}.\cr \eqn{y_i = j} if \eqn{w_{ij} > max(0,w_{i,-j})} for \eqn{j=1, \ldots, p-1} and where \eqn{w_{i,-j}} means elements of \eqn{w_i} other than the \eqn{j}th. \cr \eqn{y_i = p}, if all \eqn{w_i < 0} \eqn{\beta} is not identified. However, \eqn{\beta}/sqrt(\eqn{\sigma_{11}}) and \eqn{\Sigma}/\eqn{\sigma_{11}} are identified. See reference or example below for details. \eqn{\beta} \eqn{\sim}{~} \eqn{N(betabar,A^{-1})} \cr \eqn{\Sigma} \eqn{\sim}{~} \eqn{IW(nu,V)} \cr } \subsection{Argument Details}{ \emph{\code{Data = list(y, X, p)}} \tabular{ll}{ \code{y: } \tab \eqn{n x 1} vector of multinomial outcomes (1, \ldots, p) \cr \code{X: } \tab \eqn{n*(p-1) x k} design matrix. To make \eqn{X} matrix use \code{\link{createX}} with \code{DIFF=TRUE} \cr \code{p: } \tab number of alternatives } \emph{\code{Prior = list(betabar, A, nu, V)} [optional]} \tabular{ll}{ \code{betabar: } \tab \eqn{k x 1} prior mean (def: 0) \cr \code{A: } \tab \eqn{k x k} prior precision matrix (def: 0.01*I) \cr \code{nu: } \tab d.f. parameter for Inverted Wishart prior (def: (p-1)+3) \cr \code{V: } \tab PDS location parameter for Inverted Wishart prior (def: nu*I) } \emph{\code{Mcmc = list(R, keep, nprint, beta0, sigma0)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) \cr \code{beta0: } \tab initial value for beta (def: 0) \cr \code{sigma0: } \tab initial value for sigma (def: I) } } } \value{ A list containing: \item{betadraw }{\eqn{R/keep x k} matrix of betadraws} \item{sigmadraw }{\eqn{R/keep x (p-1)*(p-1)} matrix of sigma draws -- each row is the vector form of sigma} } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 4, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rmvpGibbs}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) simmnp = function(X, p, n, beta, sigma) { indmax = function(x) {which(max(x)==x)} Xbeta = X\%*\%beta w = as.vector(crossprod(chol(sigma),matrix(rnorm((p-1)*n),ncol=n))) + Xbeta w = matrix(w, ncol=(p-1), byrow=TRUE) maxw = apply(w, 1, max) y = apply(w, 1, indmax) y = ifelse(maxw < 0, p, y) return(list(y=y, X=X, beta=beta, sigma=sigma)) } p = 3 n = 500 beta = c(-1,1,1,2) Sigma = matrix(c(1, 0.5, 0.5, 1), ncol=2) k = length(beta) X1 = matrix(runif(n*p,min=0,max=2),ncol=p) X2 = matrix(runif(n*p,min=0,max=2),ncol=p) X = createX(p, na=2, nd=NULL, Xa=cbind(X1,X2), Xd=NULL, DIFF=TRUE, base=p) simout = simmnp(X,p,500,beta,Sigma) Data1 = list(p=p, y=simout$y, X=simout$X) Mcmc1 = list(R=R, keep=1) out = rmnpGibbs(Data=Data1, Mcmc=Mcmc1) cat(" Summary of Betadraws ", fill=TRUE) betatilde = out$betadraw / sqrt(out$sigmadraw[,1]) attributes(betatilde)$class = "bayesm.mat" summary(betatilde, tvalues=beta) cat(" Summary of Sigmadraws ", fill=TRUE) sigmadraw = out$sigmadraw / out$sigmadraw[,1] attributes(sigmadraw)$class = "bayesm.var" summary(sigmadraw, tvalues=as.vector(Sigma[upper.tri(Sigma,diag=TRUE)])) ## plotting examples if(0){plot(betatilde,tvalues=beta)} } \keyword{models} bayesm/man/nmat.Rd0000755000176000001440000000164213117541521013571 0ustar ripleyusers\name{nmat} \alias{nmat} \title{Convert Covariance Matrix to a Correlation Matrix} \description{ \code{nmat} converts a covariance matrix (stored as a vector, col by col) to a correlation matrix (also stored as a vector). } \usage{nmat(vec)} \arguments{ \item{vec}{ \eqn{k x k} Cov matrix stored as a \eqn{k*k x 1} vector (col by col) } } \details{ This routine is often used with apply to convert an \eqn{R x (k*k)} array of covariance MCMC draws to correlations. As in \code{corrdraws = apply(vardraws, 1, nmat)}. } \value{\eqn{k*k x 1} vector with correlation matrix} \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \examples{ set.seed(66) X = matrix(rnorm(200,4), ncol=2) Varmat = var(X) nmat(as.vector(Varmat)) } \keyword{utilities} \keyword{array} bayesm/man/orangeJuice.Rd0000644000176000001440000001132513117541521015061 0ustar ripleyusers\name{orangeJuice} \alias{orangeJuice} \docType{data} \title{Store-level Panel Data on Orange Juice Sales} \description{ Weekly sales of refrigerated orange juice at 83 stores. Contains demographic information on those stores. } \usage{data(orangeJuice)} \format{ The \code{orangeJuice} object is a list containing two data frames, \code{yx} and \code{storedemo}. } \details{ In the \code{yx} data frame: \tabular{ll}{ \ldots\code{$store } \tab store number \cr \ldots\code{$brand } \tab brand indicator \cr \ldots\code{$week } \tab week number \cr \ldots\code{$logmove } \tab log of the number of units sold \cr \ldots\code{$constant } \tab a vector of 1s \cr \ldots\code{$price# } \tab price of brand # \cr \ldots\code{$deal } \tab in-store coupon activity \cr \ldots\code{$feature } \tab feature advertisement \cr \ldots\code{$profit } \tab profit } The price variables correspond to the following brands: \tabular{ll}{ 1 \tab Tropicana Premium 64 oz \cr 2 \tab Tropicana Premium 96 oz \cr 3 \tab Florida's Natural 64 oz \cr 4 \tab Tropicana 64 oz \cr 5 \tab Minute Maid 64 oz \cr 6 \tab Minute Maid 96 oz \cr 7 \tab Citrus Hill 64 oz \cr 8 \tab Tree Fresh 64 oz \cr 9 \tab Florida Gold 64 oz \cr 10 \tab Dominicks 64 oz \cr 11 \tab Dominicks 128 oz } In the \code{storedemo} data frame: \tabular{ll}{ \ldots\code{$STORE } \tab store number \cr \ldots\code{$AGE60 } \tab percentage of the population that is aged 60 or older \cr \ldots\code{$EDUC } \tab percentage of the population that has a college degree \cr \ldots\code{$ETHNIC } \tab percent of the population that is black or Hispanic \cr \ldots\code{$INCOME } \tab median income \cr \ldots\code{$HHLARGE } \tab percentage of households with 5 or more persons \cr \ldots\code{$WORKWOM } \tab percentage of women with full-time jobs \cr \ldots\code{$HVAL150 } \tab percentage of households worth more than $150,000 \cr \ldots\code{$SSTRDIST } \tab distance to the nearest warehouse store \cr \ldots\code{$SSTRVOL } \tab ratio of sales of this store to the nearest warehouse store \cr \ldots\code{$CPDIST5 } \tab average distance in miles to the nearest 5 supermarkets \cr \ldots\code{$CPWVOL5 } \tab ratio of sales of this store to the average of the nearest five stores } } \source{Alan L. Montgomery (1997), "Creating Micro-Marketing Pricing Strategies Using Supermarket Scanner Data," \emph{Marketing Science} 16(4) 315--337.} \references{Chapter 5, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch\cr \url{http://www.perossi.org/home/bsm-1}} \examples{ ## load data data(orangeJuice) ## print some quantiles of yx data cat("Quantiles of the Variables in yx data",fill=TRUE) mat = apply(as.matrix(orangeJuice$yx), 2, quantile) print(mat) ## print some quantiles of storedemo data cat("Quantiles of the Variables in storedemo data",fill=TRUE) mat = apply(as.matrix(orangeJuice$storedemo), 2, quantile) print(mat) ## processing for use with rhierLinearModel if(0) { ## select brand 1 for analysis brand1 = orangeJuice$yx[(orangeJuice$yx$brand==1),] store = sort(unique(brand1$store)) nreg = length(store) nvar = 14 regdata=NULL for (reg in 1:nreg) { y = brand1$logmove[brand1$store==store[reg]] iota = c(rep(1,length(y))) X = cbind(iota,log(brand1$price1[brand1$store==store[reg]]), log(brand1$price2[brand1$store==store[reg]]), log(brand1$price3[brand1$store==store[reg]]), log(brand1$price4[brand1$store==store[reg]]), log(brand1$price5[brand1$store==store[reg]]), log(brand1$price6[brand1$store==store[reg]]), log(brand1$price7[brand1$store==store[reg]]), log(brand1$price8[brand1$store==store[reg]]), log(brand1$price9[brand1$store==store[reg]]), log(brand1$price10[brand1$store==store[reg]]), log(brand1$price11[brand1$store==store[reg]]), brand1$deal[brand1$store==store[reg]], brand1$feat[brand1$store==store[reg]] ) regdata[[reg]] = list(y=y, X=X) } ## storedemo is standardized to zero mean. Z = as.matrix(orangeJuice$storedemo[,2:12]) dmean = apply(Z, 2, mean) for (s in 1:nreg) {Z[s,] = Z[s,] - dmean} iotaz = c(rep(1,nrow(Z))) Z = cbind(iotaz, Z) nz = ncol(Z) Data = list(regdata=regdata, Z=Z) Mcmc = list(R=R, keep=1) out = rhierLinearModel(Data=Data, Mcmc=Mcmc) summary(out$Deltadraw) summary(out$Vbetadraw) ## plotting examples if(0){ plot(out$betadraw) } } } \keyword{datasets} bayesm/man/rdirichlet.Rd0000755000176000001440000000142413117541521014761 0ustar ripleyusers\name{rdirichlet} \alias{rdirichlet} \concept{dirichlet distribution} \concept{simulation} \title{Draw From Dirichlet Distribution} \description{ \code{rdirichlet} draws from Dirichlet } \usage{rdirichlet(alpha)} \arguments{ \item{alpha}{vector of Dirichlet parms (must be > 0)} } \value{Vector of draws from Dirichlet} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 2, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \examples{ set.seed(66) rdirichlet(c(rep(3,5))) } \keyword{distribution} bayesm/man/momMix.Rd0000644000176000001440000000343413117541521014076 0ustar ripleyusers\name{momMix} \alias{momMix} \concept{mcmc} \concept{normal mixture} \concept{posterior moments} \title{Compute Posterior Expectation of Normal Mixture Model Moments} \description{ \code{momMix} averages the moments of a normal mixture model over MCMC draws. } \usage{momMix(probdraw, compdraw)} \arguments{ \item{probdraw}{ \eqn{R x ncomp} list of draws of mixture probs } \item{compdraw}{ list of length \eqn{R} of draws of mixture component moments } } \details{ \tabular{ll}{ \code{R } \tab is the number of MCMC draws in argument list above. \cr \code{ncomp } \tab is the number of mixture components fitted.\cr \code{compdraw } \tab is a list of lists of lists with mixture components. \cr \code{compdraw[[i]] } \tab is \eqn{i}th draw. \cr \code{compdraw[[i]][[j]][[1]] } \tab is the mean parameter vector for the \eqn{j}th component, \eqn{i}th MCMC draw. \cr \code{compdraw[[i]][[j]][[2]] } \tab is the UL decomposition of \eqn{\Sigma^{-1}} for the \eqn{j}th component, \eqn{i}th MCMC draw } } \value{ A list containing: \item{mu }{posterior expectation of mean} \item{sigma }{posterior expectation of covariance matrix} \item{sd }{posterior expectation of vector of standard deviations} \item{corr }{posterior expectation of correlation matrix} } \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 5, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rmixGibbs}}} \keyword{multivariate} bayesm/man/mnpProb.Rd0000755000176000001440000000326313117541521014250 0ustar ripleyusers\name{mnpProb} \alias{mnpProb} \concept{MNP} \concept{Multinomial Probit Model} \concept{GHK} \concept{market share simulator} \title{Compute MNP Probabilities} \description{ \code{mnpProb} computes MNP probabilities for a given \eqn{X} matrix corresponding to one observation. This function can be used with output from \code{rmnpGibbs} to simulate the posterior distribution of market shares or fitted probabilties. } \usage{mnpProb(beta, Sigma, X, r)} \arguments{ \item{beta}{ MNP coefficients } \item{Sigma}{ Covariance matrix of latents } \item{X}{ \eqn{X} array for one observation -- use \code{createX} to make } \item{r}{ number of draws used in GHK (def: 100)} } \details{ See \code{\link{rmnpGibbs}} for definition of the model and the interpretation of the beta and Sigma parameters. Uses the GHK method to compute choice probabilities. To simulate a distribution of probabilities, loop over the beta and Sigma draws from \code{rmnpGibbs} output. } \value{\eqn{p x 1} vector of choice probabilites} \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{ For further discussion, see Chapters 2 and 4, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rmnpGibbs}}, \code{\link{createX}} } \examples{ ## example of computing MNP probabilites ## here Xa has the prices of each of the 3 alternatives Xa = matrix(c(1,.5,1.5), nrow=1) X = createX(p=3, na=1, nd=NULL, Xa=Xa, Xd=NULL, DIFF=TRUE) beta = c(1,-1,-2) ## beta contains two intercepts and the price coefficient Sigma = matrix(c(1, 0.5, 0.5, 1), ncol=2) mnpProb(beta, Sigma, X) } \keyword{models} bayesm/man/tuna.Rd0000644000176000001440000000543413117541521013601 0ustar ripleyusers\name{tuna} \alias{tuna} \docType{data} \title{Canned Tuna Sales Data} \description{ Volume of canned tuna sales as well as a measure of display activity, log price, and log wholesale price. Weekly data aggregated to the chain level. This data is extracted from the Dominick's Finer Foods database maintained by the Kilts Center for Marketing at the University of Chicago's Booth School of Business. Brands are seven of the top 10 UPCs in the canned tuna product category. } \usage{data(tuna)} \format{ A data frame with 338 observations on 30 variables. \tabular{ll}{ \ldots\code{$WEEK } \tab a numeric vector \cr \ldots\code{$MOVE# } \tab unit sales of brand # \cr \ldots\code{$NSALE# } \tab a measure of display activity of brand # \cr \ldots\code{$LPRICE# } \tab log of price of brand # \cr \ldots\code{$LWHPRIC# } \tab log of wholesale price of brand # \cr \ldots\code{$FULLCUST } \tab total customers visits } The brands are: \tabular{ll}{ 1. \tab Star Kist 6 oz. \cr 2. \tab Chicken of the Sea 6 oz. \cr 3. \tab Bumble Bee Solid 6.12 oz. \cr 4. \tab Bumble Bee Chunk 6.12 oz. \cr 5. \tab Geisha 6 oz. \cr 6. \tab Bumble Bee Large Cans. \cr 7. \tab HH Chunk Lite 6.5 oz. } } \source{Chevalier, Judith, Anil Kashyap, and Peter Rossi (2003), "Why Don't Prices Rise During Periods of Peak Demand? Evidence from Scanner Data," \emph{The American Economic Review} , 93(1), 15--37.} \references{Chapter 7, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \examples{ data(tuna) cat(" Quantiles of sales", fill=TRUE) mat = apply(as.matrix(tuna[,2:5]), 2, quantile) print(mat) ## example of processing for use with rivGibbs if(0) { data(tuna) t = dim(tuna)[1] customers = tuna[,30] sales = tuna[,2:8] lnprice = tuna[,16:22] lnwhPrice = tuna[,23:29] share = sales/mean(customers) shareout = as.vector(1-rowSums(share)) lnprob = log(share/shareout) ## create w matrix I1 = as.matrix(rep(1,t)) I0 = as.matrix(rep(0,t)) intercept = rep(I1,4) brand1 = rbind(I1, I0, I0, I0) brand2 = rbind(I0, I1, I0, I0) brand3 = rbind(I0, I0, I1, I0) w = cbind(intercept, brand1, brand2, brand3) ## choose brand 1 to 4 y = as.vector(as.matrix(lnprob[,1:4])) X = as.vector(as.matrix(lnprice[,1:4])) lnwhPrice = as.vector(as.matrix(lnwhPrice[1:4])) z = cbind(w, lnwhPrice) Data = list(z=z, w=w, x=X, y=y) Mcmc = list(R=R, keep=1) set.seed(66) out = rivGibbs(Data=Data, Mcmc=Mcmc) cat(" betadraws ", fill=TRUE) summary(out$betadraw) ## plotting examples if(0){plot(out$betadraw)} } } \keyword{datasets} bayesm/man/mnlHess.Rd0000644000176000001440000000213513117541521014236 0ustar ripleyusers\name{mnlHess} \alias{mnlHess} \concept{multinomial logit} \concept{hessian} \title{ Computes --Expected Hessian for Multinomial Logit} \description{\code{mnlHess} computes expected Hessian (\eqn{E[H]}) for Multinomial Logit Model.} \usage{mnlHess(beta, y, X)} \arguments{ \item{beta}{ \eqn{k x 1} vector of coefficients } \item{y}{ \eqn{n x 1} vector of choices, (\eqn{1,\ldots,p}) } \item{X}{ \eqn{n*p x k} Design matrix } } \details{ See \code{\link{llmnl}} for information on structure of X array. Use \code{\link{createX}} to make X. } \value{\eqn{k x k} matrix} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{llmnl}}, \code{\link{createX}}, \code{\link{rmnlIndepMetrop}} } \examples{ \dontrun{mnlHess(beta, y, X)} } \keyword{models} bayesm/man/Scotch.Rd0000755000176000001440000000313613117541521014055 0ustar ripleyusers\name{Scotch} \alias{Scotch} \docType{data} \title{Survey Data on Brands of Scotch Consumed} \description{ Data from Simmons Survey. Brands used in last year for those respondents who report consuming scotch. } \usage{data(Scotch)} \format{ A data frame with 2218 observations on 21 brand variables. \cr All variables are numeric vectors that are coded 1 if consumed in last year, 0 if not. } \source{Edwards, Yancy and Greg Allenby (2003), "Multivariate Analysis of Multiple Response Data," \emph{Journal of Marketing Research} 40, 321--334.} \references{ Chapter 4, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch\cr \url{http://www.perossi.org/home/bsm-1}} \examples{ data(Scotch) cat(" Frequencies of Brands", fill=TRUE) mat = apply(as.matrix(Scotch), 2, mean) print(mat) ## use Scotch data to run Multivariate Probit Model if(0) { y = as.matrix(Scotch) p = ncol(y) n = nrow(y) dimnames(y) = NULL y = as.vector(t(y)) y = as.integer(y) I_p = diag(p) X = rep(I_p,n) X = matrix(X, nrow=p) X = t(X) R = 2000 Data = list(p=p, X=X, y=y) Mcmc = list(R=R) set.seed(66) out = rmvpGibbs(Data=Data, Mcmc=Mcmc) ind = (0:(p-1))*p + (1:p) cat(" Betadraws ", fill=TRUE) mat = apply(out$betadraw/sqrt(out$sigmadraw[,ind]), 2 , quantile, probs=c(0.01, 0.05, 0.5, 0.95, 0.99)) attributes(mat)$class = "bayesm.mat" summary(mat) rdraw = matrix(double((R)*p*p), ncol=p*p) rdraw = t(apply(out$sigmadraw, 1, nmat)) attributes(rdraw)$class = "bayesm.var" cat(" Draws of Correlation Matrix ", fill=TRUE) summary(rdraw) } } \keyword{datasets} bayesm/man/rnmixGibbs.Rd0000644000176000001440000001163113117570164014737 0ustar ripleyusers\name{rnmixGibbs} \alias{rnmixGibbs} \concept{bayes} \concept{MCMC} \concept{normal mixtures} \concept{Gibbs Sampling} \title{Gibbs Sampler for Normal Mixtures} \description{ \code{rnmixGibbs} implements a Gibbs Sampler for normal mixtures. } \usage{rnmixGibbs(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(y)} \item{Prior}{list(Mubar, A, nu, V, a, ncomp)} \item{Mcmc }{list(R, keep, nprint, Loglike)} } \details{ \subsection{Model and Priors}{ \eqn{y_i} \eqn{\sim}{~} \eqn{N(\mu_{ind_i}, \Sigma_{ind_i})} \cr ind \eqn{\sim}{~} iid multinomial(p) with \eqn{p} an \eqn{ncomp x 1} vector of probs \eqn{\mu_j} \eqn{\sim}{~} \eqn{N(mubar, \Sigma_j (x) A^{-1})} with \eqn{mubar=vec(Mubar)} \cr \eqn{\Sigma_j} \eqn{\sim}{~} \eqn{IW(nu, V)} \cr Note: this is the natural conjugate prior -- a special case of multivariate regression \cr \eqn{p} \eqn{\sim}{~} Dirchlet(a) } \subsection{Argument Details}{ \emph{\code{Data = list(y)}} \tabular{ll}{ \code{y: } \tab \eqn{n x k} matrix of data (rows are obs) } \emph{\code{Prior = list(Mubar, A, nu, V, a, ncomp)} [only \code{ncomp} required]} \tabular{ll}{ \code{Mubar: } \tab \eqn{1 x k} vector with prior mean of normal component means (def: 0) \cr \code{A: } \tab \eqn{1 x 1} precision parameter for prior on mean of normal component (def: 0.01) \cr \code{nu: } \tab d.f. parameter for prior on Sigma (normal component cov matrix) (def: k+3) \cr \code{V: } \tab \eqn{k x k} location matrix of IW prior on Sigma (def: nu*I) \cr \code{a: } \tab \eqn{ncomp x 1} vector of Dirichlet prior parameters (def: \code{rep(5,ncomp)}) \cr \code{ncomp: } \tab number of normal components to be included } \emph{\code{Mcmc = list(R, keep, nprint, Loglike)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) \cr \code{LogLike: } \tab logical flag for whether to compute the log-likelihood (def: \code{FALSE}) } } \subsection{\code{nmix} Details}{ \code{nmix} is a list with 3 components. Several functions in the \code{bayesm} package that involve a Dirichlet Process or mixture-of-normals return \code{nmix}. Across these functions, a common structure is used for \code{nmix} in order to utilize generic summary and plotting functions. \tabular{ll}{ \code{probdraw:} \tab \eqn{ncomp x R/keep} matrix that reports the probability that each draw came from a particular component \cr \code{zdraw: } \tab \eqn{R/keep x nobs} matrix that indicates which component each draw is assigned to \cr \code{compdraw:} \tab A list of \eqn{R/keep} lists of \eqn{ncomp} lists. Each of the inner-most lists has 2 elemens: a vector of draws for \code{mu} and a matrix of draws for the Cholesky root of \code{Sigma}. } } } \value{ A list containing: \item{ll }{ \eqn{R/keep x 1} vector of log-likelihood values} \item{nmix }{ a list containing: \code{probdraw}, \code{zdraw}, \code{compdraw} (see \dQuote{\code{nmix} Details} section)} } \note{ In this model, the component normal parameters are not-identified due to label-switching. However, the fitted mixture of normals density is identified as it is invariant to label-switching. See chapter 5 of Rossi et al below for details. Use \code{eMixMargDen} or \code{momMix} to compute posterior expectation or distribution of various identified parameters. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rmixture}}, \code{\link{rmixGibbs}} ,\code{\link{eMixMargDen}}, \code{\link{momMix}}, \code{\link{mixDen}}, \code{\link{mixDenBi}}} \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) dim = 5 k = 3 # dimension of simulated data and number of "true" components sigma = matrix(rep(0.5,dim^2), nrow=dim) diag(sigma) = 1 sigfac = c(1,1,1) mufac = c(1,2,3) compsmv = list() for(i in 1:k) compsmv[[i]] = list(mu=mufac[i]*1:dim, sigma=sigfac[i]*sigma) # change to "rooti" scale comps = list() for(i in 1:k) comps[[i]] = list(mu=compsmv[[i]][[1]], rooti=solve(chol(compsmv[[i]][[2]]))) pvec = (1:k) / sum(1:k) nobs = 500 dm = rmixture(nobs, pvec, comps) Data1 = list(y=dm$x) ncomp = 9 Prior1 = list(ncomp=ncomp) Mcmc1 = list(R=R, keep=1) out = rnmixGibbs(Data=Data1, Prior=Prior1, Mcmc=Mcmc1) cat("Summary of Normal Mixture Distribution", fill=TRUE) summary(out$nmix) tmom = momMix(matrix(pvec,nrow=1), list(comps)) mat = rbind(tmom$mu, tmom$sd) cat(" True Mean/Std Dev", fill=TRUE) print(mat) ## plotting examples if(0){plot(out$nmix,Data=dm$x)} } \keyword{multivariate} bayesm/man/rtrun.Rd0000755000176000001440000000266013117541521014005 0ustar ripleyusers\name{rtrun} \alias{rtrun} \concept{truncated normal} \concept{simulation} \title{Draw from Truncated Univariate Normal} \description{ \code{rtrun} draws from a truncated univariate normal distribution. } \usage{rtrun(mu, sigma, a, b)} \arguments{ \item{mu}{ mean } \item{sigma}{ standard deviation } \item{a}{ lower bound } \item{b}{ upper bound } } \details{ Note that due to the vectorization of the \code{rnorm} and \code{qnorm} commands in R, all arguments can be vectors of equal length. This makes the inverse CDF method the most efficient to use in R. } \value{Draw (possibly a vector)} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. **Note also that \code{rtrun} is currently affected by the numerical accuracy of the inverse CDF function when trunctation points are far out in the tails of the distribution, where \dQuote{far out} means \eqn{|a - \mu| / \sigma > 6} and/or \eqn{|b - \mu| / \sigma > 6}. A fix will be implemented in a future version of \code{bayesm}. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 2, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \examples{ set.seed(66) rtrun(mu=c(rep(0,10)), sigma=c(rep(1,10)), a=c(rep(0,10)), b=c(rep(2,10))) } \keyword{distribution} bayesm/man/rmixGibbs.Rd0000644000176000001440000000270113117541521014552 0ustar ripleyusers\name{rmixGibbs} \alias{rmixGibbs} \title{ Gibbs Sampler for Normal Mixtures w/o Error Checking} \description{ \code{rmixGibbs} makes one draw using the Gibbs Sampler for a mixture of multivariate normals. \code{rmixGibbs} is not designed to be called directly. Instead, use \code{rnmixGibbs} wrapper function. } \usage{ rmixGibbs(y, Bbar, A, nu, V, a, p, z) } \arguments{ \item{y }{ data array where rows are obs } \item{Bbar }{ prior mean for mean vector of each norm comp } \item{A }{ prior precision parameter} \item{nu }{ prior d.f. parm } \item{V }{ prior location matrix for covariance prior } \item{a }{ Dirichlet prior parms } \item{p }{ prior prob of each mixture component } \item{z }{ component identities for each observation -- "indicators" } } \value{ a list containing: \item{p}{ draw of mixture probabilities} \item{z}{ draw of indicators of each component} \item{comps}{ new draw of normal component parameters } } \author{Rob McCulloch (Arizona State University) and Peter Rossi (Anderson School, UCLA), \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 5 \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \seealso{ \code{\link{rnmixGibbs}} } \keyword{multivariate} bayesm/man/rbiNormGibbs.Rd0000644000176000001440000000240213117541521015201 0ustar ripleyusers\name{rbiNormGibbs} \alias{rbiNormGibbs} \concept{bayes} \concept{Gibbs Sampling} \concept{MCMC} \concept{normal distribution} \title{Illustrate Bivariate Normal Gibbs Sampler} \description{ \code{rbiNormGibbs} implements a Gibbs Sampler for the bivariate normal distribution. Intermediate moves are plotted and the output is contrasted with the iid sampler. This function is designed for illustrative/teaching purposes.} \usage{rbiNormGibbs(initx=2, inity=-2, rho, burnin=100, R=500)} \arguments{ \item{initx }{ initial value of parameter on x axis (def: 2)} \item{inity }{ initial value of parameter on y axis (def: -2)} \item{rho }{ correlation for bivariate normals} \item{burnin }{ burn-in number of draws (def: 100)} \item{R }{ number of MCMC draws (def: 500)} } \details{ \eqn{(\theta_1, \theta_2) ~ N( (0,0), \Sigma}) with \eqn{\Sigma} = \code{matrix(c(1,rho,rho,1),ncol=2)} } \value{ \eqn{R x 2} matrix of draws } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapters 2 and 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \examples{ \dontrun{out=rbiNormGibbs(rho=0.95)} } \keyword{distribution} bayesm/man/rhierMnlDP.Rd0000644000176000001440000002464713117570164014652 0ustar ripleyusers\name{rhierMnlDP} \alias{rhierMnlDP} \concept{bayes} \concept{MCMC} \concept{Multinomial Logit} \concept{normal mixture} \concept{Dirichlet Process Prior} \concept{heterogeneity} \concept{hierarchical models} \title{MCMC Algorithm for Hierarchical Multinomial Logit with Dirichlet Process Prior Heterogeneity} \description{ \code{rhierMnlDP} is a MCMC algorithm for a hierarchical multinomial logit with a Dirichlet Process prior for the distribution of heteorogeneity. A base normal model is used so that the DP can be interpreted as allowing for a mixture of normals with as many components as there are panel units. This is a hybrid Gibbs Sampler with a RW Metropolis step for the MNL coefficients for each panel unit. This procedure can be interpreted as a Bayesian semi-parameteric method in the sense that the DP prior can accomodate heterogeniety of an unknown form. } \usage{rhierMnlDP(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(lgtdata, Z, p)} \item{Prior}{list(deltabar, Ad, Prioralpha, lambda_hyper)} \item{Mcmc }{list(R, keep, nprint, s, w, maxunique, gridsize)} } \details{ \subsection{Model and Priors}{ \eqn{y_i} \eqn{\sim}{~} \eqn{MNL(X_i, \beta_i)} with \eqn{i = 1, \ldots, length(lgtdata)} and where \eqn{\theta_i} is \eqn{nvar x 1} \eqn{\beta_i = Z\Delta}[i,] + \eqn{u_i} \cr Note: Z\eqn{\Delta} is the matrix \eqn{Z * \Delta}; [i,] refers to \eqn{i}th row of this product \cr Delta is an \eqn{nz x nvar} matrix \eqn{\beta_i} \eqn{\sim}{~} \eqn{N(\mu_i, \Sigma_i)} \eqn{\theta_i = (\mu_i, \Sigma_i)} \eqn{\sim}{~} \eqn{DP(G_0(\lambda), alpha)}\cr \eqn{G_0(\lambda):}\cr \eqn{\mu_i | \Sigma_i} \eqn{\sim}{~} \eqn{N(0, \Sigma_i (x) a^{-1})}\cr \eqn{\Sigma_i} \eqn{\sim}{~} \eqn{IW(nu, nu*v*I)}\cr \eqn{delta = vec(\Delta)} \eqn{\sim}{~} \eqn{N(deltabar, A_d^{-1})}\cr \eqn{\lambda(a, nu, v):}\cr \eqn{a} \eqn{\sim}{~} uniform[alim[1], alimb[2]]\cr \eqn{nu} \eqn{\sim}{~} dim(data)-1 + exp(z) \cr \eqn{z} \eqn{\sim}{~} uniform[dim(data)-1+nulim[1], nulim[2]]\cr \eqn{v} \eqn{\sim}{~} uniform[vlim[1], vlim[2]] \eqn{alpha} \eqn{\sim}{~} \eqn{(1-(alpha-alphamin) / (alphamax-alphamin))^{power}} \cr alpha = alphamin then expected number of components = \code{Istarmin} \cr alpha = alphamax then expected number of components = \code{Istarmax} \eqn{Z} should NOT include an intercept and is centered for ease of interpretation. The mean of each of the \code{nlgt} \eqn{\beta}s is the mean of the normal mixture. Use \code{summary()} to compute this mean from the \code{compdraw} output. We parameterize the prior on \eqn{\Sigma_i} such that \eqn{mode(\Sigma) = nu/(nu+2) vI}. The support of nu enforces a non-degenerate IW density; \eqn{nulim[1] > 0}. The default choices of alim, nulim, and vlim determine the location and approximate size of candidate "atoms" or possible normal components. The defaults are sensible given a reasonable scaling of the X variables. You want to insure that alim is set for a wide enough range of values (remember a is a precision parameter) and the v is big enough to propose Sigma matrices wide enough to cover the data range. A careful analyst should look at the posterior distribution of a, nu, v to make sure that the support is set correctly in alim, nulim, vlim. In other words, if we see the posterior bunched up at one end of these support ranges, we should widen the range and rerun. If you want to force the procedure to use many small atoms, then set nulim to consider only large values and set vlim to consider only small scaling constants. Set alphamax to a large number. This will create a very "lumpy" density estimate somewhat like the classical Kernel density estimates. Of course, this is not advised if you have a prior belief that densities are relatively smooth. } \subsection{Argument Details}{ \emph{\code{Data = list(lgtdata, Z, p)} [\code{Z} optional]} \tabular{ll}{ \code{lgtdata: } \tab list of lists with each cross-section unit MNL data \cr \code{lgtdata[[i]]$y: } \tab \eqn{n_i x 1} vector of multinomial outcomes (1, \ldots, m) \cr \code{lgtdata[[i]]$X: } \tab \eqn{n_i x nvar} design matrix for \eqn{i}th unit \cr \code{Z: } \tab \eqn{nreg x nz} matrix of unit characteristics (def: vector of ones) \cr \code{p: } \tab number of choice alternatives } \emph{\code{Prior = list(deltabar, Ad, Prioralpha, lambda_hyper)} [optional]} \tabular{ll}{ \code{deltabar: } \tab \eqn{nz*nvar x 1} vector of prior means (def: 0) \cr \code{Ad: } \tab prior precision matrix for vec(D) (def: 0.01*I) \cr \code{Prioralpha: } \tab \code{list(Istarmin, Istarmax, power)} \cr \code{$Istarmin: } \tab expected number of components at lower bound of support of alpha def(1) \cr \code{$Istarmax: } \tab expected number of components at upper bound of support of alpha (def: min(50, 0.1*nlgt)) \cr \code{$power: } \tab power parameter for alpha prior (def: 0.8) \cr \code{lambda_hyper: } \tab \code{list(alim, nulim, vlim)} \cr \code{$alim: } \tab defines support of a distribution (def: \code{c(0.01, 2)}) \cr \code{$nulim: } \tab defines support of nu distribution (def: \code{c(0.001, 3)}) \cr \code{$vlim: } \tab defines support of v distribution (def: \code{c(0.1, 4)}) } \emph{\code{Mcmc = list(R, keep, nprint, s, w, maxunique, gridsize)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) \cr \code{s: } \tab scaling parameter for RW Metropolis (def: 2.93/\code{sqrt(nvar)}) \cr \code{w: } \tab fractional likelihood weighting parameter (def: 0.1) \cr \code{maxuniq: } \tab storage constraint on the number of unique components (def: 200) \cr \code{gridsize: } \tab number of discrete points for hyperparameter priors, (def: 20) } } \subsection{\code{nmix} Details}{ \code{nmix} is a list with 3 components. Several functions in the \code{bayesm} package that involve a Dirichlet Process or mixture-of-normals return \code{nmix}. Across these functions, a common structure is used for \code{nmix} in order to utilize generic summary and plotting functions. \tabular{ll}{ \code{probdraw:} \tab \eqn{ncomp x R/keep} matrix that reports the probability that each draw came from a particular component (here, a one-column matrix of 1s) \cr \code{zdraw: } \tab \eqn{R/keep x nobs} matrix that indicates which component each draw is assigned to (here, null) \cr \code{compdraw:} \tab A list of \eqn{R/keep} lists of \eqn{ncomp} lists. Each of the inner-most lists has 2 elemens: a vector of draws for \code{mu} and a matrix of draws for the Cholesky root of \code{Sigma}. } } } \value{ A list containing: \item{Deltadraw }{ \eqn{R/keep x nz*nvar} matrix of draws of Delta, first row is initial value} \item{betadraw }{ \eqn{nlgt x nvar x R/keep} array of draws of betas} \item{nmix }{ a list containing: \code{probdraw}, \code{zdraw}, \code{compdraw} (see \dQuote{\code{nmix} Details} section)} \item{adraw }{ \eqn{R/keep} draws of hyperparm a} \item{vdraw }{ \eqn{R/keep} draws of hyperparm v} \item{nudraw }{ \eqn{R/keep} draws of hyperparm nu} \item{Istardraw }{ \eqn{R/keep} draws of number of unique components} \item{alphadraw }{ \eqn{R/keep} draws of number of DP tightness parameter} \item{loglike }{ \eqn{R/keep} draws of log-likelihood} } \note{ As is well known, Bayesian density estimation involves computing the predictive distribution of a "new" unit parameter, \eqn{\theta_{n+1}} (here "n"=nlgt). This is done by averaging the normal base distribution over draws from the distribution of \eqn{\theta_{n+1}} given \eqn{\theta_1}, ..., \eqn{\theta_n}, alpha, lambda, data. To facilitate this, we store those draws from the predictive distribution of \eqn{\theta_{n+1}} in a list structure compatible with other \code{bayesm} routines that implement a finite mixture of normals. Large \code{R} values may be required (>20,000). } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 5, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rhierMnlRwMixture}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=20000} else {R=10} set.seed(66) p = 3 # num of choice alterns ncoef = 3 nlgt = 300 # num of cross sectional units nz = 2 Z = matrix(runif(nz*nlgt),ncol=nz) Z = t(t(Z)-apply(Z,2,mean)) # demean Z ncomp = 3 # no of mixture components Delta=matrix(c(1,0,1,0,1,2),ncol=2) comps = NULL comps[[1]] = list(mu=c(0,-1,-2), rooti=diag(rep(2,3))) comps[[2]] = list(mu=c(0,-1,-2)*2, rooti=diag(rep(2,3))) comps[[3]] = list(mu=c(0,-1,-2)*4, rooti=diag(rep(2,3))) pvec=c(0.4, 0.2, 0.4) ## simulate from MNL model conditional on X matrix simmnlwX = function(n,X,beta) { k = length(beta) Xbeta = X\%*\%beta j = nrow(Xbeta) / n Xbeta = matrix(Xbeta, byrow=TRUE, ncol=j) Prob = exp(Xbeta) iota = c(rep(1,j)) denom = Prob\%*\%iota Prob = Prob / as.vector(denom) y = vector("double", n) ind = 1:j for (i in 1:n) { yvec = rmultinom(1, 1, Prob[i,]) y[i] = ind\%*\%yvec} return(list(y=y, X=X, beta=beta, prob=Prob)) } ## simulate data with a mixture of 3 normals simlgtdata = NULL ni = rep(50,300) for (i in 1:nlgt) { betai = Delta\%*\%Z[i,] + as.vector(rmixture(1,pvec,comps)$x) Xa = matrix(runif(ni[i]*p,min=-1.5,max=0), ncol=p) X = createX(p, na=1, nd=NULL, Xa=Xa, Xd=NULL, base=1) outa = simmnlwX(ni[i], X, betai) simlgtdata[[i]] = list(y=outa$y, X=X, beta=betai) } ## plot betas if(0){ bmat = matrix(0, nlgt, ncoef) for(i in 1:nlgt) { bmat[i,] = simlgtdata[[i]]$beta } par(mfrow = c(ncoef,1)) for(i in 1:ncoef) { hist(bmat[,i], breaks=30, col="magenta") } } ## set Data and Mcmc lists keep = 5 Mcmc1 = list(R=R, keep=keep) Data1 = list(p=p, lgtdata=simlgtdata, Z=Z) out = rhierMnlDP(Data=Data1, Mcmc=Mcmc1) cat("Summary of Delta draws", fill=TRUE) summary(out$Deltadraw, tvalues=as.vector(Delta)) ## plotting examples if(0) { plot(out$betadraw) plot(out$nmix) } } \keyword{models} bayesm/man/rhierBinLogit.Rd0000644000176000001440000001136513117541521015373 0ustar ripleyusers\name{rhierBinLogit} \alias{rhierBinLogit} \concept{bayes} \concept{MCMC} \concept{hierarchical models} \concept{binary logit} \title{MCMC Algorithm for Hierarchical Binary Logit} \description{ \bold{This function has been deprecated. Please use \code{rhierMnlRwMixture} instead.} \code{rhierBinLogit} implements an MCMC algorithm for hierarchical binary logits with a normal heterogeneity distribution. This is a hybrid sampler with a RW Metropolis step for unit-level logit parameters. \code{rhierBinLogit} is designed for use on choice-based conjoint data with partial profiles. The Design matrix is based on differences of characteristics between two alternatives. See Appendix A of \emph{Bayesian Statistics and Marketing} for details. } \usage{rhierBinLogit(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(lgtdata, Z)} \item{Prior}{list(Deltabar, ADelta, nu, V)} \item{Mcmc }{list(R, keep, sbeta)} } \details{ \subsection{Model and Priors}{ \eqn{y_{hi} = 1} with \eqn{Pr = exp(x_{hi}'\beta_h) / (1+exp(x_{hi}'\beta_h)} and \eqn{\beta_h} is \eqn{nvar x 1} \cr \eqn{h = 1, \ldots, length(lgtdata)} units (or "respondents" for survey data) \eqn{\beta_h} = ZDelta[h,] + \eqn{u_h} \cr Note: here ZDelta refers to \code{Z\%*\%Delta} with ZDelta[h,] the \eqn{h}th row of this product\cr Delta is an \eqn{nz x nvar} array \eqn{u_h} \eqn{\sim}{~} \eqn{N(0, V_{beta})}. \cr \eqn{delta = vec(Delta)} \eqn{\sim}{~} \eqn{N(vec(Deltabar), V_{beta}(x) ADelta^{-1})}\cr \eqn{V_{beta}} \eqn{\sim}{~} \eqn{IW(nu, V)} } \subsection{Argument Details}{ \emph{\code{Data = list(lgtdata, Z)} [\code{Z} optional]} \tabular{ll}{ \code{lgtdata: } \tab list of lists with each cross-section unit MNL data \cr \code{lgtdata[[h]]$y:} \tab \eqn{n_h x 1} vector of binary outcomes (0,1) \cr \code{lgtdata[[h]]$X:} \tab \eqn{n_h x nvar} design matrix for h'th unit \cr \code{Z: } \tab \eqn{nreg x nz} mat of unit chars (def: vector of ones) } \emph{\code{Prior = list(Deltabar, ADelta, nu, V)} [optional]} \tabular{ll}{ \code{Deltabar:} \tab \eqn{nz x nvar} matrix of prior means (def: 0) \cr \code{ADelta: } \tab prior precision matrix (def: 0.01I) \cr \code{nu: } \tab d.f. parameter for IW prior on normal component Sigma (def: nvar+3) \cr \code{V: } \tab pds location parm for IW prior on normal component Sigma (def: nuI) } \emph{\code{Mcmc = list(R, keep, sbeta)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parm -- keep every \code{keep}th draw (def: 1) \cr \code{sbeta: } \tab scaling parm for RW Metropolis (def: 0.2) } } } \value{ A list containing: \item{Deltadraw }{ \eqn{R/keep x nz*nvar} matrix of draws of Delta} \item{betadraw }{ \eqn{nlgt x nvar x R/keep} array of draws of betas} \item{Vbetadraw }{ \eqn{R/keep x nvar*nvar} matrix of draws of Vbeta} \item{llike }{ \eqn{R/keep x 1} vector of log-like values} \item{reject }{ \eqn{R/keep x 1} vector of reject rates over nlgt units} } \note{Some experimentation with the Metropolis scaling paramter (\code{sbeta}) may be required.} \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 5, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=10000} else {R=10} set.seed(66) nvar = 5 ## number of coefficients nlgt = 1000 ## number of cross-sectional units nobs = 10 ## number of observations per unit nz = 2 ## number of regressors in mixing distribution Z = matrix(c(rep(1,nlgt),runif(nlgt,min=-1,max=1)), nrow=nlgt, ncol=nz) Delta = matrix(c(-2, -1, 0, 1, 2, -1, 1, -0.5, 0.5, 0), nrow=nz, ncol=nvar) iota = matrix(1, nrow=nvar, ncol=1) Vbeta = diag(nvar) + 0.5*iota\%*\%t(iota) lgtdata=NULL for (i in 1:nlgt) { beta = t(Delta)\%*\%Z[i,] + as.vector(t(chol(Vbeta))\%*\%rnorm(nvar)) X = matrix(runif(nobs*nvar), nrow=nobs, ncol=nvar) prob = exp(X\%*\%beta) / (1+exp(X\%*\%beta)) unif = runif(nobs, 0, 1) y = ifelse(unif max(w_{-j})} and \eqn{w_j >0} \cr if \eqn{y=p, w < 0} \cr To use GHK, we must transform so that these are rectangular regions e.g. if \eqn{y=1, w_1 > 0} and \eqn{w_1 - w_{-1} > 0}. Define \eqn{A_j} such that if \eqn{j=1,\ldots,p-1} then \eqn{A_jw = A_jmu + A_je > 0} is equivalent to \eqn{y=j}. Thus, if \eqn{y=j}, we have \eqn{A_je > -A_jmu}. Lower truncation is \eqn{-A_jmu} and \eqn{cov = A_jSigmat(A_j)}. For \eqn{j=p}, \eqn{e < - mu}. } \value{Value of log-likelihood (sum of log prob of observed multinomial outcomes)} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{ For further discussion, see Chapters 2 and 4, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{createX}}, \code{\link{rmnpGibbs}} } \examples{ \dontrun{ll=llmnp(beta,Sigma,X,y,r)} } \keyword{models} bayesm/man/rmvpGibbs.Rd0000644000176000001440000000760013117541521014562 0ustar ripleyusers\name{rmvpGibbs} \alias{rmvpGibbs} \concept{bayes} \concept{multivariate probit} \concept{MCMC} \concept{Gibbs Sampling} \title{Gibbs Sampler for Multivariate Probit} \description{ \code{rmvpGibbs} implements the Edwards/Allenby Gibbs Sampler for the multivariate probit model. } \usage{rmvpGibbs(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(y, X, p)} \item{Prior}{list(betabar, A, nu, V)} \item{Mcmc }{list(R, keep, nprint, beta0 ,sigma0)} } \details{ \subsection{Model and Priors}{ \eqn{w_i = X_i\beta + e} with \eqn{e} \eqn{\sim}{~} N(0,\eqn{\Sigma}). Note: \eqn{w_i} is \eqn{p x 1}. \cr \eqn{y_{ij} = 1} if \eqn{w_{ij} > 0}, else \eqn{y_i = 0}. \eqn{j = 1, \ldots, p} \cr beta and Sigma are not identifed. Correlation matrix and the betas divided by the appropriate standard deviation are. See reference or example below for details. \eqn{\beta} \eqn{\sim}{~} \eqn{N(betabar, A^{-1})} \cr \eqn{\Sigma} \eqn{\sim}{~} \eqn{IW(nu, V)} \cr To make \eqn{X} matrix use \code{createX} } \subsection{Argument Details}{ \emph{\code{Data = list(y, X, p)}} \tabular{ll}{ \code{X: } \tab \eqn{n*p x k} Design Matrix \cr \code{y: } \tab \eqn{n*p x 1} vector of 0/1 outcomes \cr \code{p: } \tab dimension of multivariate probit } \emph{\code{Prior = list(betabar, A, nu, V)} [optional]} \tabular{ll}{ \code{betabar: } \tab \eqn{k x 1} prior mean (def: 0) \cr \code{A: } \tab \eqn{k x k} prior precision matrix (def: 0.01*I) \cr \code{nu: } \tab d.f. parameter for Inverted Wishart prior (def: (p-1)+3) \cr \code{V: } \tab PDS location parameter for Inverted Wishart prior (def: nu*I) } \emph{\code{Mcmc = list(R, keep, nprint, beta0 ,sigma0)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) \cr \code{beta0: } \tab initial value for beta \cr \code{sigma0: } \tab initial value for sigma } } } \value{ A list containing: \item{betadraw }{\eqn{R/keep x k} matrix of betadraws} \item{sigmadraw }{\eqn{R/keep x p*p} matrix of sigma draws -- each row is the vector form of sigma} } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 4, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rmnpGibbs}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) simmvp = function(X, p, n, beta, sigma) { w = as.vector(crossprod(chol(sigma),matrix(rnorm(p*n),ncol=n))) + X\%*\%beta y = ifelse(w<0, 0, 1) return(list(y=y, X=X, beta=beta, sigma=sigma)) } p = 3 n = 500 beta = c(-2,0,2) Sigma = matrix(c(1, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 1), ncol=3) k = length(beta) I2 = diag(rep(1,p)) xadd = rbind(I2) for(i in 2:n) { xadd=rbind(xadd,I2) } X = xadd simout = simmvp(X,p,500,beta,Sigma) Data1 = list(p=p, y=simout$y, X=simout$X) Mcmc1 = list(R=R, keep=1) out = rmvpGibbs(Data=Data1, Mcmc=Mcmc1) ind = seq(from=0, by=p, length=k) inda = 1:3 ind = ind + inda cat(" Betadraws ", fill=TRUE) betatilde = out$betadraw / sqrt(out$sigmadraw[,ind]) attributes(betatilde)$class = "bayesm.mat" summary(betatilde, tvalues=beta/sqrt(diag(Sigma))) rdraw = matrix(double((R)*p*p), ncol=p*p) rdraw = t(apply(out$sigmadraw, 1, nmat)) attributes(rdraw)$class = "bayesm.var" tvalue = nmat(as.vector(Sigma)) dim(tvalue) = c(p,p) tvalue = as.vector(tvalue[upper.tri(tvalue,diag=TRUE)]) cat(" Draws of Correlation Matrix ", fill=TRUE) summary(rdraw, tvalues=tvalue) ## plotting examples if(0){plot(betatilde, tvalues=beta/sqrt(diag(Sigma)))} } \keyword{models} \keyword{multivariate} bayesm/man/logMargDenNR.Rd0000755000176000001440000000176713117541521015121 0ustar ripleyusers\name{logMargDenNR} \alias{logMargDenNR} \concept{Newton-Raftery approximation} \concept{bayes} \concept{marginal likelihood} \concept{density} \title{Compute Log Marginal Density Using Newton-Raftery Approx} \description{ \code{logMargDenNR} computes log marginal density using the Newton-Raftery approximation. } \usage{logMargDenNR(ll)} \arguments{ \item{ll}{ vector of log-likelihoods evaluated at \code{length(ll)} MCMC draws } } \value{Approximation to log marginal density value.} \section{Warning}{ This approximation can be influenced by outliers in the vector of log-likelihoods; use with \strong{care}. This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 6, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \keyword{distribution} bayesm/man/rhierMnlRwMixture.Rd0000644000176000001440000002354313117570164016307 0ustar ripleyusers\name{rhierMnlRwMixture} \alias{rhierMnlRwMixture} \concept{bayes} \concept{MCMC} \concept{Multinomial Logit} \concept{mixture of normals} \concept{normal mixture} \concept{heterogeneity} \concept{hierarchical models} \title{MCMC Algorithm for Hierarchical Multinomial Logit with Mixture-of-Normals Heterogeneity} \description{ \code{rhierMnlRwMixture} is a MCMC algorithm for a hierarchical multinomial logit with a mixture of normals heterogeneity distribution. This is a hybrid Gibbs Sampler with a RW Metropolis step for the MNL coefficients for each panel unit. } \usage{rhierMnlRwMixture(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(lgtdata, Z, p)} \item{Prior}{list(a, deltabar, Ad, mubar, Amu, nu, V, a, ncomp, SignRes)} \item{Mcmc }{list(R, keep, nprint, s, w)} } \details{ \subsection{Model and Priors}{ \eqn{y_i} \eqn{\sim}{~} \eqn{MNL(X_i,\beta_i)} with \eqn{i = 1, \ldots,} length(lgtdata) and where \eqn{\beta_i} is \eqn{nvar x 1} \eqn{\beta_i} = \eqn{Z\Delta}[i,] + \eqn{u_i} \cr Note: Z\eqn{\Delta} is the matrix Z * \eqn{\Delta} and [i,] refers to \eqn{i}th row of this product \cr Delta is an \eqn{nz x nvar} array \eqn{u_i} \eqn{\sim}{~} \eqn{N(\mu_{ind},\Sigma_{ind})} with \eqn{ind} \eqn{\sim}{~} multinomial(pvec) \eqn{pvec} \eqn{\sim}{~} dirichlet(a) \cr \eqn{delta = vec(\Delta)} \eqn{\sim}{~} \eqn{N(deltabar, A_d^{-1})} \cr \eqn{\mu_j} \eqn{\sim}{~} \eqn{N(mubar, \Sigma_j (x) Amu^{-1})} \cr \eqn{\Sigma_j} \eqn{\sim}{~} \eqn{IW(nu, V)} Note: \eqn{Z} should NOT include an intercept and is centered for ease of interpretation. The mean of each of the \code{nlgt} \eqn{\beta}s is the mean of the normal mixture. Use \code{summary()} to compute this mean from the \code{compdraw} output.\cr Be careful in assessing prior parameter \code{Amu}: 0.01 is too small for many applications. See chapter 5 of Rossi et al for full discussion. } \subsection{Argument Details}{ \emph{\code{Data = list(lgtdata, Z, p)} [\code{Z} optional]} \tabular{ll}{ \code{lgtdata: } \tab list of \code{nlgt=length(lgtdata)} lists with each cross-section unit MNL data \cr \code{lgtdata[[i]]$y: } \tab \eqn{n_i x 1} vector of multinomial outcomes (1, \ldots, m) \cr \code{lgtdata[[i]]$X: } \tab \eqn{n_i*p x nvar} design matrix for \eqn{i}th unit \cr \code{Z: } \tab \eqn{nreg x nz} matrix of unit chars (def: vector of ones) \cr \code{p: } \tab number of choice alternatives } \emph{\code{Prior = list(a, deltabar, Ad, mubar, Amu, nu, V, a, ncomp, SignRes)} [all but \code{ncomp} are optional]} \tabular{ll}{ \code{a: } \tab \eqn{ncomp x 1} vector of Dirichlet prior parameters (def: \code{rep(5,ncomp)}) \cr \code{deltabar: } \tab \eqn{nz*nvar x 1} vector of prior means (def: 0) \cr \code{Ad: } \tab prior precision matrix for vec(D) (def: 0.01*I) \cr \code{mubar: } \tab \eqn{nvar x 1} prior mean vector for normal component mean (def: 0 if unrestricted; 2 if restricted) \cr \code{Amu: } \tab prior precision for normal component mean (def: 0.01 if unrestricted; 0.1 if restricted) \cr \code{nu: } \tab d.f. parameter for IW prior on normal component Sigma (def: nvar+3 if unrestricted; nvar+15 if restricted) \cr \code{V: } \tab PDS location parameter for IW prior on normal component Sigma (def: nu*I if unrestricted; nu*D if restricted with d_pp = 4 if unrestricted and d_pp = 0.01 if restricted) \cr \code{ncomp: } \tab number of components used in normal mixture \cr \code{SignRes: } \tab \eqn{nvar x 1} vector of sign restrictions on the coefficient estimates (def: \code{rep(0,nvar)}) } \emph{\code{Mcmc = list(R, keep, nprint, s, w)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) \cr \code{s: } \tab scaling parameter for RW Metropolis (def: 2.93/\code{sqrt(nvar)}) \cr \code{w: } \tab fractional likelihood weighting parameter (def: 0.1) } } \subsection{Sign Restrictions}{ If \eqn{\beta_ik} has a sign restriction: \eqn{\beta_ik = SignRes[k] * exp(\beta*_ik)} To use sign restrictions on the coefficients, \code{SignRes} must be an \eqn{nvar x 1} vector containing values of either 0, -1, or 1. The value 0 means there is no sign restriction, -1 ensures that the coefficient is \emph{negative}, and 1 ensures that the coefficient is \emph{positive}. For example, if \code{SignRes = c(0,1,-1)}, the first coefficient is unconstrained, the second will be positive, and the third will be negative. The sign restriction is implemented such that if the the \eqn{k}'th \eqn{\beta} has a non-zero sign restriction (i.e., it is constrained), we have \eqn{\beta_k = SignRes[k] * exp(\beta*_k)}. The sign restrictions (if used) will be reflected in the \code{betadraw} output. However, the unconstrained mixture components are available in \code{nmix}. \bold{Important:} Note that draws from \code{nmix} are distributed according to the mixture of normals but \bold{not} the coefficients in \code{betadraw}. Care should be taken when selecting priors on any sign restricted coefficients. See related vignette for additional information. } \subsection{\code{nmix} Details}{ \code{nmix} is a list with 3 components. Several functions in the \code{bayesm} package that involve a Dirichlet Process or mixture-of-normals return \code{nmix}. Across these functions, a common structure is used for \code{nmix} in order to utilize generic summary and plotting functions. \tabular{ll}{ \code{probdraw:} \tab \eqn{ncomp x R/keep} matrix that reports the probability that each draw came from a particular component \cr \code{zdraw: } \tab \eqn{R/keep x nobs} matrix that indicates which component each draw is assigned to (here, null) \cr \code{compdraw:} \tab A list of \eqn{R/keep} lists of \eqn{ncomp} lists. Each of the inner-most lists has 2 elemens: a vector of draws for \code{mu} and a matrix of draws for the Cholesky root of \code{Sigma}. } } } \value{ A list containing: \item{Deltadraw }{ \eqn{R/keep x nz*nvar} matrix of draws of Delta, first row is initial value} \item{betadraw }{ \eqn{nlgt x nvar x R/keep} array of beta draws} \item{nmix }{ a list containing: \code{probdraw}, \code{zdraw}, \code{compdraw} (see \dQuote{\code{nmix} Details} section)} \item{loglike }{ \eqn{R/keep x 1} vector of log-likelihood for each kept draw} \item{SignRes }{ \eqn{nvar x 1} vector of sign restrictions} } \note{ Note: as of version 2.0-2 of \code{bayesm}, the fractional weight parameter has been changed to a weight between 0 and 1. \eqn{w} is the fractional weight on the normalized pooled likelihood. This differs from what is in Rossi et al chapter 5, i.e. \eqn{like_i^{(1-w)} x like_pooled^{((n_i/N)*w)}} Large \code{R} values may be required (>20,000). } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 5, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rmnlIndepMetrop}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=10000} else {R=10} set.seed(66) p = 3 # num of choice alterns ncoef = 3 nlgt = 300 # num of cross sectional units nz = 2 Z = matrix(runif(nz*nlgt),ncol=nz) Z = t(t(Z) - apply(Z,2,mean)) # demean Z ncomp = 3 # num of mixture components Delta = matrix(c(1,0,1,0,1,2),ncol=2) comps=NULL comps[[1]] = list(mu=c(0,-1,-2), rooti=diag(rep(1,3))) comps[[2]] = list(mu=c(0,-1,-2)*2, rooti=diag(rep(1,3))) comps[[3]] = list(mu=c(0,-1,-2)*4, rooti=diag(rep(1,3))) pvec = c(0.4, 0.2, 0.4) ## simulate from MNL model conditional on X matrix simmnlwX= function(n,X,beta) { k = length(beta) Xbeta = X\%*\%beta j = nrow(Xbeta) / n Xbeta = matrix(Xbeta, byrow=TRUE, ncol=j) Prob = exp(Xbeta) iota = c(rep(1,j)) denom = Prob\%*\%iota Prob = Prob/as.vector(denom) y = vector("double",n) ind = 1:j for (i in 1:n) { yvec = rmultinom(1, 1, Prob[i,]) y[i] = ind\%*\%yvec } return(list(y=y, X=X, beta=beta, prob=Prob)) } ## simulate data simlgtdata = NULL ni = rep(50, 300) for (i in 1:nlgt) { betai = Delta\%*\%Z[i,] + as.vector(rmixture(1,pvec,comps)$x) Xa = matrix(runif(ni[i]*p,min=-1.5,max=0), ncol=p) X = createX(p, na=1, nd=NULL, Xa=Xa, Xd=NULL, base=1) outa = simmnlwX(ni[i], X, betai) simlgtdata[[i]] = list(y=outa$y, X=X, beta=betai) } ## plot betas if(0){ bmat = matrix(0, nlgt, ncoef) for(i in 1:nlgt) {bmat[i,] = simlgtdata[[i]]$beta} par(mfrow = c(ncoef,1)) for(i in 1:ncoef) { hist(bmat[,i], breaks=30, col="magenta") } } ## set parms for priors and Z Prior1 = list(ncomp=5) keep = 5 Mcmc1 = list(R=R, keep=keep) Data1 = list(p=p, lgtdata=simlgtdata, Z=Z) ## fit model without sign constraints out1 = rhierMnlRwMixture(Data=Data1, Prior=Prior1, Mcmc=Mcmc1) cat("Summary of Delta draws", fill=TRUE) summary(out1$Deltadraw, tvalues=as.vector(Delta)) cat("Summary of Normal Mixture Distribution", fill=TRUE) summary(out1$nmix) ## plotting examples if(0) { plot(out1$betadraw) plot(out1$nmix) } ## fit model with constraint that beta_i2 < 0 forall i Prior2 = list(ncomp=5, SignRes=c(0,-1,0)) out2 = rhierMnlRwMixture(Data=Data1, Prior=Prior2, Mcmc=Mcmc1) cat("Summary of Delta draws", fill=TRUE) summary(out2$Deltadraw, tvalues=as.vector(Delta)) cat("Summary of Normal Mixture Distribution", fill=TRUE) summary(out2$nmix) ## plotting examples if(0) { plot(out2$betadraw) plot(out2$nmix) } } \keyword{models} bayesm/man/customerSat.Rd0000644000176000001440000000262513117541521015142 0ustar ripleyusers\name{customerSat} \alias{customerSat} \docType{data} \title{Customer Satisfaction Data} \description{ Responses to a satisfaction survey for a Yellow Pages advertising product. All responses are on a 10 point scale from 1 to 10 (1 is "Poor" and 10 is "Excellent"). } \usage{data(customerSat)} \format{ A data frame with 1811 observations on the following 10 variables: \tabular{ll}{ \ldots\code{$q1 } \tab Overall Satisfaction \cr \ldots\code{$q2 } \tab Setting Competitive Prices \cr \ldots\code{$q3 } \tab Holding Price Increase to a Minimum \cr \ldots\code{$q4 } \tab Appropriate Pricing given Volume \cr \ldots\code{$q5 } \tab Demonstrating Effectiveness of Purchase \cr \ldots\code{$q6 } \tab Reach a Large Number of Customers \cr \ldots\code{$q7 } \tab Reach of Advertising \cr \ldots\code{$q8 } \tab Long-term Exposure \cr \ldots\code{$q9 } \tab Distribution \cr \ldots\code{$q10} \tab Distribution to Right Geographic Areas } } \source{Rossi, Peter, Zvi Gilula, and Greg Allenby (2001), "Overcoming Scale Usage Heterogeneity," \emph{Journal of the American Statistical Association} 96, 20--31.} \references{Case Study 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch.\cr \url{http://www.perossi.org/home/bsm-1}} \examples{ data(customerSat) apply(as.matrix(customerSat),2,table) ## see also examples for 'rscaleUsage' } \keyword{datasets} bayesm/man/margarine.Rd0000644000176000001440000000703113117541521014572 0ustar ripleyusers\name{margarine} \alias{margarine} \docType{data} \title{Household Panel Data on Margarine Purchases} \description{ Panel data on purchases of margarine by 516 households. Demographic variables are included. } \usage{data(margarine)} \format{ The \code{detailing} object is a list containing two data frames, \code{choicePrice} and \code{demos}. } \details{ In the \code{choicePrice} data frame: \tabular{ll}{ \ldots\code{$hhid } \tab household ID \cr \ldots\code{$choice} \tab multinomial indicator of one of the 10 products } The products are indicated by brand and type. Brands: \tabular{ll}{ \ldots\code{$Pk } \tab Parkay \cr \ldots\code{$BB } \tab BlueBonnett \cr \ldots\code{$Fl } \tab Fleischmanns \cr \ldots\code{$Hse } \tab house \cr \ldots\code{$Gen } \tab generic \cr \ldots\code{$Imp } \tab Imperial \cr \ldots\code{$SS } \tab Shed Spread } Product type: \tabular{ll}{ \ldots\code{$_Stk} \tab stick \cr \ldots\code{$_Tub} \tab tub } In the \code{demos} data frame: \tabular{ll}{ \ldots\code{$Fs3_4 } \tab dummy for family size 3-4 \cr \ldots\code{$Fs5 } \tab dummy for family size >= 5 \cr \ldots\code{$college } \tab dummy for education status \cr \ldots\code{$whtcollar} \tab dummy for job status \cr \ldots\code{$retired } \tab dummy for retirement status } All prices are in U.S. dollars. } \source{Allenby, Greg and Peter Rossi (1991), "Quality Perceptions and Asymmetric Switching Between Brands," \emph{Marketing Science} 10, 185--205. } \references{ Chapter 5, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \examples{ data(margarine) cat(" Table of Choice Variable ", fill=TRUE) print(table(margarine$choicePrice[,2])) cat(" Means of Prices", fill=TRUE) mat=apply(as.matrix(margarine$choicePrice[,3:12]), 2, mean) print(mat) cat(" Quantiles of Demographic Variables", fill=TRUE) mat=apply(as.matrix(margarine$demos[,2:8]), 2, quantile) print(mat) ## example of processing for use with 'rhierMnlRwMixture' if(0) { select = c(1:5,7) ## select brands chPr = as.matrix(margarine$choicePrice) ## make sure to log prices chPr = cbind(chPr[,1], chPr[,2], log(chPr[,2+select])) demos = as.matrix(margarine$demos[,c(1,2,5)]) ## remove obs for other alts chPr = chPr[chPr[,2] <= 7,] chPr = chPr[chPr[,2] != 6,] ## recode choice chPr[chPr[,2] == 7,2] = 6 hhidl = levels(as.factor(chPr[,1])) lgtdata = NULL nlgt = length(hhidl) p = length(select) ## number of choice alts ind = 1 for (i in 1:nlgt) { nobs = sum(chPr[,1]==hhidl[i]) if(nobs >=5) { data = chPr[chPr[,1]==hhidl[i],] y = data[,2] names(y) = NULL X = createX(p=p, na=1, Xa=data[,3:8], nd=NULL, Xd=NULL, INT=TRUE, base=1) lgtdata[[ind]] = list(y=y, X=X, hhid=hhidl[i]) ind = ind+1 } } nlgt = length(lgtdata) ## now extract demos corresponding to hhs in lgtdata Z = NULL nlgt = length(lgtdata) for(i in 1:nlgt){ Z = rbind(Z, demos[demos[,1]==lgtdata[[i]]$hhid, 2:3]) } ## take log of income and family size and demean Z = log(Z) Z[,1] = Z[,1] - mean(Z[,1]) Z[,2] = Z[,2] - mean(Z[,2]) keep = 5 R = 20000 mcmc1 = list(keep=keep, R=R) out = rhierMnlRwMixture(Data=list(p=p,lgtdata=lgtdata, Z=Z), Prior=list(ncomp=1), Mcmc=mcmc1) summary(out$Deltadraw) summary(out$nmix) ## plotting examples if(0){ plot(out$nmix) plot(out$Deltadraw) } } } \keyword{datasets} bayesm/man/summary.bayesm.var.Rd0000644000176000001440000000340013117541521016364 0ustar ripleyusers\name{summary.bayesm.var} \alias{summary.bayesm.var} \title{Summarize Draws of Var-Cov Matrices} \description{ \code{summary.bayesm.var} is an S3 method to summarize marginal distributions given an array of draws } \usage{\method{summary}{bayesm.var}(object, names, burnin = trunc(0.1 * nrow(Vard)), tvalues, QUANTILES = FALSE , ...)} \arguments{ \item{object }{ \code{object} (herafter, \code{Vard}) is an array of draws of a covariance matrix } \item{names }{ optional character vector of names for the columns of \code{Vard}} \item{burnin }{ number of draws to burn-in (def: \eqn{0.1*nrow(Vard)})} \item{tvalues }{ optional vector of "true" values for use in simulation examples } \item{QUANTILES }{ logical for should quantiles be displayed (def: \code{TRUE})} \item{... }{ optional arguments for generic function } } \details{ Typically, \code{summary.bayesm.var} will be invoked by a call to the generic summary function as in \code{summary(object)} where \code{object} is of class \code{bayesm.var}. Mean, Std Dev, Numerical Standard error (of estimate of posterior mean), relative numerical efficiency (see \code{numEff}), and effective sample size are displayed. If \code{QUANTILES=TRUE}, quantiles of marginal distirbutions in the columns of \code{Vard} are displayed. \cr \code{Vard} is an array of draws of a covariance matrix stored as vectors. Each row is a different draw. \cr The posterior mean of the vector of standard deviations and the correlation matrix are also displayed } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \seealso{ \code{\link{summary.bayesm.mat}}, \code{\link{summary.bayesm.nmix}}} \examples{ \dontrun{out=rmnpGibbs(Data,Prior,Mcmc); summary(out$sigmadraw)} } \keyword{ univar } bayesm/man/summary.bayesm.nmix.Rd0000644000176000001440000000266213117541521016560 0ustar ripleyusers\name{summary.bayesm.nmix} \alias{summary.bayesm.nmix} \title{Summarize Draws of Normal Mixture Components} \description{ \code{summary.bayesm.nmix} is an S3 method to display summaries of the distribution implied by draws of Normal Mixture Components. Posterior means and variance-covariance matrices are displayed.\cr Note: 1st and 2nd moments may not be very interpretable for mixtures of normals. This summary function can take a minute or so. The current implementation is not efficient. } \usage{\method{summary}{bayesm.nmix}(object, names, burnin=trunc(0.1*nrow(probdraw)), ...)} \arguments{ \item{object }{ an object of class \code{bayesm.nmix}, a list of lists of draws} \item{names }{ optional character vector of names fo reach dimension of the density} \item{burnin }{ number of draws to burn-in (def: \eqn{0.1*nrow(probdraw)})} \item{... }{ parms to send to summary} } \details{ An object of class \code{bayesm.nmix} is a list of three components: \describe{ \item{probdraw }{ a matrix of \eqn{R/keep} rows by dim of normal mix of mixture prob draws} \item{second comp }{ not used} \item{compdraw }{ list of list of lists with draws of mixture comp parms} } } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \seealso{ \code{\link{summary.bayesm.mat}}, \code{\link{summary.bayesm.var}}} \examples{ \dontrun{out=rnmix(Data,Prior,Mcmc); summary(out)} } \keyword{plot} bayesm/man/plot.bayesm.mat.Rd0000644000176000001440000000407613117541521015650 0ustar ripleyusers\name{plot.bayesm.mat} \alias{plot.bayesm.mat} \concept{MCMC} \concept{S3 method} \concept{plot} \title{Plot Method for Arrays of MCMC Draws} \description{ \code{plot.bayesm.mat} is an S3 method to plot arrays of MCMC draws. The columns in the array correspond to parameters and the rows to MCMC draws. } \usage{\method{plot}{bayesm.mat}(x,names,burnin,tvalues,TRACEPLOT,DEN,INT,CHECK_NDRAWS, ...)} \arguments{ \item{x }{ An object of either S3 class, \code{bayesm.mat}, or S3 class, \code{mcmc} } \item{names }{ optional character vector of names for coefficients} \item{burnin }{ number of draws to discard for burn-in (def: \eqn{0.1*nrow(X))}} \item{tvalues }{ vector of true values} \item{TRACEPLOT }{ logical, \code{TRUE} provide sequence plots of draws and acfs (def: \code{TRUE})} \item{DEN }{ logical, \code{TRUE} use density scale on histograms (def: \code{TRUE})} \item{INT }{ logical, \code{TRUE} put various intervals and points on graph (def: \code{TRUE})} \item{CHECK_NDRAWS }{ logical, \code{TRUE} check that there are at least 100 draws (def: \code{TRUE})} \item{... }{ standard graphics parameters } } \details{ Typically, \code{plot.bayesm.mat} will be invoked by a call to the generic plot function as in \code{plot(object)} where object is of class \code{bayesm.mat}. All of the \code{bayesm} MCMC routines return draws in this class (see example below). One can also simply invoke \code{plot.bayesm.mat} on any valid 2-dim array as in \code{plot.bayesm.mat(betadraws)}. \cr \cr \code{plot.bayesm.mat} paints (by default) on the histogram: \cr \cr green "[]" delimiting 95\% Bayesian Credibility Interval \cr yellow "()" showing +/- 2 numerical standard errors \cr red "|" showing posterior mean \cr \cr \code{plot.bayesm.mat} is also exported for use as a standard function, as in \code{plot.bayesm.mat(matrix)} } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \examples{ \dontrun{out=runiregGibbs(Data,Prior,Mcmc); plot(out$betadraw)} } \keyword{hplot} bayesm/man/rsurGibbs.Rd0000644000176000001440000000672513117541521014600 0ustar ripleyusers\name{rsurGibbs} \alias{rsurGibbs} \concept{bayes} \concept{Gibbs Sampler} \concept{regression} \concept{SUR model} \concept{Seemingly Unrelated Regression} \concept{MCMC} \title{Gibbs Sampler for Seemingly Unrelated Regressions (SUR)} \description{ \code{rsurGibbs} implements a Gibbs Sampler to draw from the posterior of the Seemingly Unrelated Regression (SUR) Model of Zellner. } \usage{rsurGibbs(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(regdata)} \item{Prior}{list(betabar, A, nu, V)} \item{Mcmc }{list(R, keep)} } \details{ \subsection{Model and Priors}{ \eqn{y_i = X_i\beta_i + e_i} with \eqn{i=1,\ldots,m} for \eqn{m} regressions \cr (\eqn{e(k,1), \ldots, e(k,m)})' \eqn{\sim}{~} \eqn{N(0, \Sigma)} with \eqn{k=1, \ldots, n} Can be written as a stacked model: \cr \eqn{y = X\beta + e} where \eqn{y} is a \eqn{nobs*m} vector and \eqn{p} = \code{length(beta)} = \code{sum(length(beta_i))} Note: must have the same number of observations (\eqn{n}) in each equation but can have a different number of \eqn{X} variables (\eqn{p_i}) for each equation where \eqn{p = \sum p_i}. \eqn{\beta} \eqn{\sim}{~} \eqn{N(betabar, A^{-1})} \cr \eqn{\Sigma} \eqn{\sim}{~} \eqn{IW(nu,V)} } \subsection{Argument Details}{ \emph{\code{Data = list(regdata)}} \tabular{ll}{ \code{regdata: } \tab list of lists, \code{regdata[[i]] = list(y=y_i, X=X_i)}, where \code{y_i} is \eqn{n x 1} and \code{X_i} is \eqn{n x p_i} } \emph{\code{Prior = list(betabar, A, nu, V)} [optional]} \tabular{ll}{ \code{betabar: } \tab \eqn{p x 1} prior mean (def: 0) \cr \code{A: } \tab \eqn{p x p} prior precision matrix (def: 0.01*I) \cr \code{nu: } \tab d.f. parameter for Inverted Wishart prior (def: m+3) \cr \code{V: } \tab \eqn{m x m} scale parameter for Inverted Wishart prior (def: nu*I) } \emph{\code{Mcmc = list(R, keep)} [only \code{R} required]} \tabular{ll}{ \code{R: }\tab number of MCMC draws \cr \code{keep: }\tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: }\tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) } } } \value{ A list containing: \item{betadraw }{ \eqn{R x p} matrix of betadraws} \item{Sigmadraw }{ \eqn{R x (m*m)} array of Sigma draws} } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{rmultireg}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=1000} else {R=10} set.seed(66) ## simulate data from SUR beta1 = c(1,2) beta2 = c(1,-1,-2) nobs = 100 nreg = 2 iota = c(rep(1, nobs)) X1 = cbind(iota, runif(nobs)) X2 = cbind(iota, runif(nobs), runif(nobs)) Sigma = matrix(c(0.5, 0.2, 0.2, 0.5), ncol=2) U = chol(Sigma) E = matrix(rnorm(2*nobs),ncol=2)\%*\%U y1 = X1\%*\%beta1 + E[,1] y2 = X2\%*\%beta2 + E[,2] ## run Gibbs Sampler regdata = NULL regdata[[1]] = list(y=y1, X=X1) regdata[[2]] = list(y=y2, X=X2) out = rsurGibbs(Data=list(regdata=regdata), Mcmc=list(R=R)) cat("Summary of beta draws", fill=TRUE) summary(out$betadraw, tvalues=c(beta1,beta2)) cat("Summary of Sigmadraws", fill=TRUE) summary(out$Sigmadraw, tvalues=as.vector(Sigma[upper.tri(Sigma,diag=TRUE)])) ## plotting examples if(0){plot(out$betadraw, tvalues=c(beta1,beta2))} } \keyword{regression} bayesm/man/llmnl.Rd0000644000176000001440000000245213117541521013745 0ustar ripleyusers\name{llmnl} \alias{llmnl} \concept{multinomial logit} \concept{likelihood} \title{Evaluate Log Likelihood for Multinomial Logit Model} \description{\code{llmnl} evaluates log-likelihood for the multinomial logit model.} \usage{llmnl(beta, y, X)} \arguments{ \item{beta}{ \eqn{k x 1} coefficient vector } \item{y }{ \eqn{n x 1} vector of obs on y (1,\ldots, p) } \item{X }{ \eqn{n*p x k} design matrix (use \code{createX} to create \eqn{X}) } } \details{ Let \eqn{\mu_i = X_i beta}, then \eqn{Pr(y_i=j) = exp(\mu_{i,j}) / \sum_k exp(\mu_{i,k})}.\cr \eqn{X_i} is the submatrix of \eqn{X} corresponding to the \eqn{i}th observation. \eqn{X} has \eqn{n*p} rows. Use \code{\link{createX}} to create \eqn{X}. } \value{Value of log-likelihood (sum of log prob of observed multinomial outcomes).} \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type.} \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1} } \seealso{ \code{\link{createX}}, \code{\link{rmnlIndepMetrop}} } \examples{ \dontrun{ll=llmnl(beta,y,X)} } \keyword{models} bayesm/man/bank.Rd0000644000176000001440000001032213117541521013535 0ustar ripleyusers\name{bank} \alias{bank} \docType{data} \title{Bank Card Conjoint Data} \description{ A panel dataset from a conjoint experiment in which two partial profiles of credit cards were presented to 946 respondents from a regional bank wanting to offer credit cards to customers outside of its normal operating region. Each respondent was presented with between 13 and 17 paired comparisons. The bank and attribute levels are disguised to protect the proprietary interests of the cooperating firm. } \usage{data(bank)} \format{ The \code{bank} object is a list containing two data frames. The first, \code{choiceAtt}, provides choice attributes for the partial credit card profiles. The second, \code{demo}, provides demographic information on the respondents. } \details{ In the \code{choiceAtt} data frame: \tabular{ll}{ \ldots\code{$id } \tab respondent id \cr \ldots\code{$choice } \tab profile chosen \cr \ldots\code{$Med_FInt } \tab medium fixed interest rate \cr \ldots\code{$Low_FInt } \tab low fixed interest rate\cr \ldots\code{$Med_VInt } \tab variable interest rate\cr \ldots\code{$Rewrd_2 } \tab reward level 2 \cr \ldots\code{$Rewrd_3 } \tab reward level 3 \cr \ldots\code{$Rewrd_4 } \tab reward level 4 \cr \ldots\code{$Med_Fee } \tab medium annual fee level \cr \ldots\code{$Low_Fee } \tab low annual fee level \cr \ldots\code{$Bank_B } \tab bank offering the credit card \cr \ldots\code{$Out_State } \tab location of the bank offering the credit card \cr \ldots\code{$Med_Rebate } \tab medium rebate level \cr \ldots\code{$High_Rebate } \tab high rebate level \cr \ldots\code{$High_CredLine} \tab high credit line level \cr \ldots\code{$Long_Grace } \tab grace period } The profiles are coded as the difference in attribute levels. Thus, that a "-1" means the profile coded as a choice of "0" has the attribute. A value of 0 means that the attribute was not present in the comparison. In the \code{demo} data frame: \tabular{ll}{ \ldots\code{$id } \tab respondent id \cr \ldots\code{$age } \tab respondent age in years \cr \ldots\code{$income} \tab respondent income category \cr \ldots\code{$gender} \tab female=1 } } \source{Allenby, Gregg and James Ginter (1995), "Using Extremes to Design Products and Segment Markets," \emph{Journal of Marketing Research}, 392--403.} \references{Appendix A, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \examples{ data(bank) cat(" table of Binary Dep Var", fill=TRUE) print(table(bank$choiceAtt[,2])) cat(" table of Attribute Variables", fill=TRUE) mat = apply(as.matrix(bank$choiceAtt[,3:16]), 2, table) print(mat) cat(" means of Demographic Variables", fill=TRUE) mat=apply(as.matrix(bank$demo[,2:3]), 2, mean) print(mat) ## example of processing for use with rhierBinLogit if(0) { choiceAtt = bank$choiceAtt Z = bank$demo ## center demo data so that mean of random-effects ## distribution can be interpreted as the average respondent Z[,1] = rep(1,nrow(Z)) Z[,2] = Z[,2] - mean(Z[,2]) Z[,3] = Z[,3] - mean(Z[,3]) Z[,4] = Z[,4] - mean(Z[,4]) Z = as.matrix(Z) hh = levels(factor(choiceAtt$id)) nhh = length(hh) lgtdata = NULL for (i in 1:nhh) { y = choiceAtt[choiceAtt[,1]==hh[i], 2] nobs = length(y) X = as.matrix(choiceAtt[choiceAtt[,1]==hh[i], c(3:16)]) lgtdata[[i]] = list(y=y, X=X) } cat("Finished Reading data", fill=TRUE) Data = list(lgtdata=lgtdata, Z=Z) Mcmc = list(R=10000, sbeta=0.2, keep=20) set.seed(66) out = rhierBinLogit(Data=Data, Mcmc=Mcmc) begin = 5000/20 summary(out$Deltadraw, burnin=begin) summary(out$Vbetadraw, burnin=begin) ## plotting examples if(0){ ## plot grand means of random effects distribution (first row of Delta) index = 4*c(0:13)+1 matplot(out$Deltadraw[,index], type="l", xlab="Iterations/20", ylab="", main="Average Respondent Part-Worths") ## plot hierarchical coefs plot(out$betadraw) ## plot log-likelihood plot(out$llike, type="l", xlab="Iterations/20", ylab="", main="Log Likelihood") } } } \keyword{datasets} bayesm/man/rmixture.Rd0000644000176000001440000000231713117541521014506 0ustar ripleyusers\name{rmixture} \alias{rmixture} \concept{mixture of normals} \concept{simulation} \title{Draw from Mixture of Normals} \description{ \code{rmixture} simulates iid draws from a Multivariate Mixture of Normals } \usage{rmixture(n, pvec, comps)} \arguments{ \item{n }{ number of observations } \item{pvec }{ \eqn{ncomp x 1} vector of prior probabilities for each mixture component } \item{comps }{ list of mixture component parameters } } \details{ \code{comps} is a list of length \code{ncomp} with \code{ncomp = length(pvec)}. \cr \code{comps[[j]][[1]]} is mean vector for the \eqn{j}th component. \cr \code{comps[[j]][[2]]} is the inverse of the cholesky root of \eqn{\Sigma} for \eqn{j}th component } \value{ A list containing: \item{x: }{ an \eqn{n x} \code{length(comps[[1]][[1]])} array of iid draws } \item{z: }{ an \eqn{n x 1} vector of indicators of which component each draw is taken from } } \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \seealso{ \code{\link{rnmixGibbs}} } \keyword{multivariate} \keyword{distribution} bayesm/man/rDPGibbs.Rd0000644000176000001440000002115013117570164014264 0ustar ripleyusers\name{rDPGibbs} \alias{rDPGibbs} \concept{bayes} \concept{MCMC} \concept{normal mixtures} \concept{Dirichlet Process} \concept{Gibbs Sampling} \title{ Density Estimation with Dirichlet Process Prior and Normal Base } \description{ \code{rDPGibbs} implements a Gibbs Sampler to draw from the posterior for a normal mixture problem with a Dirichlet Process prior. A natural conjugate base prior is used along with priors on the hyper parameters of this distribution. One interpretation of this model is as a normal mixture with a random number of components that can grow with the sample size. } \usage{rDPGibbs(Prior, Data, Mcmc)} \arguments{ \item{Data }{list(y)} \item{Prior}{list(Prioralpha, lambda_hyper)} \item{Mcmc }{list(R, keep, nprint, maxuniq, SCALE, gridsize)} } \details{ \subsection{Model and Priors}{ \eqn{y_i} \eqn{\sim}{~} \eqn{N(\mu_i, \Sigma_i)} \eqn{\theta_i=(\mu_i,\Sigma_i)} \eqn{\sim}{~} \eqn{DP(G_0(\lambda),alpha)}\cr \eqn{G_0(\lambda):}\cr \eqn{\mu_i | \Sigma_i} \eqn{\sim}{~} \eqn{N(0,\Sigma_i (x) a^{-1})}\cr \eqn{\Sigma_i} \eqn{\sim}{~} \eqn{IW(nu,nu*v*I)} \eqn{\lambda(a,nu,v):}\cr \eqn{a} \eqn{\sim}{~} uniform on grid[alim[1], alimb[2]]\cr \eqn{nu} \eqn{\sim}{~} uniform on grid[dim(data)-1 + exp(nulim[1]), dim(data)-1 + exp(nulim[2])]\cr \eqn{v} \eqn{\sim}{~} uniform on grid[vlim[1], vlim[2]] \eqn{alpha} \eqn{\sim}{~} \eqn{(1-(\alpha-alphamin)/(alphamax-alphamin))^{power}} \cr \eqn{alpha} = alphamin then expected number of components = \code{Istarmin} \cr \eqn{alpha} = alphamax then expected number of components = \code{Istarmax} We parameterize the prior on \eqn{\Sigma_i} such that \eqn{mode(\Sigma)= nu/(nu+2) vI}. The support of nu enforces valid IW density; \eqn{nulim[1] > 0} We use the structure for \code{nmix} that is compatible with the \code{bayesm} routines for finite mixtures of normals. This allows us to use the same summary and plotting methods. The default choices of \code{alim}, \code{nulim}, and \code{vlim} determine the location and approximate size of candidate "atoms" or possible normal components. The defaults are sensible given that we scale the data. Without scaling, you want to insure that \code{alim} is set for a wide enough range of values (remember a is a precision parameter) and the \code{v} is big enough to propose \code{Sigma} matrices wide enough to cover the data range. A careful analyst should look at the posterior distribution of \code{a}, \code{nu}, \code{v} to make sure that the support is set correctly in \code{alim}, \code{nulim}, \code{vlim}. In other words, if we see the posterior bunched up at one end of these support ranges, we should widen the range and rerun. If you want to force the procedure to use many small atoms, then set \code{nulim} to consider only large values and set \code{vlim} to consider only small scaling constants. Set \code{Istarmax} to a large number. This will create a very "lumpy" density estimate somewhat like the classical Kernel density estimates. Of course, this is not advised if you have a prior belief that densities are relatively smooth. } \subsection{Argument Details}{ \emph{\code{Data = list(y)}} \tabular{ll}{ \code{y: } \tab \eqn{n x k} matrix of observations on \eqn{k} dimensional data } \emph{\code{Prior = list(Prioralpha, lambda_hyper)} [optional]} \tabular{ll}{ \code{Prioralpha: } \tab \code{list(Istarmin, Istarmax, power)} \cr \code{$Istarmin: } \tab is expected number of components at lower bound of support of alpha (def: 1) \cr \code{$Istarmax: } \tab is expected number of components at upper bound of support of alpha (def: \code{min(50, 0.1*nrow(y))}) \cr \code{$power: } \tab is the power parameter for alpha prior (def: 0.8) \cr \code{lambda_hyper:} \tab \code{list(alim, nulim, vlim)} \cr \code{$alim: } \tab defines support of a distribution (def: \code{c(0.01, 10)}) \cr \code{$nulim: } \tab defines support of nu distribution (def: \code{c(0.01, 3)}) \cr \code{$vlim: } \tab defines support of v distribution (def: \code{c(0.1, 4)}) } \emph{\code{Mcmc = list(R, keep, nprint, maxuniq, SCALE, gridsize)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) \cr \code{maxuniq: } \tab storage constraint on the number of unique components (def: 200) \cr \code{SCALE: } \tab should data be scaled by mean,std deviation before posterior draws (def: \code{TRUE}) \cr \code{gridsize: } \tab number of discrete points for hyperparameter priors (def: 20) } } \subsection{\code{nmix} Details}{ \code{nmix} is a list with 3 components. Several functions in the \code{bayesm} package that involve a Dirichlet Process or mixture-of-normals return \code{nmix}. Across these functions, a common structure is used for \code{nmix} in order to utilize generic summary and plotting functions. \tabular{ll}{ \code{probdraw:} \tab \eqn{ncomp x R/keep} matrix that reports the probability that each draw came from a particular component \cr \code{zdraw: } \tab \eqn{R/keep x nobs} matrix that indicates which component each draw is assigned to \cr \code{compdraw:} \tab A list of \eqn{R/keep} lists of \eqn{ncomp} lists. Each of the inner-most lists has 2 elemens: a vector of draws for \code{mu} and a matrix of draws for the Cholesky root of \code{Sigma}. } } } \value{ A list containing: \item{nmix }{ a list containing: \code{probdraw}, \code{zdraw}, \code{compdraw} (see \dQuote{\code{nmix} Details} section)} \item{alphadraw }{ \eqn{R/keep x 1} vector of alpha draws} \item{nudraw }{ \eqn{R/keep x 1} vector of nu draws} \item{adraw }{ \eqn{R/keep x 1} vector of a draws} \item{vdraw }{ \eqn{R/keep x 1} vector of v draws} } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \seealso{ \code{\link{rnmixGibbs}}, \code{\link{rmixture}}, \code{\link{rmixGibbs}}, \code{\link{eMixMargDen}}, \code{\link{momMix}}, \code{\link{mixDen}}, \code{\link{mixDenBi}}} \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) ## simulate univariate data from Chi-Sq N = 200 chisqdf = 8 y1 = as.matrix(rchisq(N,df=chisqdf)) ## set arguments for rDPGibbs Data1 = list(y=y1) Prioralpha = list(Istarmin=1, Istarmax=10, power=0.8) Prior1 = list(Prioralpha=Prioralpha) Mcmc = list(R=R, keep=1, maxuniq=200) out1 = rDPGibbs(Prior=Prior1, Data=Data1, Mcmc=Mcmc) if(0){ ## plotting examples rgi = c(0,20) grid = matrix(seq(from=rgi[1],to=rgi[2],length.out=50), ncol=1) deltax = (rgi[2]-rgi[1]) / nrow(grid) plot(out1$nmix, Grid=grid, Data=y1) ## plot true density with historgram plot(range(grid[,1]), 1.5*range(dchisq(grid[,1],df=chisqdf)), type="n", xlab=paste("Chisq ; ",N," obs",sep=""), ylab="") hist(y1, xlim=rgi, freq=FALSE, col="yellow", breaks=20, add=TRUE) lines(grid[,1], dchisq(grid[,1],df=chisqdf) / (sum(dchisq(grid[,1],df=chisqdf))*deltax), col="blue", lwd=2) } ## simulate bivariate data from the "Banana" distribution (Meng and Barnard) banana = function(A, B, C1, C2, N, keep=10, init=10) { R = init*keep + N*keep x1 = x2 = 0 bimat = matrix(double(2*N), ncol=2) for (r in 1:R) { x1 = rnorm(1,mean=(B*x2+C1) / (A*(x2^2)+1), sd=sqrt(1/(A*(x2^2)+1))) x2 = rnorm(1,mean=(B*x2+C2) / (A*(x1^2)+1), sd=sqrt(1/(A*(x1^2)+1))) if (r>init*keep && r\%\%keep==0) { mkeep = r/keep bimat[mkeep-init,] = c(x1,x2) } } return(bimat) } set.seed(66) nvar2 = 2 A = 0.5 B = 0 C1 = C2 = 3 y2 = banana(A=A, B=B, C1=C1, C2=C2, 1000) Data2 = list(y=y2) Prioralpha = list(Istarmin=1, Istarmax=10, power=0.8) Prior2 = list(Prioralpha=Prioralpha) Mcmc = list(R=R, keep=1, maxuniq=200) out2 = rDPGibbs(Prior=Prior2, Data=Data2, Mcmc=Mcmc) if(0){ ## plotting examples rx1 = range(y2[,1]) rx2 = range(y2[,2]) x1 = seq(from=rx1[1], to=rx1[2], length.out=50) x2 = seq(from=rx2[1], to=rx2[2], length.out=50) grid = cbind(x1,x2) plot(out2$nmix, Grid=grid, Data=y2) ## plot true bivariate density tden = matrix(double(50*50), ncol=50) for (i in 1:50) { for (j in 1:50) { tden[i,j] = exp(-0.5*(A*(x1[i]^2)*(x2[j]^2) + (x1[i]^2) + (x2[j]^2) - 2*B*x1[i]*x2[j] - 2*C1*x1[i] - 2*C2*x2[j])) }} tden = tden / sum(tden) image(x1, x2, tden, col=terrain.colors(100), xlab="", ylab="") contour(x1, x2, tden, add=TRUE, drawlabels=FALSE) title("True Density") } } \keyword{multivariate} bayesm/man/createX.Rd0000755000176000001440000000433213117541521014224 0ustar ripleyusers\name{createX} \alias{createX} \concept{multinomial logit} \concept{multinomial probit} \title{Create X Matrix for Use in Multinomial Logit and Probit Routines} \description{ \code{createX} makes up an X matrix in the form expected by Multinomial Logit (\code{\link{rmnlIndepMetrop}} and \code{\link{rhierMnlRwMixture}}) and Probit (\code{\link{rmnpGibbs}} and \code{\link{rmvpGibbs}}) routines. Requires an array of alternative-specific variables and/or an array of "demographics" (or variables constant across alternatives) which may vary across choice occasions. } \usage{createX(p, na, nd, Xa, Xd, INT = TRUE, DIFF = FALSE, base=p)} \arguments{ \item{p}{ integer number of choice alternatives } \item{na}{ integer number of alternative-specific vars in \code{Xa} } \item{nd}{ integer number of non-alternative specific vars } \item{Xa}{ \eqn{n x p*na} matrix of alternative-specific vars } \item{Xd}{ \eqn{n x nd} matrix of non-alternative specific vars } \item{INT}{ logical flag for inclusion of intercepts } \item{DIFF}{ logical flag for differencing wrt to base alternative } \item{base}{ integer index of base choice alternative } Note: \code{na}, \code{nd}, \code{Xa}, \code{Xd} can be \code{NULL} to indicate lack of \code{Xa} or \code{Xd} variables. } \value{\code{X} matrix of dimension \eqn{n*(p-DIFF) x [(INT+nd)*(p-1) + na]}.} \note{\code{\link{rmnpGibbs}} assumes that the \code{base} alternative is the default.} \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{\code{\link{rmnlIndepMetrop}}, \code{\link{rmnpGibbs}} } \examples{ na=2; nd=1; p=3 vec = c(1, 1.5, 0.5, 2, 3, 1, 3, 4.5, 1.5) Xa = matrix(vec, byrow=TRUE, ncol=3) Xa = cbind(Xa,-Xa) Xd = matrix(c(-1,-2,-3), ncol=1) createX(p=p, na=na, nd=nd, Xa=Xa, Xd=Xd) createX(p=p, na=na, nd=nd, Xa=Xa, Xd=Xd, base=1) createX(p=p, na=na, nd=nd, Xa=Xa, Xd=Xd, DIFF=TRUE) createX(p=p, na=na, nd=nd, Xa=Xa, Xd=Xd, DIFF=TRUE, base=2) createX(p=p, na=na, nd=NULL, Xa=Xa, Xd=NULL) createX(p=p, na=NULL, nd=nd, Xa=NULL, Xd=Xd) } \keyword{array} \keyword{utilities} bayesm/man/plot.bayesm.nmix.Rd0000644000176000001440000000441413117541521016036 0ustar ripleyusers\name{plot.bayesm.nmix} \alias{plot.bayesm.nmix} \concept{MCMC} \concept{S3 method} \concept{plot} \title{Plot Method for MCMC Draws of Normal Mixtures} \description{ \code{plot.bayesm.nmix} is an S3 method to plot aspects of the fitted density from a list of MCMC draws of normal mixture components. Plots of marginal univariate and bivariate densities are produced. } \usage{\method{plot}{bayesm.nmix}(x, names, burnin, Grid, bi.sel, nstd, marg, Data, ngrid, ndraw, ...)} \arguments{ \item{x }{ An object of S3 class \code{bayesm.nmix}} \item{names }{ optional character vector of names for each of the dimensions} \item{burnin }{ number of draws to discard for burn-in (def: \eqn{0.1*nrow(X)})} \item{Grid }{ matrix of grid points for densities, def: mean +/- nstd std deviations (if Data no supplied), range of Data if supplied)} \item{bi.sel }{ list of vectors, each giving pairs for bivariate distributions (def: \code{list(c(1,2))})} \item{nstd }{ number of standard deviations for default Grid (def: 2)} \item{marg }{ logical, if TRUE display marginals (def: \code{TRUE})} \item{Data }{ matrix of data points, used to paint histograms on marginals and for grid} \item{ngrid }{ number of grid points for density estimates (def: 50)} \item{ndraw }{ number of draws to average Mcmc estimates over (def: 200)} \item{... }{ standard graphics parameters} } \details{ Typically, \code{plot.bayesm.nmix} will be invoked by a call to the generic plot function as in \code{plot(object)} where object is of class bayesm.nmix. These objects are lists of three components. The first component is an array of draws of mixture component probabilties. The second component is not used. The third is a lists of lists of lists with draws of each of the normal components.\cr \cr \code{plot.bayesm.nmix} can also be used as a standard function, as in \code{plot.bayesm.nmix(list)}. } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \seealso{ \code{\link{rnmixGibbs}}, \code{\link{rhierMnlRwMixture}}, \code{\link{rhierLinearMixture}}, \code{\link{rDPGibbs}}} \examples{ ## not run # out = rnmixGibbs(Data, Prior, Mcmc) ## plot bivariate distributions for dimension 1,2; 3,4; and 1,3 # plot(out,bi.sel=list(c(1,2),c(3,4),c(1,3))) } \keyword{hplot} bayesm/man/rordprobitGibbs.Rd0000644000176000001440000000756413117541521015775 0ustar ripleyusers\name{rordprobitGibbs} \alias{rordprobitGibbs} \concept{bayes} \concept{MCMC} \concept{probit} \concept{Gibbs Sampling} \title{Gibbs Sampler for Ordered Probit} \description{ \code{rordprobitGibbs} implements a Gibbs Sampler for the ordered probit model with a RW Metropolis step for the cut-offs. } \usage{rordprobitGibbs(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(y, X, k)} \item{Prior}{list(betabar, A, dstarbar, Ad)} \item{Mcmc }{list(R, keep, nprint, s)} } \details{ \subsection{Model and Priors}{ \eqn{z = X\beta + e} with \eqn{e} \eqn{\sim}{~} \eqn{N(0, I)}\cr \eqn{y = k} if c[k] \eqn{\le z <} c[k+1] with \eqn{k = 1,\ldots,K} \cr cutoffs = \{c[1], \eqn{\ldots}, c[k+1]\} \eqn{\beta} \eqn{\sim}{~} \eqn{N(betabar, A^{-1})} \cr \eqn{dstar} \eqn{\sim}{~} \eqn{N(dstarbar, Ad^{-1})} Be careful in assessing prior parameter \code{Ad}: 0.1 is too small for many applications. } \subsection{Argument Details}{ \emph{\code{Data = list(y, X, k)}} \tabular{ll}{ \code{y: } \tab \eqn{n x 1} vector of observations, (\eqn{1, \ldots, k}) \cr \code{X: } \tab \eqn{n x p} Design Matrix \cr \code{k: } \tab the largest possible value of y } \emph{\code{Prior = list(betabar, A, dstarbar, Ad)} [optional]} \tabular{ll}{ \code{betabar: } \tab \eqn{p x 1} prior mean (def: 0) \cr \code{A: } \tab \eqn{p x p} prior precision matrix (def: 0.01*I) \cr \code{dstarbar: } \tab \eqn{ndstar x 1} prior mean, where \eqn{ndstar=k-2} (def: 0) \cr \code{Ad: } \tab \eqn{ndstar x ndstar} prior precision matrix (def: I) } \emph{\code{Mcmc = list(R, keep, nprint, s)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) \cr \code{s: } \tab scaling parameter for RW Metropolis (def: 2.93/\code{sqrt(p)}) } } } \value{ A list containing: \item{betadraw }{ \eqn{R/keep x p} matrix of betadraws} \item{cutdraw }{ \eqn{R/keep x (k-1)} matrix of cutdraws} \item{dstardraw }{ \eqn{R/keep x (k-2)} matrix of dstardraws} \item{accept }{ acceptance rate of Metropolis draws for cut-offs} } \note{ set c[1] = -100 and c[k+1] = 100. c[2] is set to 0 for identification. \cr The relationship between cut-offs and dstar is: \cr c[3] = exp(dstar[1]), \cr c[4] = c[3] + exp(dstar[2]), ..., \cr c[k] = c[k-1] + exp(dstar[k-2]) } \references{\emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch \cr \url{http://www.perossi.org/home/bsm-1}} \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \seealso{ \code{\link{rbprobitGibbs}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) ## simulate data for ordered probit model simordprobit=function(X, betas, cutoff){ z = X\%*\%betas + rnorm(nobs) y = cut(z, br = cutoff, right=TRUE, include.lowest = TRUE, labels = FALSE) return(list(y = y, X = X, k=(length(cutoff)-1), betas= betas, cutoff=cutoff )) } nobs = 300 X = cbind(rep(1,nobs),runif(nobs, min=0, max=5),runif(nobs,min=0, max=5)) k = 5 betas = c(0.5, 1, -0.5) cutoff = c(-100, 0, 1.0, 1.8, 3.2, 100) simout = simordprobit(X, betas, cutoff) Data=list(X=simout$X, y=simout$y, k=k) ## set Mcmc for ordered probit model Mcmc = list(R=R) out = rordprobitGibbs(Data=Data, Mcmc=Mcmc) cat(" ", fill=TRUE) cat("acceptance rate= ", accept=out$accept, fill=TRUE) ## outputs of betadraw and cut-off draws cat(" Summary of betadraws", fill=TRUE) summary(out$betadraw, tvalues=betas) cat(" Summary of cut-off draws", fill=TRUE) summary(out$cutdraw, tvalues=cutoff[2:k]) ## plotting examples if(0){plot(out$cutdraw)} } \keyword{models} bayesm/man/numEff.Rd0000755000176000001440000000243513117541521014053 0ustar ripleyusers\name{numEff} \alias{numEff} \concept{numerical efficiency} \title{Compute Numerical Standard Error and Relative Numerical Efficiency} \description{ \code{numEff} computes the numerical standard error for the mean of a vector of draws as well as the relative numerical efficiency (ratio of variance of mean of this time series process relative to iid sequence). } \usage{numEff(x, m = as.integer(min(length(x),(100/sqrt(5000))*sqrt(length(x)))))} \arguments{ \item{x}{ \eqn{R x 1} vector of draws } \item{m}{ number of lags for autocorrelations } } \details{ default for number of lags is chosen so that if \eqn{R=5000}, \eqn{m=100} and increases as the \eqn{sqrt(R)}. } \value{ A list containing: \item{stderr }{standard error of the mean of \eqn{x}} \item{f }{ variance ratio (relative numerical efficiency) } } \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \examples{ numEff(rnorm(1000), m=20) numEff(rnorm(1000)) } \keyword{ts} \keyword{utilities} bayesm/man/cheese.Rd0000644000176000001440000000440713117541521014065 0ustar ripleyusers\name{cheese} \alias{cheese} \docType{data} \title{Sliced Cheese Data} \description{ Panel data with sales volume for a package of Borden Sliced Cheese as well as a measure of display activity and price. Weekly data aggregated to the "key" account or retailer/market level. } \usage{data(cheese)} \format{ A data frame with 5555 observations on the following 4 variables: \tabular{ll}{ \ldots\code{$RETAILER} \tab a list of 88 retailers \cr \ldots\code{$VOLUME } \tab unit sales \cr \ldots\code{$DISP } \tab percent ACV on display (a measure of advertising display activity) \cr \ldots\code{$PRICE } \tab in U.S. dollars } } \source{Boatwright, Peter, Robert McCulloch, and Peter Rossi (1999), "Account-Level Modeling for Trade Promotion," \emph{Journal of the American Statistical Association} 94, 1063--1073.} \references{Chapter 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \examples{ data(cheese) cat(" Quantiles of the Variables ",fill=TRUE) mat = apply(as.matrix(cheese[,2:4]), 2, quantile) print(mat) ## example of processing for use with rhierLinearModel if(0) { retailer = levels(cheese$RETAILER) nreg = length(retailer) nvar = 3 regdata = NULL for (reg in 1:nreg) { y = log(cheese$VOLUME[cheese$RETAILER==retailer[reg]]) iota = c(rep(1,length(y))) X = cbind(iota, cheese$DISP[cheese$RETAILER==retailer[reg]], log(cheese$PRICE[cheese$RETAILER==retailer[reg]])) regdata[[reg]] = list(y=y, X=X) } Z = matrix(c(rep(1,nreg)), ncol=1) nz = ncol(Z) ## run each individual regression and store results lscoef = matrix(double(nreg*nvar), ncol=nvar) for (reg in 1:nreg) { coef = lsfit(regdata[[reg]]$X, regdata[[reg]]$y, intercept=FALSE)$coef if (var(regdata[[reg]]$X[,2])==0) { lscoef[reg,1]=coef[1] lscoef[reg,3]=coef[2] } else {lscoef[reg,]=coef} } R = 2000 Data = list(regdata=regdata, Z=Z) Mcmc = list(R=R, keep=1) set.seed(66) out = rhierLinearModel(Data=Data, Mcmc=Mcmc) cat("Summary of Delta Draws", fill=TRUE) summary(out$Deltadraw) cat("Summary of Vbeta Draws", fill=TRUE) summary(out$Vbetadraw) # plot hier coefs if(0) {plot(out$betadraw)} } } \keyword{datasets} bayesm/man/camera.Rd0000644000176000001440000000402013117541521014050 0ustar ripleyusers\name{camera} \alias{camera} \docType{data} \title{Conjoint Survey Data for Digital Cameras} \description{ Panel dataset from a conjoint survey for digital cameras with 332 respondents. Data exclude respondents that always answered none, always picked the same brand, always selected the highest priced offering, or who appeared to be answering randomly. } \usage{data(camera)} \format{ A list of lists. Each inner list corresponds to one survey respondent and contains a numeric vector (\code{y}) of choice indicators and a numeric matrix (\code{X}) of covariates. Each respondent participated in 16 choice scenarios each including 4 camera options (and an outside option) for a total of 80 rows per respondent. } \details{ The covariates included in each \code{X} matrix are: \tabular{ll}{ \ldots\code{$canon } \tab an indicator for brand Canon \cr \ldots\code{$sony } \tab an indicator for brand Sony \cr \ldots\code{$nikon } \tab an indicator for brand Nikon \cr \ldots\code{$panasonic } \tab an indicator for brand Panasonic \cr \ldots\code{$pixels } \tab an indicator for a higher pixel count \cr \ldots\code{$zoom } \tab an indicator for a higher level of zoom \cr \ldots\code{$video } \tab an indicator for the ability to capture video \cr \ldots\code{$swivel } \tab an indicator for a swivel video display \cr \ldots\code{$wifi } \tab an indicator for wifi capability \cr \ldots\code{$price } \tab in hundreds of U.S. dollars } } \source{ Allenby, Greg, Jeff Brazell, John Howell, and Peter Rossi (2014), "Economic Valuation of Product Features," \emph{Quantitative Marketing and Economics} 12, 421--456. Allenby, Greg, Jeff Brazell, John Howell, and Peter Rossi (2014), "Valuation of Patented Product Features," \emph{Journal of Law and Economics} 57, 629--663. } \references{ For analysis of a similar dataset, see Case Study 4, \emph{Bayesian Statistics and Marketing} Rossi, Allenby, and McCulloch \url{http://www.perossi.org/home/bsm-1} } \keyword{datasets} bayesm/man/detailing.Rd0000644000176000001440000000642613117541521014574 0ustar ripleyusers\name{detailing} \alias{detailing} \docType{data} \title{Physician Detailing Data} \description{ Monthly data on physician detailing (sales calls). 23 months of data for each of 1000 physicians; includes physician covariates. } \usage{data(detailing)} \format{ The \code{detailing} object is a list containing two data frames, \code{counts} and \code{demo}. } \details{ In the \code{counts} data frame: \tabular{ll}{ \ldots\code{$id } \tab identifies the physician \cr \ldots\code{$scrips } \tab the number of new presectiptions ordered by the physician for the drug detailed \cr \ldots\code{$detailing } \tab the number of sales called made to each physician per month \cr \ldots\code{$lagged_scripts} \tab scrips value for prior month } In the \code{demo} data frame: \tabular{ll}{ \ldots\code{$$id } \tab identifies the physician \cr \ldots\code{$generalphys } \tab dummy for if doctor is a "general practitioner" \cr \ldots\code{$specialist } \tab dummy for if the physician is a specialist in the theraputic class for which the drug is intended \cr \ldots\code{$mean_samples} \tab the mean number of free drug samples given the doctor over the sample period } } \source{Manchanda, Puneet, Pradeep Chintagunta, and Peter Rossi (2004), "Response Modeling with Non-Random Marketing Mix Variables," \emph{Journal of Marketing Research} 41, 467--478.} \examples{ data(detailing) cat(" table of Counts Dep Var", fill=TRUE) print(table(detailing$counts[,2])) cat(" means of Demographic Variables",fill=TRUE) mat = apply(as.matrix(detailing$demo[,2:4]), 2, mean) print(mat) ## example of processing for use with 'rhierNegbinRw' if(0) { data(detailing) counts = detailing$counts Z = detailing$demo # Construct the Z matrix Z[,1] = 1 Z[,2] = Z[,2] - mean(Z[,2]) Z[,3] = Z[,3] - mean(Z[,3]) Z[,4] = Z[,4] - mean(Z[,4]) Z = as.matrix(Z) id = levels(factor(counts$id)) nreg = length(id) nobs = nrow(counts$id) regdata = NULL for (i in 1:nreg) { X = counts[counts[,1] == id[i], c(3:4)] X = cbind(rep(1, nrow(X)), X) y = counts[counts[,1] == id[i], 2] X = as.matrix(X) regdata[[i]] = list(X=X, y=y) } rm(detailing, counts) cat("Finished reading data", fill=TRUE) fsh() Data = list(regdata=regdata, Z=Z) nvar = ncol(X) # Number of X variables nz = ncol(Z) # Number of Z variables deltabar = matrix(rep(0,nvar*nz), nrow=nz) Vdelta = 0.01*diag(nz) nu = nvar+3 V = 0.01*diag(nvar) a = 0.5 b = 0.1 Prior = list(deltabar=deltabar, Vdelta=Vdelta, nu=nu, V=V, a=a, b=b) R = 10000 keep = 1 s_beta = 2.93/sqrt(nvar) s_alpha = 2.93 c = 2 Mcmc = list(R=R, keep=keep, s_beta=s_beta, s_alpha=s_alpha, c=c) out = rhierNegbinRw(Data, Prior, Mcmc) ## Unit level mean beta parameters Mbeta = matrix(rep(0,nreg*nvar), nrow=nreg) ndraws = length(out$alphadraw) for (i in 1:nreg) { Mbeta[i,] = rowSums(out$Betadraw[i,,])/ndraws } cat(" Deltadraws ", fill=TRUE) summary(out$Deltadraw) cat(" Vbetadraws ", fill=TRUE) summary(out$Vbetadraw) cat(" alphadraws ", fill=TRUE) summary(out$alphadraw) ## plotting examples if(0){ plot(out$betadraw) plot(out$alphadraw) plot(out$Deltadraw) } } } \keyword{datasets} bayesm/man/runiregGibbs.Rd0000644000176000001440000000520613117541521015251 0ustar ripleyusers\name{runiregGibbs} \alias{runiregGibbs} \concept{bayes} \concept{Gibbs Sampler} \concept{regression} \concept{MCMC} \title{Gibbs Sampler for Univariate Regression} \description{ \code{runiregGibbs} implements a Gibbs Sampler to draw from posterior of a univariate regression with a conditionally conjugate prior. } \usage{runiregGibbs(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(y, X)} \item{Prior}{list(betabar, A, nu, ssq)} \item{Mcmc }{list(sigmasq, R, keep, nprint)} } \details{ \subsection{Model and Priors}{ \eqn{y = X\beta + e} with \eqn{e} \eqn{\sim}{~} \eqn{N(0, \sigma^2)} \eqn{\beta} \eqn{\sim}{~} \eqn{N(betabar, A^{-1})}\cr \eqn{\sigma^2} \eqn{\sim}{~} \eqn{(nu*ssq)/\chi^2_{nu}} } \subsection{Argument Details}{ \emph{\code{Data = list(y, X)}} \tabular{ll}{ \code{y: } \tab \eqn{n x 1} vector of observations \cr \code{X: } \tab \eqn{n x k} design matrix } \emph{\code{Prior = list(betabar, A, nu, ssq)} [optional]} \tabular{ll}{ \code{betabar: } \tab \eqn{k x 1} prior mean (def: 0) \cr \code{A: } \tab \eqn{k x k} prior precision matrix (def: 0.01*I) \cr \code{nu: } \tab d.f. parameter for Inverted Chi-square prior (def: 3) \cr \code{ssq: } \tab scale parameter for Inverted Chi-square prior (def: \code{var(y)}) } \emph{\code{Mcmc = list(sigmasq, R, keep, nprint)} [only \code{R} required]} \tabular{ll}{ \code{sigmasq: } \tab value for \eqn{\sigma^2} for first Gibbs sampler draw of \eqn{\beta}|\eqn{\sigma^2} \cr \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter -- keep every \code{keep}th draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every \code{nprint}'th draw (def: 100, set to 0 for no print) } } } \value{ A list containing: \item{betadraw }{ \eqn{R x k} matrix of betadraws } \item{sigmasqdraw }{ \eqn{R x 1} vector of sigma-sq draws} } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \seealso{ \code{\link{runireg}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=1000} else {R=10} set.seed(66) n = 200 X = cbind(rep(1,n), runif(n)) beta = c(1,2) sigsq = 0.25 y = X\%*\%beta + rnorm(n,sd=sqrt(sigsq)) out = runiregGibbs(Data=list(y=y, X=X), Mcmc=list(R=R)) cat("Summary of beta and Sigmasq draws", fill=TRUE) summary(out$betadraw, tvalues=beta) summary(out$sigmasqdraw, tvalues=sigsq) ## plotting examples if(0){plot(out$betadraw)} } \keyword{regression} bayesm/man/rwishart.Rd0000644000176000001440000000253613117541521014475 0ustar ripleyusers\name{rwishart} \alias{rwishart} \concept{Wishart distribution} \concept{Inverted Wishart} \concept{simulation} \title{ Draw from Wishart and Inverted Wishart Distribution } \description{ \code{rwishart} draws from the Wishart and Inverted Wishart distributions. } \usage{rwishart(nu, V)} \arguments{ \item{nu}{ d.f. parameter} \item{V}{ pds location matrix} } \details{ In the parameterization used here, \eqn{W} \eqn{\sim}{~} \eqn{W(nu,V)} with \eqn{E[W]=nuV}. \cr If you want to use an Inverted Wishart prior, you \emph{must invert the location matrix} before calling \code{rwishart}, e.g. \cr \eqn{\Sigma} \eqn{\sim}{~} IW(nu ,V); \eqn{\Sigma^{-1}} \eqn{\sim}{~} \eqn{W(nu, V^{-1})}. } \value{ A list containing: \item{W: }{ Wishart draw } \item{IW: }{Inverted Wishart draw} \item{C: }{ Upper tri root of W} \item{CI: }{ inv(C), \eqn{W^{-1}} = CICI'} } \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{For further discussion, see Chapter 2, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1}} \examples{ set.seed(66) rwishart(5,diag(3))$IW } \keyword{multivariate} \keyword{distribution} bayesm/man/rivDP.Rd0000644000176000001440000001700413117570164013657 0ustar ripleyusers\name{rivDP} \alias{rivDP} \concept{Instrumental Variables} \concept{Gibbs Sampler} \concept{Dirichlet Process} \concept{bayes} \concept{endogeneity} \concept{simultaneity} \concept{MCMC} \title{Linear "IV" Model with DP Process Prior for Errors} \description{ \code{rivDP} is a Gibbs Sampler for a linear structural equation with an arbitrary number of instruments. \code{rivDP} uses a mixture-of-normals for the structural and reduced form equations implemented with a Dirichlet Process prior. } \usage{rivDP(Data, Prior, Mcmc)} \arguments{ \item{Data }{list(y, x, w, z)} \item{Prior}{list(md, Ad, mbg, Abg, lambda, Prioralpha, lambda_hyper)} \item{Mcmc }{list(R, keep, nprint, maxuniq, SCALE, gridsize)} } \details{ \subsection{Model and Priors}{ \eqn{x = z'\delta + e1} \cr \eqn{y = \beta*x + w'\gamma + e2} \cr \eqn{e1,e2} \eqn{\sim}{~} \eqn{N(\theta_{i})} where \eqn{\theta_{i}} represents \eqn{\mu_{i}, \Sigma_{i}} Note: Error terms have non-zero means. DO NOT include intercepts in the \eqn{z} or \eqn{w} matrices. This is different from \code{rivGibbs} which requires intercepts to be included explicitly. \eqn{\delta} \eqn{\sim}{~} \eqn{N(md, Ad^{-1})} \cr \eqn{vec(\beta, \gamma)} \eqn{\sim}{~} \eqn{N(mbg, Abg^{-1})} \cr \eqn{\theta_{i}} \eqn{\sim}{~} \eqn{G} \cr \eqn{G} \eqn{\sim}{~} \eqn{DP(alpha, G_0)} \eqn{alpha} \eqn{\sim}{~} \eqn{(1-(alpha-alpha_{min})/(alpha_{max}-alpha{min}))^{power}} \cr where \eqn{alpha_{min}} and \eqn{alpha_{max}} are set using the arguments in the reference below. It is highly recommended that you use the default values for the hyperparameters of the prior on alpha. \eqn{G_0} is the natural conjugate prior for \eqn{(\mu,\Sigma)}: \eqn{\Sigma} \eqn{\sim}{~} \eqn{IW(nu, vI)} and \eqn{\mu|\Sigma} \eqn{\sim}{~} \eqn{N(0, \Sigma(x) a^{-1})} \cr These parameters are collected together in the list \eqn{\lambda}. It is highly recommended that you use the default settings for these hyper-parameters.\cr \eqn{\lambda(a, nu, v):}\cr \eqn{a} \eqn{\sim}{~} uniform[alim[1], alimb[2]]\cr \eqn{nu} \eqn{\sim}{~} dim(data)-1 + exp(z) \cr \eqn{z} \eqn{\sim}{~} uniform[dim(data)-1+nulim[1], nulim[2]]\cr \eqn{v} \eqn{\sim}{~} uniform[vlim[1], vlim[2]] } \subsection{Argument Details}{ \emph{\code{Data = list(y, x, w, z)}} \tabular{ll}{ \code{y: } \tab \eqn{n x 1} vector of obs on LHS variable in structural equation \cr \code{x: } \tab \eqn{n x 1} vector of obs on "endogenous" variable in structural equation \cr \code{w: } \tab \eqn{n x j} matrix of obs on "exogenous" variables in the structural equation \cr \code{z: } \tab \eqn{n x p} matrix of obs on instruments } \emph{\code{Prior = list(md, Ad, mbg, Abg, lambda, Prioralpha, lambda_hyper)} [optional]} \tabular{ll}{ \code{md: } \tab \eqn{p}-length prior mean of delta (def: 0) \cr \code{Ad: } \tab \eqn{p x p} PDS prior precision matrix for prior on delta (def: 0.01*I) \cr \code{mbg: } \tab \eqn{(j+1)}-length prior mean vector for prior on beta,gamma (def: 0) \cr \code{Abg: } \tab \eqn{(j+1)x(j+1)} PDS prior precision matrix for prior on beta,gamma (def: 0.01*I) \cr \code{Prioralpha:} \tab \code{list(Istarmin, Istarmax, power)} \cr \code{$Istarmin: } \tab is expected number of components at lower bound of support of alpha (def: 1) \cr \code{$Istarmax: } \tab is expected number of components at upper bound of support of alpha (def: \code{floor(0.1*length(y))}) \cr \code{$power: } \tab is the power parameter for alpha prior (def: 0.8) \cr \code{lambda_hyper:} \tab \code{list(alim, nulim, vlim)} \cr \code{$alim: } \tab defines support of a distribution (def: \code{c(0.01, 10)}) \cr \code{$nulim: } \tab defines support of nu distribution (def: \code{c(0.01, 3)}) \cr \code{$vlim: } \tab defines support of v distribution (def: \code{c(0.1, 4)}) } \emph{\code{Mcmc = list(R, keep, nprint, maxuniq, SCALE, gridsize)} [only \code{R} required]} \tabular{ll}{ \code{R: } \tab number of MCMC draws \cr \code{keep: } \tab MCMC thinning parameter: keep every keepth draw (def: 1) \cr \code{nprint: } \tab print the estimated time remaining for every nprint'th draw (def: 100, set to 0 for no print) \cr \code{maxuniq: } \tab storage constraint on the number of unique components (def: 200) \cr \code{SCALE: } \tab scale data (def: \code{TRUE}) \cr \code{gridsize: } \tab gridsize parameter for alpha draws (def: 20) } } \subsection{\code{nmix} Details}{ \code{nmix} is a list with 3 components. Several functions in the \code{bayesm} package that involve a Dirichlet Process or mixture-of-normals return \code{nmix}. Across these functions, a common structure is used for \code{nmix} in order to utilize generic summary and plotting functions. \tabular{ll}{ \code{probdraw:} \tab \eqn{ncomp x R/keep} matrix that reports the probability that each draw came from a particular component (here, a one-column matrix of 1s) \cr \code{zdraw: } \tab \eqn{R/keep x nobs} matrix that indicates which component each draw is assigned to (here, null) \cr \code{compdraw:} \tab A list of \eqn{R/keep} lists of \eqn{ncomp} lists. Each of the inner-most lists has 2 elemens: a vector of draws for \code{mu} and a matrix of draws for the Cholesky root of \code{Sigma}. } } } \value{ A list containing: \item{\code{deltadraw }}{ \eqn{R/keep x p} array of delta draws} \item{\code{betadraw }}{ \eqn{R/keep x 1} vector of beta draws} \item{\code{alphadraw }}{ \eqn{R/keep x 1} vector of draws of Dirichlet Process tightness parameter} \item{\code{Istardraw }}{ \eqn{R/keep x 1} vector of draws of the number of unique normal components} \item{\code{gammadraw }}{ \eqn{R/keep x j} array of gamma draws} \item{\code{nmix }}{ a list containing: \code{probdraw}, \code{zdraw}, \code{compdraw} (see \dQuote{\code{nmix} Details} section)} } \author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.} \references{ For further discussion, see "A Semi-Parametric Bayesian Approach to the Instrumental Variable Problem," by Conley, Hansen, McCulloch and Rossi, \emph{Journal of Econometrics} (2008). See also, Chapter 4, \emph{Bayesian Non- and Semi-parametric Methods and Applications} by Peter Rossi. } \seealso{\code{rivGibbs}} \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) ## simulate scaled log-normal errors and run k = 10 delta = 1.5 Sigma = matrix(c(1, 0.6, 0.6, 1), ncol=2) N = 1000 tbeta = 4 scalefactor = 0.6 root = chol(scalefactor*Sigma) mu = c(1,1) ## compute interquartile ranges ninterq = qnorm(0.75) - qnorm(0.25) error = matrix(rnorm(100000*2), ncol=2)\%*\%root error = t(t(error)+mu) Err = t(t(exp(error))-exp(mu+0.5*scalefactor*diag(Sigma))) lnNinterq = quantile(Err[,1], prob=0.75) - quantile(Err[,1], prob=0.25) ## simulate data error = matrix(rnorm(N*2), ncol=2)\%*\%root error = t(t(error)+mu) Err = t(t(exp(error))-exp(mu+0.5*scalefactor*diag(Sigma))) ## scale appropriately Err[,1] = Err[,1]*ninterq/lnNinterq Err[,2] = Err[,2]*ninterq/lnNinterq z = matrix(runif(k*N), ncol=k) x = z\%*\%(delta*c(rep(1,k))) + Err[,1] y = x*tbeta + Err[,2] ## specify data input and mcmc parameters Data = list(); Data$z = z Data$x = x Data$y = y Mcmc = list() Mcmc$maxuniq = 100 Mcmc$R = R end = Mcmc$R out = rivDP(Data=Data, Mcmc=Mcmc) cat("Summary of Beta draws", fill=TRUE) summary(out$betadraw, tvalues=tbeta) ## plotting examples if(0){ plot(out$betadraw, tvalues=tbeta) plot(out$nmix) # plot "fitted" density of the errors } } \keyword{models}