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&& rnd <= cumprob+probs[i]) { break; } else {cumprob=cumprob+probs[i];} } PutRNGstate(); return i+1 ; } /* gets a row of a matrix and returns this as a matrix by setting dim */ SEXP getrow(SEXP mat, int row, int nrow, int ncol){ int i,ind; SEXP ans, ndim; PROTECT(ans=NEW_NUMERIC(ncol)); PROTECT(ndim=NEW_INTEGER(2)); for(i =0; i < ncol; i++){ ind=i*nrow+row; NUMERIC_POINTER(ans)[i]=NUMERIC_POINTER(mat)[ind]; } INTEGER_POINTER(ndim)[0]=1; INTEGER_POINTER(ndim)[1]=ncol; SET_DIM(ans,ndim); UNPROTECT(2); return(ans); } /* theta draw routine to be used with .Call */ SEXP thetadraw( SEXP y, SEXP ydenmatO, SEXP indicO, SEXP q0v, SEXP p, SEXP theta, SEXP lambda, SEXP eta, SEXP thetaD, SEXP yden, SEXP maxuniqS,SEXP nuniqueS, SEXP rho) { int nunique,n,ncol,j,i,maxuniq,inc,index,ii,jj,ind ; SEXP R_fc_thetaD, R_fc_yden, yrow, ydim, onetheta, lofone, newrow, ydenmat, ydendim ; double *probs; int *indmi; int *indic; double sprob; nunique=INTEGER_VALUE(nuniqueS); n=length(theta); maxuniq=INTEGER_VALUE(maxuniqS); /* create new lists for use and output */ PROTECT(lofone=NEW_LIST(1)); /* create R function call object, lang4 creates a pairwise (linked) list with 4 values -- function, first arg, sec arg, third arg. R_NilValue is a placeholder until we associate first argument (which varies in our case) */ PROTECT(R_fc_thetaD=lang4(thetaD,R_NilValue,lambda,eta)); PROTECT(R_fc_yden=lang4(yden,R_NilValue,y,eta)); PROTECT(ydim=GET_DIM(y)); ncol=INTEGER_POINTER(ydim)[1]; PROTECT(yrow=NEW_NUMERIC(ncol)); PROTECT(newrow=NEW_NUMERIC(n)); PROTECT(ydenmat=NEW_NUMERIC(maxuniq*n)); PROTECT(ydendim=NEW_INTEGER(2)); INTEGER_POINTER(ydendim)[0]=maxuniq; INTEGER_POINTER(ydendim)[1]=n; /* copy iformation from R objects that will be modified note that we must access elements in the lists (generic vectors) by using VECTOR_ELT we can't use the pointer and deferencing directly like we can for numeric and integer vectors */ for(j=0;j < maxuniq*n; j++){NUMERIC_POINTER(ydenmat)[j]=NUMERIC_POINTER(ydenmatO)[j];} SET_DIM(ydenmat,ydendim); /* allocate space for local vectors */ probs=(double *)R_alloc(n,sizeof(double)); indmi=(int *)R_alloc((n-1),sizeof(int)); indic=(int *)R_alloc(n,sizeof(int)); /* copy information from R object indicO to indic */ for(j=0;j < n; j++) {indic[j]=NUMERIC_POINTER(indicO)[j];} /* start loop over observations */ for(i=0;i < n; i++){ probs[n-1]=NUMERIC_POINTER(q0v)[i]*NUMERIC_POINTER(p)[n-1]; /* make up indmi -- vector of length n-1 consisting of -i as in R notation -- 1, ...,i-1, ,i+1,...,n */ inc=0; for(j=0;j < (n-1); j++){ if(j==i) {inc=inc+1;}; indmi[j]=inc; inc=inc+1; } for(j=0;j < (n-1); j++){ ii=indic[indmi[j]]; jj=i; /* find element ydenmat(ii,jj+1) */ index=jj*maxuniq+(ii-1); probs[j]=NUMERIC_POINTER(p)[j]*NUMERIC_POINTER(ydenmat)[index]; } sprob=0.0; for(j=0;j (maxuniq-1)) {error("max number of unique thetas exceeded");} /* check to make sure we don't exceed max number of unique theta */ SET_ELEMENT(lofone,0,onetheta); SETCADR(R_fc_yden,lofone); newrow=eval(R_fc_yden,rho); for(j=0;j #include extern "C" { #include #include }; extern "C" void getC(double *ep,int *kp, double *m1p, double *m2p, double *c); extern "C" void dy(int *p, int *nob, double *y, int *x, double *c, double *mu, double *beta, double *s, double *tau, double *sigma); void getC(double *ep,int *kp, double *m1p, double *m2p, double *c) { double e = *ep; int k = *kp; double m1 = *m1p; double m2 = *m2p; //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 = (double)(k-1); double s1=0.0,s2=0.0,s3=0.0,s4=0.0; for(int i=1;i #include #include void condmom(double *x, double *mu, double *sigi, int p, int j, double *m, double *csig) { /* function to compute moments of x[j] | x[-j] */ int ind,i,jm1; double csigsq; jm1=j-1; ind = p*jm1; csigsq = 1./sigi[ind+jm1]; *m = 0.0; for (i=0 ; i < p; ++i) { if (i != jm1) {*m += - csigsq*sigi[ind+i]*(x[i]-mu[i]);} } *m=mu[jm1]+*m ; *csig=sqrt(csigsq); } double rtrun(double mu, double sigma,double trunpt, int above) { /* function to draw truncated normal above=1 means from above b=trunpt, a=-inf above=0 means from below a=trunpt, b= +inf modified by rossi 6/05 to check arg to qnorm */ double FA,FB,rnd,result,arg ; if (above) { FA=0.0; FB=pnorm(((trunpt-mu)/(sigma)),0.0,1.0,1,0); } else { FB=1.0; FA=pnorm(((trunpt-mu)/(sigma)),0.0,1.0,1,0); } GetRNGstate(); rnd=unif_rand(); arg=rnd*(FB-FA)+FA; if(arg > .999999999) arg=.999999999; if(arg < .0000000001) arg=.0000000001; result = mu + sigma*qnorm(arg,0.0,1.0,1,0); PutRNGstate(); return result; } void drawwi(double *w, double *mu, double *sigmai,int *p, int *y) { /* function to draw w_i by Gibbing's thru p vector */ int i,j,above; double bound; double mean, csig; for (i=0; i < *p; ++i) { bound=0.0; for (j=0; j < *p ; ++j) { if (j != i) {bound=fmax2(bound,w[j]); }} if (*y == i+1) above = 0; else above = 1; condmom(w,mu,sigmai,*p,(i+1),&mean,&csig); w[i]=rtrun(mean,csig,bound,above); } } void draww(double *w, double *mu, double *sigmai, int *n, int *p, int *y) { /* function to gibbs down entire w vector for all n obs */ int i, ind; for (i=0; i < *n; ++i) { ind= *p * i; drawwi(w+ind,mu+ind,sigmai,p,y+i); } } void drawwi_mvp(double *w, double *mu, double *sigmai,int *p, int *y) { /* function to draw w_i for Multivariate Probit */ int i,above; double mean, csig; for (i=0; i < *p; ++i) { if (y[i]) above = 0; else above = 1; condmom(w,mu,sigmai,*p,(i+1),&mean,&csig); w[i]=rtrun(mean,csig,0.0,above); } } void draww_mvp(double *w, double *mu, double *sigmai, int *n, int *p, int *y) { /* function to gibbs down entire w vector for all n obs */ int i, ind; for (i=0; i < *n; ++i) { ind= *p * i; drawwi_mvp(w+ind,mu+ind,sigmai,p,y+ind); } } double root(double c1, double c2, double *tol,int *iterlim) { /* function to find root of c1 - c2u = lnu */ int iter; double uold, unew; uold=1.; unew=0.00001; iter=0; 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; } void callroot(int *n,double *c1, double *c2, double *tol, int *iterlim,double *u) { int i; for (i=0;i < *n; ++i) { u[i]=root(c1[i],c2[i],tol,iterlim); } } void ghk_oneside(double *L, double* trunpt, int *above, int *dim, int *n, double *res) /* routine to implement ghk with a region defined by truncation only on one- side r mcculloch 8/04 if above=1, then we truncate component i from above at point trunpt[i-1] L is lower triangular root of Sigma random vector is assumed to have zero mean n is number of draws to use in GHK modified 6/05 by rossi to check arg into qnorm */ { int i,j,k; double mu,tpz,u,prod,pa,pb,arg; double *z; z = (double *)R_alloc(*dim,sizeof(double)); GetRNGstate(); *res = 0.0; for(i=0;i<*n;i++) { prod=1.0; for(j=0;j<*dim;j++) { mu=0.0; for(k=0;k .999999999) arg=.999999999; if(arg < .0000000001) arg=.0000000001; z[j] = qnorm(arg,0.0,1.0,1,0); } *res += prod; } *res /= (double)(*n); PutRNGstate(); } void ghk(double *L, double* a, double *b, int *dim, int *n, double *res) /* 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 modified 6/05 by rossi to check arg into qnorm */ { int i,j,k; double aa,bb,pa,pb,u,prod,mu,arg; double *z; z = (double *)R_alloc(*dim,sizeof(double)); GetRNGstate(); *res=0.0; for(i=0;i<*n;i++) { prod = 1.0; for(j=0;j<*dim;j++) { mu=0.0; for(k=0;k .999999999) arg=.999999999; if(arg < .0000000001) arg=.0000000001; z[j] = qnorm(arg,0.0,1.0,1,0); } *res += prod; } *res /= (double)(*n); PutRNGstate(); } void ghk_vec(int *n,double *L, double *trunpt,int *above, int *dim, int *r, double *res) { /* routine to call ghk_oneside for n different truncation points stacked in to the vector trunpt -- puts n results in vector res p rossi 12/04 */ int i, ind; for (i=0; i < *n; ++i) { ind = *dim * i; ghk_oneside(L,trunpt + ind,above,dim,r,res+i); } } void cuttov(double *ut,double *v, int *dim) /* purpose: write upper triangular (ut) to vector (v), goes down columns, omitting zeros arguments: ut: upper triangular matrix, stored as series of columns (including the zeros) v: vector ut is copied to, on input must have correct length dim: ut is dim x dim, v is dim*(dim+1)/2 */ { int ind=0; int i,j; for(i=0;i<(*dim);i++) { for(j=0;j<=i;j++) { v[ind] = ut[i*(*dim)+j]; ind += 1; } } } void cvtout(double *v, double *ut, int *dim) /* purpose: write vector (v) to upper triangular (inverse of cuttov above) arguments: v: vector ut: upper triangulare matrix, columns stacked, zeros included dim: ut is dim x dim, v is dim*(dim+1)/2 */ { int ind=0; int i,j; for(i=0;i<(*dim);i++) { for(j=(i+1);j<(*dim);j++) ut[i*(*dim)+j]=0.0; for(j=0;j<=i;j++) { ut[i*(*dim)+j] = v[ind]; ind += 1; } } } void clmvn(double *x, double *mu, double *riv, int *dim, double *res) /* purpose: calculate log of multivariate density evaluated at x mean is mu, and covariance matrix t(R)%*%R and riv is vector version of the inverse of R arguments: x: compute log(f(x)) mu, riv: x~N(mu,t(R)%*%R), riv is vector version of R^{-1} dim: dimension of x res: place to put result */ { int i,j; double sum = 0.0; double prod = 1.0; double z; int ind = 0; for(i=0;i<(*dim);i++) { z = 0.0; for(j=0;j<=i;j++) {z += riv[ind]*(x[j]-mu[j]); ind += 1;} sum += z*z; prod *= riv[ind-1]; } *res = log(prod) -.5*sum; } void crdisc(double *p, int *res) /* purpose: draw from a discrete distribution arguments: p: vector of probabilities res: draw is in {1,2,...length(p)}, giving the draw's category */ { double u,sum; GetRNGstate(); u = unif_rand(); *res = 1; sum = p[*res -1]; while(sum max) max = *(post+i); } sum = 0.0; for(i=0;i<(*nc);i++) { post[i] = exp(post[i]-max)*p[i]; sum += post[i];} for(i=0;i<(*nc);i++) post[i] /= sum; crdisc(post,res); } void crcomps(double *x, double *mu, double *riv, double *p, int *dim, int *nc, int *nob, int *res) /* purpose: x represents a matrix, whose columns are draws from a normal mixture, draw component membership for each x arguments: all the same as crcomp, except x is now column stacked version of dim x nob matrix and nob is the number of observations res is now of length nob */ { int i; for(i=0;i<(*nob);i++) { crcomp(x+i*(*dim),mu,riv,p,dim,nc,res+i); } } bayesm/R/0000755000176000001440000000000011751111710011756 5ustar ripleyusersbayesm/R/summary.bayesm.var.R0000755000176000001440000000270610572075611015665 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)$class="bayesm.mat" summary(uppertri,names=plabels,tvalues=tvalues,QUANTILES=QUANTILES) invisible() } bayesm/R/summary.bayesm.nmix.R0000755000176000001440000000261710647461730016055 0ustar ripleyuserssummary.bayesm.nmix=function(object,names,burnin=trunc(.1*nrow(probdraw)),...){ nmixlist=object if(mode(nmixlist) != "list") stop(" Argument must be a list \n") probdraw=nmixlist[[1]]; compdraw=nmixlist[[3]] if(!is.matrix(probdraw)) stop(" First Element of List (probdraw) must be a matrix \n") if(mode(compdraw) != "list") stop(" Third Element of List (compdraw) must be a list \n") ncomp=length(compdraw[[1]]) if(ncol(probdraw) != ncomp) stop(" Dim of First Element of List not compatible with Dim of Second \n") # # function to summarize draws of normal mixture components # R=nrow(probdraw) if(R < 100) {cat("fewer than 100 draws submitted \n"); return(invisible())} datad=length(compdraw[[1]][[1]]$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/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$f)} } mat=rbind(mat,num_se,rel_eff,eff_s_size) colnames(mat)=names rownames(mat)[1]="mean" rownames(mat)[2]="std dev" rownames(mat)[3]="num se" rownames(mat)[4]="rel eff" rownames(mat)[5]="sam size" if(!missing(tvalues)) {if(mode(tvalues)!="numeric") stop("true values arguments must be numeric \n") if(length(tvalues) != nx) stop("true values argument is wrong length \n") mat=rbind(tvalues,mat) } cat("Summary of Posterior Marginal Distributions ") cat("\nMoments \n") print(t(mat),digits=2) if(QUANTILES){ qmat=apply(X,2,quantile,probs=c(.025,.05,.5,.95,.975)) colnames(qmat)=names if(!missing(tvalues)) { qmat=rbind(tvalues,qmat)} cat("\nQuantiles \n") print(t(qmat),digits=2)} if(TRAILER) cat(paste(" based on ",nrow(X)," valid draws (burn-in=",burnin,") \n",sep="")) invisible(t(mat)) } bayesm/R/simnhlogit.R0000755000176000001440000000272510225410260014264 0ustar ripleyuserssimnhlogit= function(theta,lnprices,Xexpend) { # function to simulate non-homothetic logit model # creates y a n x 1 vector with indicator of choice (1,...,m) # lnprices is n x m array of log-prices faced # Xexpend is n x d array of variables predicting expenditure # # non-homothetic model specifies ln(psi_i(u))= alpha_i - exp(k_i)u # # structure of theta vector: # alpha (m x 1) # k (m x1 ) # gamma (k x 1) expenditure function coefficients # tau -- scaling of v # root=function(c1,c2,tol,iterlim) { u=double(length(c1)) .C("callroot",as.integer(length(c1)),as.double(c1),as.double(c2),as.double(tol), as.integer(iterlim),r=as.double(u))$r} 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=root(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/rwishart.R0000755000176000001440000000116310225367647013771 0ustar ripleyusersrwishart= function(nu,V){ # # 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) # # m=nrow(V) df=(nu+nu-m+1)-(nu-m+1):nu if(m >1) { T=diag(sqrt(rchisq(c(rep(1,m)),df))) T[lower.tri(T)]=rnorm((m*(m+1)/2-m))} else {T=sqrt(rchisq(1,df))} U=chol(V) C=t(T)%*%U CI=backsolve(C,diag(m)) # # 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! # return(list(W=crossprod(C),IW=crossprod(t(CI)),C=C,CI=CI)) # W is Wishart draw, IW is W^-1 } bayesm/R/runiregGibbs.R0000755000176000001440000000763210571572611014550 0ustar ripleyusersruniregGibbs= function(Data,Prior,Mcmc) { # # revision history: # P. Rossi 1/17/05 # 3/07 added classes # 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 # # 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 # pandterm=function(message) {stop(message,call.=FALSE)} 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$sigmasq)) {sigmasq=var(y)} else {sigmasq=Mcmc$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,fill=TRUE) cat(" ",fill=TRUE) sigmasqdraw=double(floor(Mcmc$R/keep)) betadraw=matrix(double(floor(Mcmc$R*nvar/keep)),ncol=nvar) XpX=crossprod(X) Xpy=crossprod(X,y) sigmasq=as.vector(sigmasq) itime=proc.time()[3] cat("MCMC Iteration (est time to end - min) ",fill=TRUE) fsh() for (rep in 1:Mcmc$R) { # # first draw beta | sigmasq # IR=backsolve(chol(XpX/sigmasq+A),diag(nvar)) btilde=crossprod(t(IR))%*%(Xpy/sigmasq+A%*%betabar) beta = btilde + IR%*%rnorm(nvar) # # now draw sigmasq | beta # res=y-X%*%beta s=t(res)%*%res sigmasq=(nu*ssq + s)/rchisq(1,nu+nobs) sigmasq=as.vector(sigmasq) # # print time to completion and draw # every 100th draw # if(rep%%100 == 0) {ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh()} if(rep%%keep == 0) {mkeep=rep/keep; betadraw[mkeep,]=beta; sigmasqdraw[mkeep]=sigmasq} } ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') attributes(betadraw)$class=c("bayesm.mat","mcmc") attributes(betadraw)$mcpar=c(1,R,keep) attributes(sigmasqdraw)$class=c("bayesm.mat","mcmc") attributes(sigmasqdraw)$mcpar=c(1,R,keep) return(list(betadraw=betadraw,sigmasqdraw=sigmasqdraw)) } bayesm/R/runireg.R0000755000176000001440000000760610571572621013603 0ustar ripleyusersrunireg= function(Data,Prior,Mcmc) { # # revision history: # P. Rossi 1/17/05 # revised 9/05 to put in Data,Prior,Mcmc calling convention # 3/07 added classes # Purpose: # perform iid draws from posterior of regression model using # conjugate prior # # Arguments: # Data -- list of data # y,X # Prior -- list of prior hyperparameters # betabar,A prior mean, prior precision # nu, ssq prior on sigmasq # Mcmc -- list of MCMC parms # R number of draws # keep -- thinning parameter # # Output: # list of beta, sigmasq # # Model: # y = Xbeta + e e ~N(0,sigmasq) # y is n x 1 # X is n x k # beta is k x 1 vector of coefficients # # Priors: beta ~ N(betabar,sigmasq*A^-1) # sigmasq ~ (nu*ssq)/chisq_nu # # # check arguments # pandterm=function(message) {stop(message,call.=FALSE)} if(missing(Data)) {pandterm("Requires Data argument -- list of y and X")} if(is.null(Data$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$keep} } # # print out problem # cat(" ", fill=TRUE) cat("Starting IID Sampler for Univariate Regression Model",fill=TRUE) cat(" with ",nobs," observations",fill=TRUE) cat(" ", fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat("A",fill=TRUE) print(A) cat("nu = ",nu," ssq= ",ssq,fill=TRUE) cat(" ", fill=TRUE) cat("MCMC parms: ",fill=TRUE) cat("R= ",R," keep= ",keep,fill=TRUE) cat(" ",fill=TRUE) sigmasqdraw=double(floor(Mcmc$R/keep)) betadraw=matrix(double(floor(Mcmc$R*nvar/keep)),ncol=nvar) itime=proc.time()[3] cat("IID Iteration (est time to end - min) ",fill=TRUE) fsh() for (rep in 1:Mcmc$R){ # # first draw Sigma # RA=chol(A) W=rbind(X,RA) z=c(y,as.vector(RA%*%betabar)) IR=backsolve(chol(crossprod(W)),diag(nvar)) # W'W=R'R ; (W'W)^-1 = IR IR' -- this is UL decomp btilde=crossprod(t(IR))%*%crossprod(W,z) res=z-W%*%btilde s=t(res)%*%res # # first draw Sigma # # sigmasq=(nu*ssq + s)/rchisq(1,nu+nobs) # # now draw beta given Sigma # beta = btilde + as.vector(sqrt(sigmasq))*IR%*%rnorm(nvar) # # print time to completion and draw # every 100th draw # if(rep%%100 == 0) {ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh()} if(rep%%keep == 0) {mkeep=rep/keep; betadraw[mkeep,]=beta; sigmasqdraw[mkeep]=sigmasq} } ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') attributes(betadraw)$class=c("bayesm.mat","mcmc") attributes(betadraw)$mcpar=c(1,R,keep) attributes(sigmasqdraw)$class=c("bayesm.mat","mcmc") attributes(sigmasqdraw)$mcpar=c(1,R,keep) return(list(betadraw=betadraw,sigmasqdraw=sigmasqdraw)) } bayesm/R/rtrun.R0000755000176000001440000000044310225374047013270 0ustar ripleyusersrtrun= function(mu,sigma,a,b){ # # function to draw from univariate truncated norm # a is vector of lower bounds for truncation # b is vector of upper bounds for truncation # FA=pnorm(((a-mu)/sigma)) FB=pnorm(((b-mu)/sigma)) return(mu+sigma*qnorm(runif(length(mu))*(FB-FA)+FA)) } bayesm/R/rsurGibbs.R0000755000176000001440000001224610571644366014074 0ustar ripleyusersrsurGibbs= function(Data,Prior,Mcmc) { # # revision history: # P. Rossi 9/05 # 3/07 added classes # 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 # # 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 # pandterm=function(message) {stop(message,call.=FALSE)} 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]]$y)} } indreg[nreg+1]=nvar+1 # # check for Prior # if(missing(Prior)) { betabar=c(rep(0,nvar)); A=.01*diag(nvar); nu=nreg+3; V=nu*diag(nreg)} else { if(is.null(Prior$betabar)) {betabar=c(rep(0,nvar))} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=.01*diag(nvar)} else {A=Prior$A} if(is.null(Prior$nu)) {nu=nreg+3} 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=1} else {keep=Mcmc$keep} } # # print out problem # cat(" ", fill=TRUE) cat("Starting Gibbs Sampler for SUR Regression Model",fill=TRUE) cat(" with ",nreg," regressions",fill=TRUE) cat(" and ",nobs," observations for each regression",fill=TRUE) cat(" ", fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat("A",fill=TRUE) print(A) cat("nu = ",nu,fill=TRUE) cat("V = ",fill=TRUE) print(V) cat(" ", fill=TRUE) cat("MCMC parms: ",fill=TRUE) cat("R= ",R," keep= ",keep,fill=TRUE) cat(" ",fill=TRUE) Sigmadraw=matrix(double(floor(R*nreg*nreg/keep)),ncol=nreg*nreg) betadraw=matrix(double(floor(R*nvar/keep)),ncol=nvar) # # set initial value of Sigma # E=matrix(double(nobs*nreg),ncol=nreg) for (reg in 1:nreg) { E[,reg]=lm(y~.-1,data=data.frame(y=regdata[[reg]]$y,regdata[[reg]]$X))$residuals } Sigma=crossprod(E)/nobs L=t(backsolve(chol(Sigma),diag(nreg))) Y=y dim(Y)=c(nobs,nreg) Xti=matrix(0,ncol=nvar,nrow=nreg*nobs) itime=proc.time()[3] cat("MCMC Iteration (est time to end - min) ",fill=TRUE) fsh() for (rep in 1:R) { # # first draw beta | Sigma # # compute Xtilde # for (reg in 1:nreg){ Xti[,indreg[reg]:(indreg[reg+1]-1)]=L[,reg]%x%regdata[[reg]]$X } IR=backsolve(chol(crossprod(Xti)+A),diag(nvar)) # # compute ytilde yti=as.vector(Y%*%t(L)) btilde=crossprod(t(IR))%*%(crossprod(Xti,yti)+A%*%betabar) beta = btilde + IR%*%rnorm(nvar) # # now draw Sigma | beta # for(reg in 1:nreg){ E[,reg]=regdata[[reg]]$y-regdata[[reg]]$X%*%beta[indreg[reg]:(indreg[reg+1]-1)] } Sigma=rwishart(nu+nobs,chol2inv(chol(crossprod(E)+V)))$IW L=t(backsolve(chol(Sigma),diag(nreg))) # # print time to completion and draw # every 100th draw # if(rep%%100 == 0) {ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh()} if(rep%%keep == 0) {mkeep=rep/keep; betadraw[mkeep,]=beta; Sigmadraw[mkeep,]=Sigma} } ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') attributes(betadraw)$class=c("bayesm.mat","mcmc") attributes(betadraw)$mcpar=c(1,R,keep) attributes(Sigmadraw)$class=c("bayesm.var","bayesm.mat","mcmc") attributes(Sigmadraw)$mcpar=c(1,R,keep) return(list(betadraw=betadraw,Sigmadraw=Sigmadraw)) } bayesm/R/rscaleUsage.R0000755000176000001440000003566710572125345014374 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 Lamda # 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 # printevery: how often to print out how many draws are done # e,y,mu,Sigma,sigma,tau,Lamda: 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,Lamda21,Lamda12,Lamda22) # # define functions needed # # ----------------------------------------------------------------------------------- rlpx = function(x,e,k,mu,tau,Sigma,sigma,nd=500) { n=nrow(x); p = ncol(x) cc = cgetC(e,k) L=t(chol(Sigma)) lpv = rep(0,n) offset = p*log(k) for(i in 1:n) { Li = sigma[i]*L a = cc[x[i,]]-mu-tau[i]; b = cc[x[i,]+1]-mu-tau[i] ghkres = rghk(Li,a,b,nd) lghkres = log(ghkres) if(is.nan(lghkres)) { #print("nan in ghk:") #print(paste('ghkres: ',ghkres)) lghkres = log(1e-320) } if(is.infinite(lghkres)) { #print("infinite in ghk:") #print(paste('ghkres: ',ghkres)) lghkres = log(1e-320) } lpv[i] = lghkres + offset } sum(lpv) } rghk = function(L,a,b,nd) { .C('ghk',as.double(L),as.double(a),as.double(b),as.integer(nrow(L)), as.integer(nd),res=double(1))$res } condd = function(Sigma) { p = nrow(Sigma) Si = solve(Sigma) cbeta = matrix(0,p-1,p) for(i in 1:p) { ind = (1:p)[-i] cbeta[,i] = -Si[ind,i]/Si[i,i] } list(beta=cbeta,s=sqrt(1/diag(Si))) } pandterm = function(message) { stop(paste("in rscaleUsage: ",message),call.=FALSE) } myin = function(i,ind) {i %in% ind} getS = function(Lam,n,moms) { S=matrix(0.0,2,2) S[1,1] = (n-1)*moms[3] + n*moms[1]^2 S[1,2] = (n-1)*moms[4] + n*moms[1]*(moms[2]-Lam[2,2]) S[2,1] = S[1,2] S[2,2] = (n-1)*moms[5] + n*(moms[2]-Lam[2,2])^2 S } llL = function(Lam,n,S,V,nu) { dlam = Lam[1,1]*Lam[2,2]-Lam[1,2]^2 M = (S+V) %*% chol2inv(chol(Lam)) ll = -.5*(n+nu+3)*log(dlam) -.5*sum(diag(M)) } ispd = function(mat,d=nrow(mat)) { if(!is.matrix(mat)) { res = FALSE } else if(!((nrow(mat)==d) & (ncol(mat)==d))) { res = FALSE } else { diff = (t(mat)+mat)/2 - mat perdiff = sum(diff^2)/sum(mat^2) res = ((det(mat)>0) & (perdiff < 1e-10)) } res } #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ # print out components of inputs ---------------------------------------------- cat('\nIn function rscaleUsage\n\n') if(!missing(Data)) { cat(' Data has components: ') cat(paste(names(Data),collapse=' ')[1],'\n') } if(!missing(Prior)) { cat(' Prior has components: ') cat(paste(names(Prior),collapse=' ')[1],'\n') } if(!missing(Mcmc)) { cat(' Mcmc has components: ') cat(paste(names(Mcmc),collapse=' ')[1],'\n') } cat('\n') # ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ # process Data argument -------------------------- if(missing(Data)) {pandterm("Requires Data argument - list of k=question scale and x = data")} if(is.null(Data$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 = as.integer(1000) keep = as.integer(1) ndghk= as.integer(100) printevery = as.integer(10) 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$printevery)) { printevery = as.integer(Mcmc$printevery) } } 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(printevery<1) { pandterm('printevery must be positive') } #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) #Lamda = matrix(c(3.7,-.22,-.22,.32),ncol=2) #Lamda = matrix(c((k/4)^2,(k/4)*.5*(-.2),0,.25),nrow=2); Lamda[1,2]=Lamda[2,1] Lamda = 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$Lambda)) { Lamda = Mcmc$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(Lamda,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(!is.vector(tau)) { pandterm('tau must be a vector') } 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 doLamda=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$doLambda)) { doLamda = Mcmc$doLambda } if(!is.null(Mcmc$doe)) { doe = Mcmc$doe } } #++++++++++++++++++++++++++++++++++++++ #process Prior argument ---------------------------------- nu = p+3 V= nu*diag(p) mubar = matrix(rep(k/2,p),ncol=1) Am = .0001*diag(p) gs = 200 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)*Lamda 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)*Lamda } 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,printevery: ', R,keep,ndghk,printevery,'\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: ',doLamda,'\n') #++++++++++++++++++++++++++++++++++++++++++++ nk = floor(R/keep) ndpost = nk*keep drSigma=matrix(0.0,nk,p^2) drmu = matrix(0.0,nk,p) drtau = matrix(0.0,nk,n) drsigma = matrix(0.0,nk,n) drLamda = matrix(0.0,nk,4) dre = rep(0,nk) itime = proc.time()[3] cat("Mcmc Iteration (est time to end - min)",'\n') for(rep in 1:ndpost) { if(1) { # y cc = cgetC(e,k) bs = condd(Sigma) y = matrix(.C('dy',as.integer(p),as.integer(n),y=as.double(t(y)),as.integer(t(x)),as.double(cc),as.double(mu),as.double(bs$beta),as.double(bs$s), as.double(tau),as.double(sigma))$y,ncol=p,byrow=TRUE) } if(doSigma) { #Sigma Res = (t(t(y)-mu)-tau)/sigma S = crossprod(Res) Sigma = rwishart(nu+n,chol2inv(chol(V+S)))$IW } if(domu) { #mu yd = y-tau Si = chol2inv(chol(Sigma)) Vmi = sum(1/sigma^2)*Si + Am R = chol(Vmi) Ri = backsolve(R,diag(p)) Vm = chol2inv(chol(Vmi)) mm = Vm %*% (Si %*% (t(yd) %*% matrix(1/sigma^2,ncol=1)) + Am %*% mubar) mu = as.vector(mm + Ri %*% matrix(rnorm(p),ncol=1)) } if(dotau) { #tau Ai = Lamda[1,1] - (Lamda[1,2]^2)/Lamda[2,2] A = 1.0/Ai onev = matrix(1.0,p,1) R = chol(Sigma) xx = backsolve(R,onev,transpose=TRUE) yy = backsolve(R,t(y)-mu,transpose=TRUE) xtx = sum(xx^2) xty = as.vector(t(xx) %*% yy) beta = A*Lamda[1,2]/Lamda[2,2] for(j in 1:n) { s2 = xtx/sigma[j]^2 + A s2 = 1.0/s2 m = s2*((xty[j]/sigma[j]^2) + beta*(log(sigma[j])-Lamda[2,2])) tau[j] = m + sqrt(s2)*rnorm(1) } } if(dosigma) { #sigma R = chol(Sigma) eps = backsolve(R,t(y-tau)-mu,transpose=TRUE) ete = as.vector(matrix(rep(1,p),nrow=1) %*% eps^2) a= Lamda[2,2] b= Lamda[1,2]/Lamda[1,1] s=sqrt(Lamda[2,2]-(Lamda[1,2]^2/Lamda[1,1])) for(j in 1:n) { pv = -(p+1)*log(gsigma) -.5*ete[j]/gsigma^2 -.5*((log(gsigma)-(a+b*tau[j]))/s)^2 pv = exp(pv-max(pv)) pv = pv/sum(pv) sigma[j] = sample(gsigma,size=1,prob=pv) } } if(doLamda) { # Lamda h=log(sigma) dat = cbind(tau,h) temp = var(dat) moms = c(mean(tau),mean(h),temp[1,1],temp[1,2],temp[2,2]) SS = getS(Lamda,n,moms) rgl11 = gl11[gl11 > (Lamda[1,2]^2/Lamda[2,2])] ng = length(rgl11) pv = rep(0,ng) for(j in 1:ng) { Lamda[1,1] = rgl11[j] pv[j] = llL(Lamda,n,SS,VL,nuL) } pv = exp(pv-max(pv)); pv = pv/sum(pv) Lamda[1,1] = sample(rgl11,size=1,prob=pv) rgl12 = gl12[(gl12-sqrt(Lamda[1,1]*Lamda[2,2]))] ng = length(rgl12) pv = rep(0,ng) for(j in 1:ng) { Lamda[1,2] = rgl12[j]; Lamda[2,1]=Lamda[1,2] pv[j] = llL(Lamda,n,SS,VL,nuL) } pv = exp(pv-max(pv)); pv = pv/sum(pv) Lamda[1,2] = sample(rgl12,size=1,prob=pv) Lamda[2,1]=Lamda[1,2] rgl22 = gl22[gl22 > (Lamda[1,2]^2/Lamda[1,1])] ng = length(rgl22) pv = rep(0,ng) for(j in 1:ng) { Lamda[2,2] = rgl22[j] SS = getS(Lamda,n,moms) pv[j] = llL(Lamda,n,SS,VL,nuL) } pv = exp(pv-max(pv)); pv = pv/sum(pv) Lamda[2,2] = sample(rgl22,size=1,prob=pv) } if(doe) { # e ng = length(ge) ei = which.min(abs(e-ge)) if(ei==1) { pi =2 qr = .5 } else if(ei==ng) { pi = ng-1 qr = .5 } else { pi = ei + rbinom(1,1,.5)*2-1 qr = 1 } eold = ge[ei] eprop = ge[pi] llold = rlpx(x,eold,k,mu,tau,Sigma,sigma,ndghk) llprop = rlpx(x,eprop,k,mu,tau,Sigma,sigma,ndghk) lrat = llprop - llold + log(qr) if(lrat>0) { e = eprop } else { paccept = min(1,exp(lrat)) e = ifelse(rbinom(1,1,paccept),eprop,eold) } } mkeep = rep/keep if(mkeep == floor(mkeep)) { drSigma[mkeep,] = Sigma drmu[mkeep,] = mu drtau[mkeep,] = tau drsigma[mkeep,] = sigma drLamda[mkeep,] = Lamda dre[mkeep] = e } if((rep/printevery)==floor(rep/printevery)) { ctime = proc.time()[3] timetoend = ((ctime-itime)/rep)*(ndpost-rep) cat(rep,' (', round(timetoend/60,1), ') \n') fsh() } } ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') R=ndpost mudraw=drmu; taudraw=drtau; sigmadraw=drsigma; Lambdadraw=drLamda; edraw=dre; Sigmadraw=drSigma attributes(mudraw)$class=c("bayesm.mat","mcmc") attributes(mudraw)$mcpar=c(1,R,keep) attributes(taudraw)$class=c("bayesm.mat","mcmc") attributes(taudraw)$mcpar=c(1,R,keep) attributes(sigmadraw)$class=c("bayesm.mat","mcmc") attributes(sigmadraw)$mcpar=c(1,R,keep) attributes(Lambdadraw)$class=c("bayesm.mat","mcmc") attributes(Lambdadraw)$mcpar=c(1,R,keep) attributes(edraw)$class=c("bayesm.mat","mcmc") attributes(edraw)$mcpar=c(1,R,keep) attributes(Sigmadraw)$class=c("bayesm.var","bayesm.mat","mcmc") attributes(Sigmadraw)$mcpar=c(1,R,keep) return(list(Sigmadraw=Sigmadraw,mudraw=mudraw,taudraw = taudraw, sigmadraw=sigmadraw,Lambdadraw=Lambdadraw,edraw=edraw)) } bayesm/R/rordprobitGibbs.R0000755000176000001440000002113610576270576015270 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 # 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 # breg1= function(root,X,y,Abetabar) { # # p.rossi 12/04 # # Purpose: draw from posterior for linear regression, sigmasq=1.0 # # Arguments: # root is chol((X'X+A)^-1) # Abetabar = A*betabar # # Output: draw from posterior # # Model: y = Xbeta + e e ~ N(0,I) # Prior: beta ~ N(betabar,A^-1) # cov=crossprod(root,root) betatilde=cov%*%(crossprod(X,y)+Abetabar) betatilde+t(root)%*%rnorm(length(betatilde)) } # # 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))) } dstarRwMetrop= function(y,mu,olddstar,s,inc.root,dstarbar,oldll,rootdi){ # # function to execute rw metropolis for the dstar # y is n vector with element = 1,...,j # X is n x k matrix of x values # RW increments are N(0,s^2*t(inc.root)%*%inc.root) # prior on dstar is N(dstarbar,Sigma) Sigma^-1=rootdi*t(rootdi) # inc.root, rootdi are upper triangular # this means that we are using the UL decomp of Sigma^-1 for prior # olddstar is the current stay=0 dstarc=olddstar + s*t(inc.root)%*%(matrix(rnorm(ncut),ncol=1)) cll=lldstar(dstarc,y,mu) clpost=cll+lndMvn(dstarc,dstarbar,rootdi) ldiff=clpost-oldll-lndMvn(olddstar,dstarbar,rootdi) alpha=min(1,exp(ldiff)) if(alpha < 1) {unif=runif(1)} else {unif=0} if (unif <= alpha) {dstardraw=dstarc; oldll=cll} else {dstardraw=olddstar; stay=1} return(list(dstardraw=dstardraw,oldll=oldll, stay=stay)) } pandterm=function(message) {stop(message,call.=FALSE)} # # ---------------------------------------------------------------------- # # 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=.01*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$A)) {A=.01*diag(nvar)} else {A=Prior$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$keep)) {keep=1} else {keep=Mcmc$keep} if(is.null(Mcmc$s)) {s=2.93/sqrt(ndstar)} else {s=Mcmc$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,"s= ",s, fill=TRUE) cat(" ",fill=TRUE) betadraw=matrix(double(floor(R/keep)*nvar),ncol=nvar) cutdraw=matrix(double(floor(R/keep)*ncuts),ncol=ncuts) dstardraw=matrix(double(floor(R/keep)*ndstar),ncol=ndstar) staydraw=array(0,dim=c(R/keep)) sigma=c(rep(1,nrow(X))) root=chol(chol2inv(chol((crossprod(X,X)+A)))) Abetabar=crossprod(A,betabar) rootdi=chol(chol2inv(chol(Ad))) # 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$hessian+Ad)))) # chol((H+Ad)^-1) # set initial values for MCMC olddstar = c(rep(0,ndstar)) beta = betahat cutoffs = dstartoc (olddstar) oldll = lldstar(olddstar,y,mu=X%*%betahat) # # # start main iteration loop # itime=proc.time()[3] cat("MCMC Iteration (est time to end - min) ",fill=TRUE) fsh() # print time to completion and draw # every 100th draw # for (rep in 1:R) { # draw z given beta(i-1), sigma, y, cut-offs z = rtrun (X%*%beta, sigma=sigma, a=cutoffs[y] , b=cutoffs[y+1]) # draw beta given z and rest beta= breg1(root,X,z, Abetabar) # draw gamma given z metropout = dstarRwMetrop(y,X%*%beta,olddstar,s,inc.root,dstarbar,oldll,rootdi) olddstar = metropout$dstardraw oldll = metropout$oldll cutoffs = dstartoc (olddstar) stay = metropout$stay # print time to completion and draw # every 100th draw if(rep%%100 == 0) {ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh()} if(rep%%keep == 0) {mkeep=rep/keep; cutdraw[mkeep,]=cutoffs; dstardraw[mkeep,]=olddstar;betadraw[mkeep,]=beta;staydraw[mkeep]=stay } } accept=1-sum(staydraw)/(R/keep) ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') cutdraw=cutdraw[,2:k] attributes(cutdraw)$class="bayesm.mat" attributes(betadraw)$class="bayesm.mat" attributes(dstardraw)$class="bayesm.mat" attributes(cutdraw)$mcpar=c(1,R,keep) attributes(betadraw)$mcpar=c(1,R,keep) attributes(dstardraw)$mcpar=c(1,R,keep) return(list(cutdraw=cutdraw,betadraw=betadraw, dstardraw=dstardraw, accept=accept)) } bayesm/R/rnmixGibbs.R0000755000176000001440000001371411071420671014222 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 # # 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 and keep (thinning parameter) # 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 # pandterm=function(message) {stop(message,call.=FALSE)} # # ----------------------------------------------------------------------------------------- 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(c(.01),ncol=1)} else {A=Prior$A} if(is.null(Prior$nu)) {nu=dimy+2} 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(5,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=1} else {keep=Mcmc$keep} if(is.null(Mcmc$LogLike)) {LogLike=FALSE} else {LogLike=Mcmc$LogLike} } # # print out the problem # cat(" Starting Gibbs Sampler for Mixture of Normals",fill=TRUE) cat(" ",nobs," observations on ",dimy," dimensional data",fill=TRUE) cat(" using ",ncomp," mixture components",fill=TRUE) cat(" ",fill=TRUE) cat(" Prior Parms: ",fill=TRUE) cat(" mu_j ~ N(mubar,Sigma (x) A^-1)",fill=TRUE) cat(" mubar = ",fill=TRUE) print(Mubar) cat(" precision parm for prior variance of mu vectors (A)= ",A,fill=TRUE) cat(" Sigma_j ~ IW(nu,V) nu= ",nu,fill=TRUE) cat(" V =",fill=TRUE) print(V) cat(" Dirichlet parameters ",fill=TRUE) print(a) cat(" ",fill=TRUE) cat(" Mcmc Parms: R= ",R," keep= ",keep," LogLike= ",LogLike,fill=TRUE) pdraw=matrix(double(floor(R/keep)*ncomp),ncol=ncomp) zdraw=matrix(double(floor(R/keep)*nobs),ncol=nobs) compdraw=list() compsd=list() if(LogLike) ll=double(floor(R/keep)) # # set initial values of z # z=rep(c(1:ncomp),(floor(nobs/ncomp)+1)) z=z[1:nobs] cat(" ",fill=TRUE) cat("starting value for z",fill=TRUE) print(table(z)) cat(" ",fill=TRUE) p=c(rep(1,ncomp))/ncomp # note this is not used # # start main iteration loop # itime=proc.time()[3] cat("MCMC Iteration (est time to end -min) ",fill=TRUE) fsh() for(rep in 1:R) { out = rmixGibbs(y,Mubar,A,nu,V,a,p,z,compsd) compsd=out$comps p=out$p z=out$z if(rep%%100==0) { ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh() } if(rep%%keep ==0) { mkeep=rep/keep pdraw[mkeep,]=p zdraw[mkeep,]=z compdraw[[mkeep]]=compsd if(LogLike) ll[mkeep]=llnmix(y,z,compsd) } } ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') nmix=list(probdraw=pdraw,zdraw=zdraw,compdraw=compdraw) attributes(nmix)$class="bayesm.nmix" if(LogLike) {return(list(ll=ll,nmix=nmix))} else {return(list(nmix=nmix))} } bayesm/R/rnegbinRw.R0000755000176000001440000001526411754550760014070 0ustar ripleyusersrnegbinRw = function(Data, Prior, Mcmc) { # Revision History # Sridhar Narayanan - 05/2005 # P. Rossi 6/05 # 3/07 added classes # # 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) # 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 # # # 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)) } lpostbetai = function(beta, alpha, X, y, betabar, A) { # Computes the unnormalized log posterior for beta lambda = exp(X %*% beta) p = alpha/(alpha + lambda) residual = as.vector(beta - betabar) sum(alpha * log(p) + y * log(1-p)) - 0.5*( t(residual)%*%A%*%residual) } lpostalpha = function(alpha, beta, X,y, a, b) { # Computes the unnormalized log posterior for alpha sum(log(dnbinom(y,size=alpha,mu=exp(X%*%beta)))) + (a-1)*log(alpha) - b* alpha } # # Error Checking # pandterm=function(message) {stop(message,call.=FALSE)} 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$y} nvar = ncol(X) if (length(y) != nrow(X)) {pandterm("Mismatch in the number of observations in X and y")} nobs=length(y) # # check for prior elements # if(missing(Prior)) { betabar=rep(0,nvar); A=0.01*diag(nvar) ; a=0.5; b=0.1; } else { if(is.null(Prior$betabar)) {betabar=rep(0,nvar)} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=0.01*diag(nvar)} else {A=Prior$A} if(is.null(Prior$a)) {a=0.5} else {a=Prior$a} if(is.null(Prior$b)) {b=0.1} 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=1} else {keep=Mcmc$keep} if(is.null(Mcmc$s_alpha)) {cat("Using default s_alpha = 2.93",fill=TRUE); s_alpha=2.93} 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=2.93/sqrt(nvar)} else {s_beta = Mcmc$s_beta} # # print out problem # cat(" ",fill=TRUE) cat("Starting Random Walk Metropolis Sampler for Negative Binomial Regression",fill=TRUE) cat(" ",nobs," obs; ",nvar," covariates (including intercept); ",fill=TRUE) cat("Prior Parameters:",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat("A",fill=TRUE) print(A) cat("a",fill=TRUE) print(a) cat("b",fill=TRUE) print(b) cat(" ",fill=TRUE) cat("MCMC Parms: ",fill=TRUE) cat(" ",R," reps; keeping every ",keep,"th draw",fill=TRUE) cat("s_alpha = ",s_alpha,fill=TRUE) cat("s_beta = ",s_beta,fill=TRUE) cat(" ",fill=TRUE) par = rep(0,(nvar+1)) cat(" Initializing RW Increment Covariance Matrix...",fill=TRUE) fsh() mle = optim(par,llnegbin, X=X, y=y, nvar=nvar, method="L-BFGS-B", upper=c(Inf,Inf,Inf,log(100000000)), hessian=TRUE, control=list(fnscale=-1)) fsh() beta_mle=mle$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)) 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() oldlpostbeta = 0 nacceptbeta = 0 nacceptalpha = 0 clpostbeta = 0 alphadraw = rep(0,floor(R/keep)) betadraw=matrix(double(floor(R/keep)*(nvar)),ncol=nvar) llike=rep(0,floor(R/keep)) # # start main iteration loop # itime=proc.time()[3] cat(" ",fill=TRUE) cat("MCMC Iteration (est time to end - min) ",fill=TRUE) fsh() for (r in 1:R) { # Draw beta betac = beta + betaroot%*%rnorm(nvar) oldlpostbeta = lpostbetai(beta, alpha, X, y, betabar,A) clpostbeta = lpostbetai(betac, alpha, X, y, betabar,A) ldiff=clpostbeta-oldlpostbeta acc=min(1,exp(ldiff)) if(acc < 1) {unif=runif(1)} else {unif=0} if (unif <= acc) { beta=betac nacceptbeta=nacceptbeta+1 } # Draw alpha logalphac = rnorm(1,mean=log(alpha), sd=alphacroot) oldlpostalpha = lpostalpha(alpha, beta, X, y, a, b) clpostalpha = lpostalpha(exp(logalphac), beta, X, y, a, b) ldiff=clpostalpha-oldlpostalpha acc=min(1,exp(ldiff)) if(acc < 1) {unif=runif(1)} else {unif=0} if (unif <= acc) { alpha=exp(logalphac) nacceptalpha=nacceptalpha+1 } if(r%%100 == 0) {ctime=proc.time()[3] timetoend=((ctime-itime)/r)*(R-r) cat(" ",r," (",round(timetoend/60,1),")",fill=TRUE) fsh()} if(r%%keep == 0) { mkeep=r/keep betadraw[mkeep,]=beta alphadraw[mkeep] = alpha llike[mkeep]=llnegbin(c(beta,alpha),X,y,nvar) } } ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') attributes(betadraw)$class=c("bayesm.mat","mcmc") attributes(betadraw)$mcpar=c(1,R,keep) attributes(alphadraw)$class=c("bayesm.mat","mcmc") attributes(alphadraw)$mcpar=c(1,R,keep) return(list(llike=llike,betadraw=betadraw,alphadraw=alphadraw, acceptrbeta=nacceptbeta/R*100,acceptralpha=nacceptalpha/R*100)) } bayesm/R/rmvst.R0000755000176000001440000000035210225373225013265 0ustar ripleyusersrmvst= function(nu,mu,root){ # # function to draw from MV s-t with nu df, mean mu, Sigma=t(root)%*%root # root is upper triangular cholesky root nvec=t(root)%*%rnorm(length(mu)) return(nvec/sqrt(rchisq(1,nu)/nu) + mu) } bayesm/R/rmvpGibbs.R0000755000176000001440000001401210571567422014053 0ustar ripleyusersrmvpGibbs= function(Data,Prior,Mcmc) { # # Revision History: # modified by rossi 12/18/04 to include error checking # 3/07 added classes # # 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 # # 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 # pandterm=function(message) {stop(message,call.=FALSE)} 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=.01*diag(k) ; nu=p+3; V=nu*diag(p)} else {if(is.null(Prior$betabar)) {betabar=rep(0,k)} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=.01*diag(k)} else {A=Prior$A} if(is.null(Prior$nu)) {nu=p+3} else {nu=Prior$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$keep)) {keep=1} else {keep=Mcmc$keep} # # 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(" ",R," reps; keeping every ",keep,"th draw",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= ",R,fill=TRUE) cat("initial beta= ",beta0,fill=TRUE) cat("initial sigma= ",fill=TRUE) print(sigma0) cat(" ",fill=TRUE) # # allocate space for draws # sigmadraw=matrix(double(floor(R/keep)*p*p),ncol=p*p) betadraw=matrix(double(floor(R/keep)*k),ncol=k) wnew=double(nrow(X)) betanew=double(k) # # set initial values of w,beta, sigma (or root of inv) # wold=c(rep(0,nrow(X))) betaold=beta0 C=chol(solve(sigma0)) # # C is upper triangular root of sigma^-1 (G) = C'C # # create functions needed # drawwMvpC=function(w,mu,y,sigi) { p=ncol(sigi) .C("draww_mvp",w=as.double(w),as.double(mu),as.double(sigi), as.integer(length(w)/p),as.integer(p),as.integer(y))$w} drawwMvp= function(w,X,y,beta,sigmai){ # # draw latent vector # # w is n x (p-1) vector # X ix n(p-1) x k matrix # y is n x (p-1) vector of binary (0,1) outcomes # beta is k x 1 vector # sigmai is (p-1) x (p-1) # Xbeta=as.vector(X%*%beta) drawwMvpC(w,Xbeta,y,sigmai) } itime=proc.time()[3] cat("MCMC Iteration (est time to end - min) ",fill=TRUE) for (rep in 1:R) { # # draw w given beta(rep-1),sigma(rep-1) # sigmai=crossprod(C) wnew=drawwMvp(wold,X,y,betaold,sigmai) # # draw beta given w(rep) and sigma(rep-1) # # note: if Sigma^-1 (G) = C'C then Var(Ce)=CSigmaC' = I # first, transform w_i = X_ibeta + e_i by premultiply by C # zmat=matrix(cbind(wnew,X),nrow=p) zmat=C%*%zmat zmat=matrix(zmat,nrow=nrow(X)) betanew=breg(zmat[,1],zmat[,2:(k+1)],betabar,A) # # draw sigmai given w and beta # epsilon=matrix((wnew-X%*%betanew),nrow=p) S=crossprod(t(epsilon)) W=rwishart(nu+n,chol2inv(chol(V+S))) C=W$C # # print time to completion and draw # every 100th draw # if(rep%%100 == 0) {ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R+1-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh()} # # save every keepth draw # if(rep%%keep ==0) {mkeep=rep/keep betadraw[mkeep,]=betanew sigmadraw[mkeep,]=as.vector(W$IW)} wold=wnew betaold=betanew } ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') attributes(betadraw)$class=c("bayesm.mat","mcmc") attributes(betadraw)$mcpar=c(1,R,keep) attributes(sigmadraw)$class=c("bayesm.var","bayesm.mat","mcmc") attributes(sigmadraw)$mcpar=c(1,R,keep) return(list(betadraw=betadraw,sigmadraw=sigmadraw)) } bayesm/R/rmultireg.R0000755000176000001440000000334410225367470014135 0ustar ripleyusersrmultireg= function(Y,X,Bbar,A,nu,V) { # # revision history: # changed 1/11/05 by P. Rossi to fix sum of squares error # # purpose: # draw from posterior for Multivariate Regression Model with # natural conjugate prior # arguments: # Y is n x m matrix # X is n x k # Bbar is the prior mean of regression coefficients (k x m) # A is prior precision matrix # nu, V are parameters for prior on Sigma # output: # list of B, Sigma draws of matrix of coefficients and Sigma matrix # model: # Y=XB+U cov(u_i) = Sigma # B is k x m matrix of coefficients # priors: beta|Sigma ~ N(betabar,Sigma (x) A^-1) # betabar=vec(Bbar) # beta = vec(B) # Sigma ~ IW(nu,V) or Sigma^-1 ~ W(nu, V^-1) n=nrow(Y) m=ncol(Y) k=ncol(X) # # first draw Sigma # RA=chol(A) W=rbind(X,RA) Z=rbind(Y,RA%*%Bbar) # note: Y,X,A,Bbar must be matrices! IR=backsolve(chol(crossprod(W)),diag(k)) # W'W = R'R & (W'W)^-1 = IRIR' -- this is the UL decomp! Btilde=crossprod(t(IR))%*%crossprod(W,Z) # IRIR'(W'Z) = (X'X+A)^-1(X'Y + ABbar) S=crossprod(Z-W%*%Btilde) # E'E rwout=rwishart(nu+n,chol2inv(chol(V+S))) # # now draw B given Sigma # note beta ~ N(vec(Btilde),Sigma (x) Covxxa) # Cov=(X'X + A)^-1 = IR t(IR) # Sigma=CICI' # therefore, cov(beta)= Omega = CICI' (x) IR IR' = (CI (x) IR) (CI (x) IR)' # so to draw beta we do beta= vec(Btilde) +(CI (x) IR)vec(Z_mk) # Z_mk is m x k matrix of N(0,1) # since vec(ABC) = (C' (x) A)vec(B), we have # B = Btilde + IR Z_mk CI' # B = Btilde + IR%*%matrix(rnorm(m*k),ncol=m)%*%t(rwout$CI) return(list(B=B,Sigma=rwout$IW)) } bayesm/R/rmnpGibbs.R0000755000176000001440000001421010571567315014044 0ustar ripleyusersrmnpGibbs= function(Data,Prior,Mcmc) { # # Revision History: # modified by rossi 12/18/04 to include error checking # 3/07 added classes # # purpose: Gibbs MNP model with full covariance matrix # # Arguments: # Data contains # p the number of choice alternatives # y -- a vector of length n with choices (takes on values from 1, .., p) # X -- n(p-1) x k matrix of covariates (including intercepts) # note: X is the differenced matrix unlike MNL X=stack(X_1,..,X_n) # each X_i is (p-1) x nvar # # Prior contains a list of (betabar, A, nu, V) # if elements of prior do not exist, defaults are used # # Mcmc is a list of (beta0,sigma0,R,keep) # beta0,sigma0 are intial values, if not supplied defaults are used # R is number of draws # keep is thinning parm, keep every keepth draw # # Output: a list of every keepth betadraw and sigmsdraw # # model: # w_i = X_ibeta + e e~N(0,Sigma) note w_i,e are (p-1) x 1 # y_i = j if w_ij > w_i-j j=1,...,p-1 # y_i = p if all w_i < 0 # # priors: # beta ~ N(betabar,A^-1) # Sigma ~ IW(nu,V) # # Check arguments # pandterm=function(message) {stop(message,call.=FALSE)} if(missing(Data)) {pandterm("Requires Data argument -- list of p, y, X")} if(is.null(Data$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$X # # check data for validity # levely=as.numeric(levels(as.factor(y))) if(length(levely) != p) {pandterm(paste("y takes on ",length(levely), " values -- must be ",p))} bady=FALSE for (i in 1:p) { if(levely[i] != i) bady=TRUE } cat("Table of y values",fill=TRUE) print(table(y)) if (bady) {pandterm("Invalid y")} n=length(y) k=ncol(X) pm1=p-1 if(nrow(X)/n != pm1) {pandterm(paste("X has ",nrow(X)," rows; must be = (p-1)n"))} # # check for prior elements # if(missing(Prior)) { betabar=rep(0,k) ; A=.01*diag(k) ; nu=pm1+3; V=nu*diag(pm1)} else {if(is.null(Prior$betabar)) {betabar=rep(0,k)} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=.01*diag(k)} else {A=Prior$A} if(is.null(Prior$nu)) {nu=pm1+3} 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=1} else {keep=Mcmc$keep} # # print out problem # cat(" ",fill=TRUE) cat("Starting Gibbs Sampler for MNP",fill=TRUE) cat(" ",n," obs; ",p," choice alternatives; ",k," indep vars (including intercepts)",fill=TRUE) cat(" ",R," reps; keeping every ",keep,"th draw",fill=TRUE) cat(" ",fill=TRUE) cat("Table of y values",fill=TRUE) print(table(y)) cat("Prior Parms:",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat("A",fill=TRUE) print(A) cat("nu",fill=TRUE) print(nu) cat("V",fill=TRUE) print(V) cat(" ",fill=TRUE) cat("MCMC Parms:",fill=TRUE) cat("R= ",R,fill=TRUE) cat("initial beta= ",beta0,fill=TRUE) cat("initial sigma= ",sigma0,fill=TRUE) cat(" ",fill=TRUE) # # allocate space for draws # sigmadraw=matrix(double(floor(R/keep)*pm1*pm1),ncol=pm1*pm1) betadraw=matrix(double(floor(R/keep)*k),ncol=k) wnew=double(nrow(X)) betanew=double(k) # # set initial values of w,beta, sigma (or root of inv) # wold=c(rep(0,nrow(X))) betaold=beta0 C=chol(solve(sigma0)) # # C is upper triangular root of sigma^-1 (G) = C'C # # create functions needed # drawwc=function(w,mu,y,sigi) { .C("draww",w=as.double(w),as.double(mu),as.double(sigi), as.integer(length(y)),as.integer(ncol(sigi)),as.integer(y))$w} draww= function(w,X,y,beta,sigmai){ # # draw latent vector # # w is n x (p-1) vector # X ix n(p-1) x k matrix # y is multinomial 1,..., p # beta is k x 1 vector # sigmai is (p-1) x (p-1) # Xbeta=as.vector(X%*%beta) drawwc(w,Xbeta,y,sigmai) } itime=proc.time()[3] cat("MCMC Iteration (est time to end - min) ",fill=TRUE) for (rep in 1:R) { # # draw w given beta(rep-1),sigma(rep-1) # sigmai=crossprod(C) wnew=draww(wold,X,y,betaold,sigmai) # # draw beta given w(rep) and sigma(rep-1) # # note: if Sigma^-1 (G) = C'C then Var(Ce)=CSigmaC' = I # first, transform w_i = X_ibeta + e_i by premultiply by C # zmat=matrix(cbind(wnew,X),nrow=pm1) zmat=C%*%zmat zmat=matrix(zmat,nrow=nrow(X)) betanew=breg(zmat[,1],zmat[,2:(k+1)],betabar,A) # # draw sigmai given w and beta # epsilon=matrix((wnew-X%*%betanew),nrow=pm1) S=crossprod(t(epsilon)) W=rwishart(nu+n,chol2inv(chol(V+S))) C=W$C # # print time to completion and draw # every 100th draw # if(rep%%100 == 0) {ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R+1-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh()} # # save every keepth draw # if(rep%%keep ==0) {mkeep=rep/keep betadraw[mkeep,]=betanew sigmadraw[mkeep,]=as.vector(W$IW)} wold=wnew betaold=betanew } ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') attributes(betadraw)$class=c("bayesm.mat","mcmc") attributes(betadraw)$mcpar=c(1,R,keep) attributes(sigmadraw)$class=c("bayesm.var","bayesm.mat","mcmc") attributes(sigmadraw)$mcpar=c(1,R,keep) list(betadraw=betadraw,sigmadraw=sigmadraw) } bayesm/R/rmnlIndepMetrop.R0000755000176000001440000001121610571566767015255 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 # # 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 # 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 # pandterm=function(message) {stop(message,call.=FALSE)} 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=.01*diag(nvar)} 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} } # # 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$nu)) {nu=6} else {nu=Mcmc$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," nu (df for st candidates) = ",nu,fill=TRUE) cat(" ",fill=TRUE) betadraw=matrix(double(floor(R/keep)*nvar),ncol=nvar) loglike=double(floor(R/keep)) # # 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)) # # start main iteration loop # itime=proc.time()[3] cat("MCMC Iteration (est time to end - min) ",fill=TRUE) fsh() 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 naccept=0 for (rep in 1:R) { betac=rmvst(nu,betastar,root) cloglike=llmnl(betac,y,X) clpost=cloglike+lndMvn(betac,betabar,rootpi) climp=lndMvst(betac,nu,betastar,rooti) ldiff=clpost+oldlimp-oldlpost-climp alpha=min(1,exp(ldiff)) if(alpha < 1) {unif=runif(1)} else {unif=0} if (unif <= alpha) { beta=betac oldloglike=cloglike oldlpost=clpost oldlimp=climp naccept=naccept+1} # # print time to completion and draw # every 100th draw # if(rep%%100 == 0) {ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh()} if(rep%%keep == 0) {mkeep=rep/keep; betadraw[mkeep,]=beta; loglike[mkeep]=oldloglike} } ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') attributes(betadraw)$class=c("bayesm.mat","mcmc") attributes(betadraw)$mcpar=c(1,R,keep) return(list(betadraw=betadraw,loglike=loglike,acceptr=naccept/R)) } bayesm/R/rmixture.R0000755000176000001440000000230010242121315013752 0ustar ripleyusersrmixture= function(n,pvec,comps) { # # R. McCulloch 12/04 # 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 # #---------------------------------------------------------------------------------- # define function needed # rcomp=function(comp) { # 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 invUT = function(ut) { backsolve(ut,diag(rep(1,nrow(ut)))) } as.vector(comp[[1]] + t(invUT(comp[[2]]))%*%rnorm(length(comp[[1]]))) } #---------------------------------------------------------------------------------- # z = sample(1:length(pvec), n, replace = TRUE, prob = pvec) return(list(x = t(sapply(comps[z],rcomp)),z=z)) } bayesm/R/rmixGibbs.R0000755000176000001440000000653310307656633014057 0ustar ripleyusersrmixGibbs= function(y,Bbar,A,nu,V,a,p,z,comps) { # # Revision History: # R. McCulloch 11/04 # P. Rossi 3/05 put in backsolve and improved documentation # # purpose: do gibbs sampling inference for a mixture of multivariate normals # # arguments: # y: data, rows are observations, assumed to be iid draws from normal mixture # Bbar,A,nu,V: common prior for mean and variance of each normal component # # note: Bbar should be a matrix. usually with only one row # # beta ~ N(betabar,Sigma (x) A^-1) # betabar=vec(Bbar) # Sigma ~ IW(nu,V) or Sigma^-1 ~ W(nu, V^-1) # note: if you want Sigma ~ A, use nu big and rwishart(nu,nu(A)^{-1})$IW # a: Dirichlet parameters for prior on p # p: prior probabilities of normal components # z: components indentities for each observation # (vector of intergers each in {1,2,...number of components}) # comps: list, each member is a list comp with ith normal component # ~N(comp[[1]],Sigma), Sigma = t(R)%*%R, R^{-1} = comp[[2]] # Output: # list with elements [[1]=$p, [[2]]=$z, and [[3]]=$comps, with the updated values # #------------------------------------------------------------------------------------ # define functions needed # rcompsC = function(x,p,comps) { # purpose: # draws class membership of rows of x, given x rows are iid draws from # mixture of multivariate normals # arguments: # x: observations (number of observations x dimension) # p: prior probabilities of mixture components # comps: list, each member is a list with mean and R^{-1}, Sigma = t(R)%*%R dim = ncol(x) nob = nrow(x) nc = length(comps) mumat = matrix(0.0,dim,nc) rivmat = matrix(0.0,dim*(dim+1)/2,nc) for(i in 1:nc) { mumat[,i] = comps[[i]][[1]] rivmat[,i] = uttovC(comps[[i]][[2]]) } xx=t(x) .C('crcomps',as.double(xx),as.double(mumat),as.double(rivmat),as.double(p), as.integer(dim),as.integer(nc),as.integer(nob),res=integer(nob))$res } uttovC = function(rooti) { # returns vector of square upper triangular matrix rooti, goes down columns dropping the zeros dim = nrow(rooti) n = dim*(dim+1)/2 .C('cuttov',as.double(rooti),res = double(n),as.integer(dim))$res } #----------------------------------------------------------------------------------------- nmix = length(a) #draw comps for(i in 1:nmix) { nobincomp = sum(z==i) # get number of observations "in" component i if(nobincomp>0) { # if more than one obs in this component, draw from posterior yi=y[z==i,] dim(yi)=c(nobincomp,ncol(y)) # worry about case where y has only one col (univ mixtures) or only one row # then yi gets converted to a vector temp = rmultireg(yi,matrix(rep(1,nobincomp),ncol=1),Bbar,A,nu,V) comps[[i]] = list(mu = as.vector(temp$B), rooti=backsolve(chol(temp$Sigma),diag(rep(1,nrow(temp$Sigma))))) } else { # else draw from the prior rw=rwishart(nu,chol2inv(chol(V))) comps[[i]] = list(mu = as.vector(t(Bbar) + (rw$CI %*% rnorm(length(Bbar)))/sqrt(A[1,1])), rooti=backsolve(chol(rw$IW),diag(rep(1,nrow(V))))) } } #draw z z=rcompsC(y,p,comps) #draw p for(i in 1:length(a)) a[i] = a[i] + sum(z==i) p = rdirichlet(a) return(list(p=p,z=z,comps=comps)) } bayesm/R/rivGibbs.R0000755000176000001440000001454510572125444013675 0ustar ripleyusersrivGibbs= function(Data,Prior,Mcmc) { # # revision history: # R. McCulloch original version 2/05 # p. rossi 3/05 # p. rossi 1/06 -- fixed error in nins # p. rossi 1/06 -- fixed def Prior settings for nu,V # 3/07 added classes # # purpose: # draw from posterior for linear I.V. model # # Arguments: # Data -- list of z,w,x,y # y is vector of obs on lhs var in structural equation # x is "endogenous" var in structural eqn # w is matrix of obs on "exogenous" vars in the structural eqn # z is matrix of obs on instruments # Prior -- list of md,Ad,mbg,Abg,nu,V # md is prior mean of delta # Ad is prior prec # mbg is prior mean vector for beta,gamma # Abg is prior prec of same # nu,V parms for IW on Sigma # # Mcmc -- list of R,keep # R is number of draws # keep is thinning parameter # # Output: # list of draws of delta,beta,gamma and Sigma # # Model: # # x=z'delta + e1 # y=beta*x + w'gamma + e2 # e1,e2 ~ N(0,Sigma) # # Priors # delta ~ N(md,Ad^-1) # vec(beta,gamma) ~ N(mbg,Abg^-1) # Sigma ~ IW(nu,V) # # check arguments # pandterm=function(message) {stop(message,call.=FALSE)} if(missing(Data)) {pandterm("Requires Data argument -- list of z,w,x,y")} if(is.null(Data$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$y # # check data for validity # if(!is.vector(x)) {pandterm("x must be a vector")} if(!is.vector(y)) {pandterm("y must be a vector")} n=length(y) if(!is.matrix(w)) {pandterm("w is not a matrix")} if(!is.matrix(z)) {pandterm("z is not a matrix")} dimd=ncol(z) dimg=ncol(w) if(n != length(x) ) {pandterm("length(y) ne length(x)")} if(n != nrow(w) ) {pandterm("length(y) ne nrow(w)")} if(n != nrow(z) ) {pandterm("length(y) ne nrow(z)")} # # check for Prior # if(missing(Prior)) { md=c(rep(0,dimd));Ad=.01*diag(dimd); mbg=c(rep(0,(1+dimg))); Abg=.01*diag((1+dimg)); nu=3; V=diag(2)} else { if(is.null(Prior$md)) {md=c(rep(0,dimd))} else {md=Prior$md} if(is.null(Prior$Ad)) {Ad=.01*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=.01*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=1} else {keep=Mcmc$keep} } # # print out model # cat(" ",fill=TRUE) cat("Starting Gibbs Sampler for Linear IV Model",fill=TRUE) cat(" ",fill=TRUE) cat(" nobs= ",n,"; ",ncol(z)," instruments; ",ncol(w)," included exog vars",fill=TRUE) cat(" Note: the numbers above include intercepts if in z or w",fill=TRUE) cat(" ",fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("mean of delta ",fill=TRUE) print(md) cat("Adelta",fill=TRUE) print(Ad) cat("mean of beta/gamma",fill=TRUE) print(mbg) cat("Abeta/gamma",fill=TRUE) print(Abg) cat("Sigma Prior Parms",fill=TRUE) cat("nu= ",nu," V=",fill=TRUE) print(V) cat(" ",fill=TRUE) cat("MCMC parms: R= ",R," keep= ",keep,fill=TRUE) cat(" ",fill=TRUE) deltadraw = matrix(double(floor(R/keep)*dimd),ncol=dimd) betadraw = rep(0.0,floor(R/keep)) gammadraw = matrix(double(floor(R/keep)*dimg),ncol=dimg) Sigmadraw = matrix(double(floor(R/keep)*4),ncol=4) #set initial values Sigma=diag(2) delta=c(rep(.1,dimd)) # # start main iteration loop # itime=proc.time()[3] cat("MCMC Iteration (est time to end -min) ",fill=TRUE) fsh() xtd=matrix(nrow=2*n,ncol=dimd) ind=seq(1,(2*n-1),by=2) zvec=as.vector(t(z)) for(rep in 1:R) { # draw beta,gamma e1 = as.vector(x-z%*%delta) ee2 = (Sigma[1,2]/Sigma[1,1])*e1 sig = sqrt(Sigma[2,2]-(Sigma[1,2]^2/Sigma[1,1])) yt = (y-ee2)/sig xt = cbind(x,w)/sig bg = breg(yt,xt,mbg,Abg) beta = bg[1] gamma = bg[2:length(bg)] # draw delta C = matrix(c(1,beta,0,1),nrow=2) B = C%*%Sigma%*%t(C) L = t(chol(B)) Li=backsolve(L,diag(2),upper.tri=FALSE) u = as.vector((y-w%*%gamma)) yt = as.vector(Li %*% rbind(x,u)) z2=rbind(zvec,beta*zvec) z2=Li%*%z2 zt1=z2[1,] zt2=z2[2,] dim(zt1)=c(dimd,n) zt1=t(zt1) dim(zt2)=c(dimd,n) zt2=t(zt2) xtd[ind,]=zt1 xtd[-ind,]=zt2 delta = breg(yt,xtd,md,Ad) # draw Sigma Res = cbind(x-z%*%delta,y-beta*x-w%*%gamma) S = crossprod(Res) Sigma = rwishart(nu+n,chol2inv(chol(V+S)))$IW if(rep%%100==0) { ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh() } if(rep%%keep ==0) { mkeep=rep/keep deltadraw[mkeep,]=delta betadraw[mkeep]=beta gammadraw[mkeep,]=gamma Sigmadraw[mkeep,]=Sigma } } ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') attributes(deltadraw)$class=c("bayesm.mat","mcmc") attributes(deltadraw)$mcpar=c(1,R,keep) attributes(betadraw)$class=c("bayesm.mat","mcmc") attributes(betadraw)$mcpar=c(1,R,keep) attributes(gammadraw)$class=c("bayesm.mat","mcmc") attributes(gammadraw)$mcpar=c(1,R,keep) attributes(Sigmadraw)$class=c("bayesm.var","bayesm.mat","mcmc") attributes(Sigmadraw)$mcpar=c(1,R,keep) return(list(deltadraw=deltadraw,betadraw=betadraw,gammadraw=gammadraw,Sigmadraw=Sigmadraw)) } bayesm/R/rivDP.R0000755000176000001440000005114511754250740013150 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 # # 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 # 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 # pandterm=function(message) {stop(message,call.=FALSE)} 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 # if(missing(Prior)) { md=c(rep(0,dimd)) Ad=diag(0.01,dimd) if(isgamma) dimbg=1+dimg else dimbg=1 mbg=c(rep(0,dimbg)) Abg=diag(0.01,dimbg) gamma= .5772156649015328606 Istarmin=1 alphamin=exp(digamma(Istarmin)-log(gamma+log(n))) Istarmax=floor(.1*n) alphamax=exp(digamma(Istarmax)-log(gamma+log(n))) power=.8 Prioralpha=list(n=n,alphamin=alphamin,alphamax=alphamax,power=power) lambda=list(mubar=c(0,0),Amu=.2,nu=3.4,V=1.7*diag(2)) } else { if(is.null(Prior$md)) md=c(rep(0,dimd)) else md=Prior$md if(is.null(Prior$Ad)) Ad=diag(0.01,dimd) else Ad=Prior$Ad if(isgamma) dimbg=1+dimg else dimbg=1 if(is.null(Prior$mbg)) mbg=c(rep(0,dimbg)) else md=Prior$mbg if(is.null(Prior$Abg)) Abg=diag(0.01,dimbg) else md=Prior$Abg if(!is.null(Prior$Prioralpha)) {Prioralpha=Prior$Prioralpha} else {gamma= .5772156649015328606 Istarmin=1 alphamin=exp(digamma(Istarmin)-log(gamma+log(n))) Istarmax=floor(.1*n) alphamax=exp(digamma(Istarmax)-log(gamma+log(n))) power=.8 Prioralpha=list(n=n,alphamin=alphamin,alphamax=alphamax,power=power)} if(!is.null(Prior$lambda)) {lambda=Prior$lambda} else {lambda=list(mubar=c(0,0),Amu=.2,nu=3.4,V=1.7*diag(2))} } # # 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=200} else {maxuniq=Mcmc$maxuniq} if(is.null(Mcmc$R)) {pandterm("requres Mcmc argument, R")} R = Mcmc$R if(is.null(Mcmc$keep)) {keep=1} else {keep=Mcmc$keep} if(is.null(Mcmc$gridsize)) {gridsize=20} else {gridsize=Mcmc$gridsize} if(is.null(Mcmc$SCALE)) {SCALE=TRUE} else {SCALE=Mcmc$SCALE} # # scale and center # if(SCALE){ scaley=sqrt(var(y)) scalex=sqrt(var(x)) meany=mean(y) meanx=mean(x) meanz=apply(z,2,mean) y=(y-meany)/scaley; x=(x-meanx)/scalex z=scale(z,center=TRUE,scale=FALSE) if(isgamma) {meanw=apply(w,2,mean); w=scale(w,center=TRUE,scale=FALSE)} } # # print out model # cat(" ",fill=TRUE) cat("Starting Gibbs Sampler for Linear IV Model With DP Process Errors",fill=TRUE) cat(" ",fill=TRUE) cat(" nobs= ",n,"; ",ncol(z)," instruments",fill=TRUE) cat(" ",fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("mean of delta ",fill=TRUE) print(md) cat(" ",fill=TRUE) cat("Adelta",fill=TRUE) print(Ad) cat(" ",fill=TRUE) cat("mean of beta/gamma",fill=TRUE) print(mbg) cat(" ",fill=TRUE) cat("Abeta/gamma",fill=TRUE) print(Abg) cat(" ",fill=TRUE) cat("lambda contains: ", fill=TRUE) cat("mu Prior Parms:",fill=TRUE) cat("mubar= ",lambda$mubar,fill=TRUE) cat("Amu= ",lambda$Amu,fill=TRUE) cat(" ",fill=TRUE) cat("Sigma Prior Parms:",fill=TRUE) cat("nu= ",lambda$nu," V=",fill=TRUE) print(lambda$V) cat(" ",fill=TRUE) cat("Parameters of Prior on Dirichlet Process parm (alpha)",fill=TRUE) cat("alphamin= ",Prioralpha$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,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) # # define needed functions # # # # -------------------------------------------------------------------------------------------- # # get_ytxt=function(y,z,delta,x,w,ncomp,indic,comps){ yt=NULL; xt=NULL; if(missing(w)) isw=FALSE else isw=TRUE if(isw) ncolw=ncol(w) for (k in 1:ncomp) { nobs=sum(indic==k) if(nobs > 0) { if(isw) wk=matrix(w[indic==k,],ncol=ncolw) zk=matrix(z[indic==k,],ncol=length(delta)) yk=y[indic==k] xk=matrix(x[indic==k],ncol=1) Sigma=backsolve(comps[[k]][[2]],diag(2)) Sigma=crossprod(Sigma) mu=comps[[k]][[1]] e1 = as.vector(xk-zk%*%delta) ee2 = mu[2] +(Sigma[1,2]/Sigma[1,1])*(e1-mu[1]) sig = sqrt(Sigma[2,2]-(Sigma[1,2]^2/Sigma[1,1])) yt = c(yt,(yk-ee2)/sig) if(isw) {xt = rbind(xt,(cbind(xk,wk)/sig))} else {xt=rbind(xt,xk/sig)} } } return(list(xt=xt,yt=yt)) } # # # -------------------------------------------------------------------------------------------- # # get_ytxtd=function(y,z,beta,gamma,x,w,ncomp,indic,comps,dimd){ yt=NULL; xtd=NULL; if(missing(w)) isw=FALSE else isw=TRUE if(isw) ncolw=ncol(w) C = matrix(c(1,beta,0,1),nrow=2) for (k in 1:ncomp) { nobs=sum(indic==k) if(nobs > 0) { xtdk=matrix(nrow=2*nobs,ncol=dimd) ind=seq(1,(2*nobs-1),by=2) if(isw) wk=matrix(w[indic==k,],ncol=ncolw) zk=matrix(z[indic==k,],ncol=dimd) zveck=as.vector(t(zk)) yk=y[indic==k] xk=x[indic==k] Sigma=backsolve(comps[[k]][[2]],diag(2)) Sigma=crossprod(Sigma) mu=comps[[k]][[1]] B = C%*%Sigma%*%t(C) L = t(chol(B)) Li=backsolve(L,diag(2),upper.tri=FALSE) if(isw) {u=as.vector((yk-wk%*%gamma-mu[2]-beta*mu[1]))} else {u=as.vector((yk-mu[2]-beta*mu[1]))} ytk = as.vector(Li %*% rbind((xk-mu[1]),u)) z2=rbind(zveck,beta*zveck) z2=Li%*%z2 zt1=z2[1,] zt2=z2[2,] dim(zt1)=c(dimd,nobs) zt1=t(zt1) dim(zt2)=c(dimd,nobs) zt2=t(zt2) xtdk[ind,]=zt1 xtdk[-ind,]=zt2 yt=c(yt,ytk) xtd=rbind(xtd,xtdk) } } return(list(yt=yt,xtd=xtd)) } # # # -------------------------------------------------------------------------------------------- # # rthetaDP= function(maxuniq,alpha,lambda,Prioralpha,theta,thetaStar,indic,q0v,y,gridsize){ # # 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)) # note: eta is not used #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). # # define needed functions for rthetaDP # ----------------------------------------------------------------------------------------------- pandterm = function(message) { stop(message, call. = FALSE) } # ---------------------------------------------------------------------------------------------- rmultinomF= function(p) { return(sum(runif(1) > cumsum(p))+1) } # ----------------------------------------------------------------------------------------------- alphaD=function(Prioralpha,Istar,gridsize){ # # function to draw alpha using prior, p(alpha)= (1-(alpha-alphamin)/(alphamax-alphamin))**power # power=Prioralpha$power alphamin=Prioralpha$alphamin alphamax=Prioralpha$alphamax n=Prioralpha$n alpha=seq(from=alphamin,to=(alphamax-0.000001),len=gridsize) lnprob=Istar*log(alpha) + lgamma(alpha) - lgamma(n+alpha) + power*log(1-(alpha-alphamin)/(alphamax-alphamin)) lnprob=lnprob-median(lnprob) probs=exp(lnprob) probs=probs/sum(probs) return(alpha[rmultinomF(probs)]) } # ----------------------------------------------------------------------------------------------- # yden=function(thetaStar,y,eta){ # # 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 # eta is not used # # output: # length(thetaStar) x n array of values of f(y[j,]|thetaStar[[i]] # nunique=length(thetaStar) n=nrow(y) ydenmat=matrix(double(n*nunique),ncol=n) k=ncol(y) for(i in 1:nunique){ # now compute vectorized version of lndMvn # compute y_i'RIRI'y_i for all i # mu=thetaStar[[i]]$mu; rooti=thetaStar[[i]]$rooti quads=colSums((crossprod(rooti,(t(y)-mu)))^2) ydenmat[i,]=exp(-(k/2)*log(2*pi) + sum(log(diag(rooti))) - .5*quads) } return(ydenmat) } # # # ----------------------------------------------------------------------------------------- # # GD=function(lambda){ # # function to draw from prior for Multivariate Normal Model # # mu|Sigma ~ N(mubar,Sigma x Amu^-1) # Sigma ~ IW(nu,V) # # nu=lambda$nu V=lambda$V mubar=lambda$mubar Amu=lambda$Amu k=length(mubar) Sigma=rwishart(nu,chol2inv(chol(lambda$V)))$IW root=chol(Sigma) mu=mubar+(1/sqrt(Amu))*t(root)%*%matrix(rnorm(k),ncol=1) return(list(mu=as.vector(mu),rooti=backsolve(root,diag(k)))) } # # # ------------------------------------------------------------------------------------------- # # thetaD=function(y,lambda,eta){ # # 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) # eta is not used # 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 # rout=rmultireg(y,matrix(c(rep(1,nrow(y))),ncol=1),matrix(lambda$mubar,nrow=1),matrix(lambda$Amu,ncol=1), lambda$nu,lambda$V) return(list(mu=as.vector(rout$B),rooti=backsolve(chol(rout$Sigma),diag(ncol(y))))) } # # END OF REQUIRED FUNCTIONS AREA # -------------------------------------------------------------------------------------------- # n = length(theta) eta=NULL # note eta is not used thetaNp1=NULL p=c(rep(1/(alpha+(n-1)),n-1),alpha/(alpha+(n-1))) nunique=length(thetaStar) if(nunique > maxuniq ) { pandterm("maximum number of unique thetas exceeded")} ydenmat=matrix(double(maxuniq*n),ncol=n) ydenmat[1:nunique,]=yden(thetaStar,y,eta) # 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! # use .Call to draw theta list out= .Call("thetadraw",y,ydenmat,indic,q0v,p,theta,lambda,eta=eta, thetaD=thetaD,yden=yden,maxuniq,nunique,new.env()) # theta has been modified by thetadraw so we need to recreate thetaStar thetaStar=unique(theta) nunique=length(thetaStar) #thetaNp1 and remix probs=double(nunique+1) for(j in 1:nunique) { ind = which(sapply(theta,identical,thetaStar[[j]])) probs[j]=length(ind)/(alpha+n) new_utheta=thetaD(y[ind,,drop=FALSE],lambda,eta) for(i in seq(along=ind)) {theta[[ind[i]]]=new_utheta} indic[ind]=j thetaStar[[j]]=new_utheta } probs[nunique+1]=alpha/(alpha+n) ind=rmultinomF(probs) if(ind==length(probs)) { thetaNp1=GD(lambda) } else { thetaNp1=thetaStar[[ind]] } #alpha alpha=alphaD(Prioralpha,nunique,gridsize) return(list(theta=theta,indic=indic,thetaStar=thetaStar, thetaNp1=thetaNp1,alpha=alpha,Istar=nunique)) } # # # ----------------------------------------------------------------------------------------- # # q0=function(y,lambda,eta){ # # function to compute a vector of int f(y[i]|theta) p(theta|lambda)dlambda # here p(theta|lambda) is G0 the base prior # # implemented for a multivariate normal data density and standard conjugate # prior: # theta=list(mu,Sigma) # f(y|theta) is N(mu,Sigma) # lambda=list(mubar,Amu,nu,V) # mu|Sigma ~ N(mubar,Sigma (x) Amu^-1) # Sigma ~ IW(nu,V) # # arguments: # Y is n x k matrix of observations # eta is not used # lambda=list(mubar,Amu,nu,V) # # output: # vector of q0 values for each obs (row of Y) # # p. rossi 12/05 # # here y is matrix of observations (each row is an obs) mubar=lambda$mubar; nu=lambda$nu ; Amu=lambda$Amu; V=lambda$V k=ncol(y) R=chol(V) logdetR=sum(log(diag(R))) if (k > 1) {lnk1k2=(k/2)*log(2)+log((nu-k)/2)+lgamma((nu-k)/2)-lgamma(nu/2)+sum(log(nu/2-(1:(k-1))/2))} else {lnk1k2=(k/2)*log(2)+log((nu-k)/2)+lgamma((nu-k)/2)-lgamma(nu/2)} constant=-(k/2)*log(2*pi)+(k/2)*log(Amu/(1+Amu)) + lnk1k2 + 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)' # mat=sqrt(Amu/(1+Amu))*t(backsolve(R,diag(ncol(y))))%*%(t(y)-mubar) vivi=colSums(mat^2) lnq0v=constant-((nu+1)/2)*(2*logdetR+log(1+vivi)) return(exp(lnq0v)) } # # # -------------------------------------------------------------------------------------------- # # # END OF REQUIRED FUNCTIONS AREA # # #initialize comps,indic,ncomp comps=unique(theta) ncomp=length(comps) indic=double(n) for(j in 1:ncomp){ indic[which(sapply(theta,identical,comps[[j]]))]=j } # initialize eta eta=NULL # # initialize alpha alpha=1 # reserve space for draws # deltadraw = matrix(double(floor(R/keep)*dimd),ncol=dimd) betadraw = rep(0.0,floor(R/keep)) alphadraw=double(floor(R/keep)) Istardraw=double(floor(R/keep)) if(isgamma) gammadraw = matrix(double(floor(R/keep)*dimg),ncol=dimg) thetaNp1draw=vector("list",R) # # start main iteration loop # itime=proc.time()[3] cat("MCMC Iteration (est time to end -min) ",fill=TRUE) fsh() for(rep in 1:R) { # draw beta and gamma if(isgamma) {out=get_ytxt(y=y,z=z,delta=delta,x=x,w=w, ncomp=ncomp,indic=indic,comps=comps)} else {out=get_ytxt(y=y,z=z,delta=delta,x=x, ncomp=ncomp,indic=indic,comps=comps)} bg = breg(out$yt,out$xt,mbg,Abg) beta = bg[1] if(isgamma) gamma = bg[2:length(bg)] # draw delta if(isgamma) {out=get_ytxtd(y=y,z=z,beta=beta,gamma=gamma, x=x,w=w,ncomp=ncomp,indic=indic,comps=comps,dimd=dimd)} else {out=get_ytxtd(y=y,z=z,beta=beta, x=x,ncomp=ncomp,indic=indic,comps=comps,dimd=dimd)} delta = breg(out$yt,out$xtd,md,Ad) # DP process stuff- theta | lambda if(isgamma) {Err = cbind(x-z%*%delta,y-beta*x-w%*%gamma)} else {Err = cbind(x-z%*%delta,y-beta*x)} q0v = q0(Err,lambda,eta) DPout=rthetaDP(maxuniq=maxuniq,alpha=alpha,lambda=lambda,Prioralpha=Prioralpha,theta=theta, thetaStar=comps,indic=indic,q0v=q0v,y=Err,gridsize=gridsize) indic=DPout$indic theta=DPout$theta comps=DPout$thetaStar alpha=DPout$alpha Istar=DPout$Istar ncomp=length(comps) if(rep%%100==0) { ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh() } if(rep%%keep ==0) { mkeep=rep/keep deltadraw[mkeep,]=delta betadraw[mkeep]=beta alphadraw[mkeep]=alpha Istardraw[mkeep]=Istar if(isgamma) gammadraw[mkeep,]=gamma thetaNp1draw[[mkeep]]=list(DPout$thetaNp1) } } # # rescale # if(SCALE){ deltadraw=deltadraw*scalex betadraw=betadraw*scaley/scalex if(isgamma) {gammadraw=gammadraw*scaley} } ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') nmix=list(probdraw=matrix(c(rep(1,length(thetaNp1draw))),ncol=1),zdraw=NULL,compdraw=thetaNp1draw) # # densitymix is in the format to be used with the generic mixture of normals plotting # methods (plot.bayesm.nmix) # attributes(nmix)$class=c("bayesm.nmix") attributes(deltadraw)$class=c("bayesm.mat","mcmc") attributes(deltadraw)$mcpar=c(1,R,keep) attributes(betadraw)$class=c("bayesm.mat","mcmc") attributes(betadraw)$mcpar=c(1,R,keep) attributes(alphadraw)$class=c("bayesm.mat","mcmc") attributes(alphadraw)$mcpar=c(1,R,keep) attributes(Istardraw)$class=c("bayesm.mat","mcmc") attributes(Istardraw)$mcpar=c(1,R,keep) if(isgamma){ attributes(gammadraw)$class=c("bayesm.mat","mcmc") attributes(gammadraw)$mcpar=c(1,R,keep)} if(isgamma) { return(list(deltadraw=deltadraw,betadraw=betadraw,alphadraw=alphadraw,Istardraw=Istardraw, gammadraw=gammadraw,nmix=nmix))} else { return(list(deltadraw=deltadraw,betadraw=betadraw,alphadraw=alphadraw,Istardraw=Istardraw, nmix=nmix))} } bayesm/R/rhierNegbinRw.R0000755000176000001440000002571111754551011014664 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 # # 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) # 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 # # # 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)) } 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)*llnegbin(theta,X,y,nvar) + w*wgt*llnegbin(theta,Xpooled,ypooled, nvar) } lpostbetai = function(beta, alpha, X, y, Delta, Z, Vbetainv) { # Computes the unnormalized log posterior for beta at the unit level lambda = exp(X %*% as.vector(beta)) p = alpha/(alpha + lambda) residual = as.vector(beta - as.vector(Z%*%Delta)) sum(alpha * log(p) + y * log(1-p)) - 0.5*( t(residual)%*%Vbetainv%*%residual) } lpostalpha = function(alpha, beta, regdata, ypooled, a, b, nreg) { # Computes the unnormalized log posterior for alpha Xbeta=NULL for (i in 1:nreg) {Xbeta = rbind(Xbeta,regdata[[i]]$X%*%beta[i,]) } sum(log(dnbinom(ypooled,size=alpha,mu=exp(Xbeta)))) + (a-1)*log(alpha) - b* alpha } # # Error Checking # pandterm=function(message) {stop(message,call.=FALSE)} 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$Z)) { cat("Z not specified - using a column of ones instead", fill = TRUE) Z = matrix(rep(1,nreg),ncol=1) } else { if (nrow(Data$Z) != nreg) { pandterm(paste("Nrow(Z) ", nrow(Z), "ne number units ",nreg)) } else { Z = Data$Z } } nz = ncol(Z) dimfun = function(l) { c(length(l$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]]$X) } nobs= length(ypooled) nvar=ncol(Xpooled) # # check for prior elements # if(missing(Prior)) { Deltabar=matrix(rep(0,nvar*nz),nrow=nz) ; Adelta=0.01*diag(nz) ; nu=nvar+3; V=nu*diag(nvar); a=0.5; b=0.1; } else { if(is.null(Prior$Deltabar)) {Deltabar=matrix(rep(0,nvar*nz),nrow=nz)} else {Deltabar=Prior$Deltabar} if(is.null(Prior$Adelta)) {Adelta=0.01*diag(nz)} else {Adelta=Prior$Adelta} if(is.null(Prior$nu)) {nu=nvar+3} else {nu=Prior$nu} if(is.null(Prior$V)) {V=nu*diag(nvar)} else {V=Prior$V} if(is.null(Prior$a)) {a=0.5} else {a=Prior$a} if(is.null(Prior$b)) {b=0.1} 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=1} else {keep=Mcmc$keep} if(is.null(Mcmc$s_alpha)) { s_alpha=2.93} else {s_alpha= Mcmc$s_alpha } if(is.null(Mcmc$s_beta)) { s_beta=2.93/sqrt(nvar)} else {s_beta=Mcmc$s_beta } if(is.null(Mcmc$w)) { w=.1} else {w = Mcmc$w} #out = rhierNegbinRw(Data, Prior, Mcmc) # print out problem # cat(" ",fill=TRUE) cat("Starting Random Walk Metropolis Sampler for Hierarchical Negative Binomial Regression",fill=TRUE) cat(" ",nobs," obs; ",nvar," covariates (including the intercept); ",fill=TRUE) cat(" ",nz," individual characteristics (including the intercept) ",fill=TRUE) cat(" ",fill=TRUE) cat("Prior Parameters:",fill=TRUE) cat("Deltabar",fill=TRUE) print(Deltabar) cat("Adelta",fill=TRUE) print(Adelta) cat("nu",fill=TRUE) print(nu) cat("V",fill=TRUE) print(V) cat("a",fill=TRUE) print(a) cat("b",fill=TRUE) print(b) cat(" ",fill=TRUE) cat("MCMC Parameters:",fill=TRUE) cat(R," reps; keeping every ",keep,"th draw",fill=TRUE) cat("s_alpha = ",s_alpha,fill=TRUE) cat("s_beta = ",s_beta,fill=TRUE) cat("Fractional Likelihood Weight Parameter = ",w,fill=TRUE) cat(" ",fill=TRUE) par = rep(0,(nvar+1)) cat("initializing Metropolis candidate densities for ",nreg,"units ...",fill=TRUE) fsh() mle = optim(par,llnegbin, X=Xpooled, y=ypooled, nvar=nvar, method="L-BFGS-B", upper=c(Inf,Inf,Inf,log(100000000)), hessian=TRUE, control=list(fnscale=-1)) fsh() beta_mle=mle$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 = solve(Vbeta0) Vbeta = Vbeta0 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() hess_i=NULL if(nobs > 1000){ sind=sample(c(1:nobs),size=1000) ypooleds=ypooled[sind] Xpooleds=Xpooled[sind,] } # 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$par[nvar+1], method="BFGS", hessian=TRUE, control=list(fnscale=-1, trace=0)) if (mle2$convergence==0) hess_i[[i]] = list(hess=-mle2$hessian) else hess_i[[i]] = diag(rep(1,nvar)) if(i%%50 ==0) cat(" completed unit #",i,fill=TRUE) fsh() } oldlpostbeta = rep(0,nreg) nacceptbeta = 0 nacceptalpha = 0 clpostbeta = rep(0,nreg) Betadraw = array(double((floor(R/keep)) * nreg * nvar), dim = c(nreg, nvar, floor(R/keep))) alphadraw = rep(0,floor(R/keep)) llike = rep(0,floor(R/keep)) Vbetadraw=matrix(double(floor(R/keep)*(nvar*nvar)),ncol=(nvar*nvar)) Deltadraw=matrix(double(floor(R/keep)*(nvar*nz)),ncol=(nvar*nz)) # # start main iteration loop # itime=proc.time()[3] cat(" ",fill=TRUE) cat("MCMC Iteration (est time to end - min) ",fill=TRUE) fsh() for (r in 1:R) { # Draw betai for (i in 1:nreg) { betacvar = s_beta*solve(hess_i[[i]]$hess + Vbetainv) betaroot = t(chol(betacvar)) betac = as.vector(Beta[i,]) + betaroot%*%rnorm(nvar) oldlpostbeta[i] = lpostbetai(as.vector(Beta[i,]), alpha, regdata[[i]]$X, regdata[[i]]$y, Delta, Z[i,],Vbetainv) clpostbeta[i] = lpostbetai(betac, alpha, regdata[[i]]$X, regdata[[i]]$y, Delta, Z[i,],Vbetainv) ldiff=clpostbeta[i]-oldlpostbeta[i] acc=min(1,exp(ldiff)) if(acc < 1) {unif=runif(1)} else {unif=0} if (unif <= acc) { Beta[i,]=betac nacceptbeta=nacceptbeta+1 } } # Draw alpha logalphac = rnorm(1,mean=log(alpha), sd=alphacroot) oldlpostalpha = lpostalpha(alpha, Beta, regdata, ypooled, a, b, nreg) clpostalpha = lpostalpha(exp(logalphac), Beta, regdata, ypooled, a, b, nreg) ldiff=clpostalpha-oldlpostalpha acc=min(1,exp(ldiff)) if(acc < 1) {unif=runif(1)} else {unif=0} if (unif <= acc) { alpha=exp(logalphac) nacceptalpha=nacceptalpha+1 } # Draw Vbeta and Delta using rmultireg (bayesm function) temp = rmultireg(Beta,Z,Deltabar,Adelta,nu,V) Vbeta = matrix(temp$Sigma,nrow=nvar) Vbetainv = solve(Vbeta) Delta = temp$B if(r%%100 == 0) {ctime=proc.time()[3] timetoend=((ctime-itime)/r)*(R-r) cat(" ",r," (",round(timetoend/60,1),")",fill=TRUE) fsh()} if(r%%keep == 0) { mkeep=r/keep Betadraw[, ,mkeep]=Beta alphadraw[mkeep] = alpha Vbetadraw[mkeep,] = as.vector(Vbeta) Deltadraw[mkeep,] = as.vector(Delta) ll=0.0 for (i in 1:nreg) {ll=ll+llnegbin(c(Beta[i,],alpha),regdata[[i]]$X,regdata[[i]]$y,nvar)} llike[r]=ll } } ctime = proc.time()[3] attributes(alphadraw)$class=c("bayesm.mat","mcmc") attributes(alphadraw)$mcpar=c(1,R,keep) 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) attributes(Betadraw)$class=c("bayesm.hcoef") cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') return(list(llike=llike,Betadraw=Betadraw,alphadraw=alphadraw, Vbetadraw=Vbetadraw, Deltadraw=Deltadraw, acceptrbeta=nacceptbeta/(R*nreg)*100,acceptralpha=nacceptalpha/R*100)) } bayesm/R/rhierMnlRwMixture.R0000755000176000001440000003371211071420344015562 0ustar ripleyusersrhierMnlRwMixture= 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 # 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 # 9/08 changed Dirichlet a check # # 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) # 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) # # 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 # # check arguments # pandterm=function(message) { stop(message,call.=FALSE) } 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 (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]]$X)) {oldncol=ncol(lgtdata[[1]]$X)} for (i in 1:nlgt) { if(is.null(lgtdata[[i]]$y)) {pandterm(paste("Requires element y of lgtdata[[",i,"]]"))} if(is.null(lgtdata[[i]]$X)) {pandterm(paste("Requires element X of lgtdata[[",i,"]]"))} 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$ncomp} if(is.null(Prior$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(.01,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+3} 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=.01*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(5,ncomp)} else {a=Prior$a} if(length(a) != ncomp) {pandterm("Requires dim(a)= ncomp (no of components)")} bada=FALSE for(i in 1:ncomp) { if(a[i] < 0) bada=TRUE} if(bada) pandterm("invalid values in a vector") # # check on Mcmc # if(missing(Mcmc)) {pandterm("Requires Mcmc list argument")} else { if(is.null(Mcmc$s)) {s=2.93/sqrt(nvar)} else {s=Mcmc$s} if(is.null(Mcmc$w)) {w=.1} else {w=Mcmc$w} if(is.null(Mcmc$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("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),fill=TRUE) cat("",fill=TRUE) # # allocate space for draws # if(drawdelta) Deltadraw=matrix(double((floor(R/keep))*nz*nvar),ncol=nz*nvar) betadraw=array(double((floor(R/keep))*nlgt*nvar),dim=c(nlgt,nvar,floor(R/keep))) probdraw=matrix(double((floor(R/keep))*ncomp),ncol=ncomp) oldbetas=matrix(double(nlgt*nvar),ncol=nvar) oldll=double(nlgt) loglike=double(floor(R/keep)) oldcomp=NULL compdraw=NULL #-------------------------------------------------------------------------------------------------- # # create functions needed # 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))) } mnlRwMetropOnce= function(y,X,oldbeta,oldll,s,inc.root,betabar,rootpi){ # # function to execute rw metropolis for the MNL # 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 # RW increments are N(0,s^2*t(inc.root)%*%inc.root) # prior on beta is N(betabar,Sigma) Sigma^-1=rootpi*t(rootpi) # inc.root, rootpi are upper triangular # this means that we are using the UL decomp of Sigma^-1 for prior # oldbeta is the current stay=0 betac=oldbeta + s*t(inc.root)%*%(matrix(rnorm(ncol(X)),ncol=1)) cll=llmnl(betac,y,X) clpost=cll+lndMvn(betac,betabar,rootpi) ldiff=clpost-oldll-lndMvn(oldbeta,betabar,rootpi) alpha=min(1,exp(ldiff)) if(alpha < 1) {unif=runif(1)} else {unif=0} if (unif <= alpha) {betadraw=betac; oldll=cll} else {betadraw=oldbeta; stay=1} return(list(betadraw=betadraw,stay=stay,oldll=oldll)) } drawDelta= function(x,y,z,comps,deltabar,Ad){ # 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 p=ncol(y) k=ncol(x) xtx = matrix(0.0,k*p,k*p) xty = matrix(0.0,p,k) #this is the unvecced version, have to vec after sum for(i in 1:length(comps)) { nobs=sum(z==i) if(nobs > 0) { if(nobs == 1) { yi = matrix(y[z==i,],ncol=p); xi = matrix(x[z==i,],ncol=k)} else { yi = y[z==i,]; xi = x[z==i,]} yi = t(t(yi)-comps[[i]][[1]]) sigi = crossprod(t(comps[[i]][[2]])) xtx = xtx + crossprod(xi) %x% sigi xty = xty + (sigi %*% crossprod(yi,xi)) } } xty = matrix(xty,ncol=1) # then vec(t(D)) ~ N(V^{-1}(xty + Ad*deltabar),V^{-1}) V = (xtx+Ad) cov=chol2inv(chol(xtx+Ad)) return(cov%*%(xty+Ad%*%deltabar) + t(chol(cov))%*%rnorm(length(deltabar))) } #------------------------------------------------------------------------------------------------------- # # 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) 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]]$betafmle if(i%%50 ==0) cat(" completed unit #",i,fill=TRUE) fsh() } # # initialize values # # set initial values for the indicators # ind is of length(nlgt) and indicates which mixture component this obs # belongs to. # ind=NULL ninc=floor(nlgt/ncomp) for (i in 1:(ncomp-1)) {ind=c(ind,rep(i,ninc))} if(ncomp != 1) {ind = c(ind,rep(ncomp,nlgt-length(ind)))} else {ind=rep(1,nlgt)} # # initialize delta # if (drawdelta) olddelta=rep(0,nz*nvar) # # initialize probs # oldprob=rep(1/ncomp,ncomp) # # initialize comps # tcomp=list(list(mu=rep(0,nvar),rooti=diag(nvar))) oldcomp=rep(tcomp,ncomp) # # # start main iteration loop # itime=proc.time()[3] cat("MCMC Iteration (est time to end - min) ",fill=TRUE) fsh() for(rep in 1:R) { # first draw comps,ind,p | {beta_i}, delta # ind,p need initialization comps is drawn first in sub-Gibbs if(drawdelta) {mgout=rmixGibbs(oldbetas-Z%*%t(matrix(olddelta,ncol=nz)), mubar,Amu,nu,V,a,oldprob,ind,oldcomp)} else {mgout=rmixGibbs(oldbetas, mubar,Amu,nu,V,a,oldprob,ind,oldcomp)} oldprob=mgout[[1]] oldcomp=mgout[[3]] ind=mgout[[2]] # now draw delta | {beta_i}, ind, comps if(drawdelta) {olddelta=drawDelta(Z,oldbetas,ind,oldcomp,deltabar,Ad)} # # loop over all lgt equations drawing beta_i | ind[i],z[i,],mu[ind[i]],rooti[ind[i]] # for (lgt in 1:nlgt) { rootpi=oldcomp[[ind[lgt]]]$rooti # note: beta_i = Delta*z_i + u_i Delta is nvar x nz if(drawdelta) { betabar=oldcomp[[ind[lgt]]]$mu+matrix(olddelta,ncol=nz)%*%as.vector(Z[lgt,])} else { betabar=oldcomp[[ind[lgt]]]$mu } if (rep == 1) { oldll[lgt]=llmnl(oldbetas[lgt,],lgtdata[[lgt]]$y,lgtdata[[lgt]]$X)} # compute inc.root inc.root=chol(chol2inv(chol(lgtdata[[lgt]]$hess+rootpi%*%t(rootpi)))) metropout=mnlRwMetropOnce(lgtdata[[lgt]]$y,lgtdata[[lgt]]$X,oldbetas[lgt,], oldll[lgt],s,inc.root,betabar,rootpi) oldbetas[lgt,]=metropout$betadraw oldll[lgt]=metropout$oldll } # # # print time to completion and draw # every 100th draw # if(((rep/100)*100) ==(floor(rep/100)*100)) {ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R+1-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh()} # # save every keepth draw # mkeep=rep/keep if((mkeep*keep) == (floor(mkeep)*keep)) { betadraw[,,mkeep]=oldbetas probdraw[mkeep,]=oldprob loglike[mkeep]=sum(oldll) if(drawdelta) Deltadraw[mkeep,]=olddelta compdraw[[mkeep]]=oldcomp } } ctime=proc.time()[3] cat(" Total Time Elapsed: ",round((ctime-itime)/60,2),fill=TRUE) if(drawdelta){ attributes(Deltadraw)$class=c("bayesm.mat","mcmc") attributes(Deltadraw)$mcpar=c(1,R,keep)} attributes(betadraw)$class=c("bayesm.hcoef") nmix=list(probdraw=probdraw,zdraw=NULL,compdraw=compdraw) attributes(nmix)$class="bayesm.nmix" if(drawdelta) {return(list(Deltadraw=Deltadraw,betadraw=betadraw,nmix=nmix,loglike=loglike))} else {return(list(betadraw=betadraw,nmix=nmix,loglike=loglike))} } bayesm/R/rhierMnlDP.R0000644000176000001440000006667311022777164014143 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 # # 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) # # 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 #-------------------------------------------------------------------------------------------------- # # create functions needed # rDPGibbs1= function(y,theta,thetaStar,indic,lambda,alpha,Prioralpha,lambda_hyper,maxuniq,gridsize){ # # revision history: # created from rDPGibbs by Rossi 3/08 # # do one draw of DP Gibbs sampler with norma 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: # 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: # theta - list of thetas for each "obs" # 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 # # define needed functions # # ----------------------------------------------------------------------------------------- # q0= function(y,lambda,eta){ # # function to compute a vector of int f(y[i]|theta) p(theta|lambda)dlambda # here p(theta|lambda) is G0 the base prior # # implemented for a multivariate normal data density and standard conjugate # prior: # theta=list(mu,Sigma) # f(y|theta,eta) is N(mu,Sigma) # lambda=list(mubar,Amu,nu,V) # mu|Sigma ~ N(mubar,Sigma (x) Amu^-1) # Sigma ~ IW(nu,V) # # arguments: # Y is n x k matrix of observations # lambda=list(mubar,Amu,nu,V) # eta is not used # # output: # vector of q0 values for each obs (row of Y) # # p. rossi 12/05 # # here y is matrix of observations (each row is an obs) mubar=lambda$mubar; nu=lambda$nu ; Amu=lambda$Amu; V=lambda$V k=ncol(y) R=chol(V) logdetR=sum(log(diag(R))) if (k > 1) {lnk1k2=(k/2)*log(2)+log((nu-k)/2)+lgamma((nu-k)/2)-lgamma(nu/2)+sum(log(nu/2-(1:(k-1))/2))} else {lnk1k2=(k/2)*log(2)+log((nu-k)/2)+lgamma((nu-k)/2)-lgamma(nu/2)} constant=-(k/2)*log(2*pi)+(k/2)*log(Amu/(1+Amu)) + lnk1k2 + nu*logdetR # # note: here we are using the fact that |V + S_i | = |R|^2 (1 + v_i'v_i) # where v_i = sqrt(Amu/(1+Amu))*t(R^-1)*(y_i-mubar), R is chol(V) # # and S_i = Amu/(1+Amu) * (y_i-mubar)(y_i-mubar)' # mat=sqrt(Amu/(1+Amu))*t(backsolve(R,diag(ncol(y))))%*%(t(y)-mubar) vivi=colSums(mat^2) lnq0v=constant-((nu+1)/2)*(2*logdetR+log(1+vivi)) return(exp(lnq0v)) } # ---------------------------------------------------------------------------------------------- rmultinomF=function(p) { return(sum(runif(1) > cumsum(p))+1) } # ----------------------------------------------------------------------------------------------- alphaD= function(Prioralpha,Istar,gridsize){ # # function to draw alpha using prior, p(alpha)= (1-(alpha-alphamin)/(alphamax-alphamin))**power # power=Prioralpha$power alphamin=Prioralpha$alphamin alphamax=Prioralpha$alphamax n=Prioralpha$n alpha=seq(from=alphamin,to=(alphamax-0.000001),len=gridsize) lnprob=Istar*log(alpha) + lgamma(alpha) - lgamma(n+alpha) + power*log(1-(alpha-alphamin)/(alphamax-alphamin)) lnprob=lnprob-median(lnprob) probs=exp(lnprob) probs=probs/sum(probs) return(alpha[rmultinomF(probs)]) } # # ------------------------------------------------------------------------------------------ # yden= function(thetaStar,y,eta){ # # function to compute f(y | theta) # computes f for all values of theta in theta list of lists # # arguments: # thetaStar is a list of lists. thetaStar[[i]] is a list with components, mu, rooti # y |theta[[i]] ~ N(mu,(rooti %*% t(rooti))^-1) rooti is inverse of Chol root of Sigma # eta is not used # # output: # length(thetaStar) x n array of values of f(y[j,]|thetaStar[[i]] # nunique=length(thetaStar) n=nrow(y) ydenmat=matrix(double(n*nunique),ncol=n) k=ncol(y) for(i in 1:nunique){ # now compute vectorized version of lndMvn # compute y_i'RIRI'y_i for all i # mu=thetaStar[[i]]$mu; rooti=thetaStar[[i]]$rooti quads=colSums((crossprod(rooti,(t(y)-mu)))^2) ydenmat[i,]=exp(-(k/2)*log(2*pi) + sum(log(diag(rooti))) - .5*quads) } return(ydenmat) } # # ----------------------------------------------------------------------------------------- # GD= function(lambda){ # # function to draw from prior for Multivariate Normal Model # # mu|Sigma ~ N(mubar,Sigma x Amu^-1) # Sigma ~ IW(nu,V) # # note: we must insure that mu is a vector to use most efficient # lndMvn routine # nu=lambda$nu V=lambda$V mubar=lambda$mubar Amu=lambda$Amu k=length(mubar) Sigma=rwishart(nu,chol2inv(chol(lambda$V)))$IW root=chol(Sigma) mu=mubar+(1/sqrt(Amu))*t(root)%*%matrix(rnorm(k),ncol=1) return(list(mu=as.vector(mu),rooti=backsolve(root,diag(k)))) } # # ------------------------------------------------------------------------------------------- # thetaD= function(y,lambda,eta){ # # function to draw from posterior of theta given data y and base prior G0(lambda) # # here y ~ N(mu,Sigma) # theta = list(mu=mu,rooti=chol(Sigma)^-1) # mu|Sigma ~ N(mubar,Sigma (x) Amu-1) # Sigma ~ IW(nu,V) # # arguments: # y is n x k matrix of obs # lambda is list(mubar,Amu,nu,V) # eta is not used # output: # one draw of theta, list(mu,rooti) # Sigma=inv(rooti)%*%t(inv(rooti)) # # note: we assume that y is a matrix. if there is only one obs, y is a 1 x k matrix # rout=rmultireg(y,matrix(c(rep(1,nrow(y))),ncol=1),matrix(lambda$mubar,nrow=1),matrix(lambda$Amu,ncol=1), lambda$nu,lambda$V) return(list(mu=as.vector(rout$B),rooti=backsolve(chol(rout$Sigma),diag(ncol(y))))) } # # -------------------------------------------------------------------------------------------- # load a faster version of lndMvn # note: version of lndMvn below assumes x,mu is a vector! lndMvn=function (x, mu, rooti){ return(-(length(x)/2) * log(2 * pi) - 0.5 * sum(((x-mu)%*%rooti)**2) + sum(log(diag(rooti)))) } # ----------------------------------------------------------------------------------------- lambdaD=function(lambda,thetaStar,alim=c(.01,2),nulim=c(.01,2),vlim=c(.1,5),gridsize=20){ # # revision history # p. rossi 7/06 # vectorized 1/07 # changed 2/08 to paramaterize V matrix of IW prior to nu*v*I; then mode of Sigma=nu/(nu+2)vI # this means that we have a reparameterization to v* = nu*v # # function to draw (nu, v, a) using uniform priors # # theta_j=(mu_j,Sigma_j) mu_j~N(0,Sigma_j/a) Sigma_j~IW(nu,vI) # recall E[Sigma]= vI/(nu-dim-1) # # define functions needed # ---------------------------------------------------------------------------------------------- rmultinomF=function(p) { return(sum(runif(1) > cumsum(p))+1) } echo=function(lst){return(t(lst[[2]]))} rootiz=function(lst){crossprod(lst[[2]],lst[[1]])} # # ------------------------------------------------------------------------------------------ d=length(thetaStar[[1]]$mu) Istar=length(thetaStar) aseq=seq(from=alim[1],to=alim[2],len=gridsize) nuseq=d-1+exp(seq(from=nulim[1],to=nulim[2],len=gridsize)) # log uniform grid vseq=seq(from=vlim[1],to=vlim[2],len=gridsize) # # extract needed info from thetaStar list # out=double(Istar*d*d) out=sapply(thetaStar,echo) dim(out)=c(d,Istar*d) # out has the rootis in form: [t(rooti_1), t(rooti_2), ...,t(rooti_Istar)] sumdiagriri=sum(colSums(out^2)) # sum_j tr(rooti_j%*%t(rooti_j)) # now get diagonals of rooti ind=cbind(c(1:(d*Istar)),rep((1:d),Istar)) out=t(out) sumlogdiag=sum(log(out[ind])) rimu=sapply(thetaStar,rootiz) # columns of rimu contain t(rooti_j)%*%mu_j dim(rimu)=c(d,Istar) sumquads=sum(colSums(rimu^2)) # # draw a (conditionally indep of nu,v given theta_j) lnprob=double(length(aseq)) lnprob=Istar*(-(d/2)*log(2*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)] # # draw nu given v # V=lambda$V lnprob=double(length(nuseq)) arg=rep(c(1:d),gridsize) dim(arg)=c(d,gridsize) arg=t(arg) arg=(nuseq+1-arg)/2 lnprob=-Istar*log(2)*d/2*nuseq - Istar*rowSums(lgamma(arg)) + Istar*d*log(sqrt(V[1,1]))*nuseq + sumlogdiag*nuseq lnprob=lnprob-max(lnprob)+200 probs=exp(lnprob) probs=probs/sum(probs) nudraw=nuseq[rmultinomF(probs)] # # draw v given nu # lnprob=double(length(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)] # # put back into lambda # return(list(mubar=c(rep(0,d)),Amu=adraw,nu=nudraw,V=nudraw*vdraw*diag(d))) } pandterm=function(message) { stop(message,call.=FALSE) } # ----------------------------------------------------------------------------------------- for(rep in 1:1) #note: we only do one loop! { n = length(theta) eta=NULL # note eta is not used thetaNp1=NULL q0v = q0(y,lambda,eta) # now that we draw lambda we need to recompute q0v each time p=c(rep(1/(alpha+(n-1)),n-1),alpha/(alpha+(n-1))) nunique=length(thetaStar) if(nunique > maxuniq ) { pandterm("maximum number of unique thetas exceeded")} ydenmat=matrix(double(maxuniq*n),ncol=n) ydenmat[1:nunique,]=yden(thetaStar,y,eta) # 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! # use .Call to draw theta list out= .Call("thetadraw",y,ydenmat,indic,q0v,p,theta,lambda,eta=eta, thetaD=thetaD,yden=yden,maxuniq,nunique,new.env()) # theta has been modified by thetadraw so we need to recreate thetaStar thetaStar=unique(theta) nunique=length(thetaStar) #thetaNp1 and remix probs=double(nunique+1) for(j in 1:nunique) { ind = which(sapply(theta,identical,thetaStar[[j]])) probs[j]=length(ind)/(alpha+n) new_utheta=thetaD(y[ind,,drop=FALSE],lambda,eta) for(i in seq(along=ind)) {theta[[ind[i]]]=new_utheta} indic[ind]=j thetaStar[[j]]=new_utheta } probs[nunique+1]=alpha/(alpha+n) ind=rmultinomF(probs) if(ind==length(probs)) { thetaNp1=GD(lambda) } else { thetaNp1=thetaStar[[ind]] } # draw alpha alpha=alphaD(Prioralpha,nunique,gridsize=gridsize) # draw lambda lambda=lambdaD(lambda,thetaStar,alim=lambda_hyper$alim,nulim=lambda_hyper$nulim, vlim=lambda_hyper$vlim,gridsize=gridsize) } # note indic is the vector of indicators for each obs correspond to which thetaStar return(list(theta=theta,thetaStar=thetaStar,thetaNp1=thetaNp1,alpha=alpha,lambda=lambda,ind=indic)) } #-------------------------------------------------------------------------------------------------- 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))) } mnlRwMetropOnce= function(y,X,oldbeta,oldll,s,inc.root,betabar,rootpi){ # # function to execute rw metropolis for the MNL # 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 # RW increments are N(0,s^2*t(inc.root)%*%inc.root) # prior on beta is N(betabar,Sigma) Sigma^-1=rootpi*t(rootpi) # inc.root, rootpi are upper triangular # this means that we are using the UL decomp of Sigma^-1 for prior # oldbeta is the current stay=0 betac=oldbeta + s*t(inc.root)%*%(matrix(rnorm(ncol(X)),ncol=1)) cll=llmnl(betac,y,X) clpost=cll+lndMvn(betac,betabar,rootpi) ldiff=clpost-oldll-lndMvn(oldbeta,betabar,rootpi) alpha=min(1,exp(ldiff)) if(alpha < 1) {unif=runif(1)} else {unif=0} if (unif <= alpha) {betadraw=betac; oldll=cll} else {betadraw=oldbeta; stay=1} return(list(betadraw=betadraw,stay=stay,oldll=oldll)) } drawDelta= function(x,y,z,comps,deltabar,Ad){ # 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 p=ncol(y) k=ncol(x) xtx = matrix(0.0,k*p,k*p) xty = matrix(0.0,p,k) #this is the unvecced version, have to vec after sum for(i in 1:length(comps)) { nobs=sum(z==i) if(nobs > 0) { if(nobs == 1) { yi = matrix(y[z==i,],ncol=p); xi = matrix(x[z==i,],ncol=k)} else { yi = y[z==i,]; xi = x[z==i,]} yi = t(t(yi)-comps[[i]][[1]]) sigi = crossprod(t(comps[[i]][[2]])) xtx = xtx + crossprod(xi) %x% sigi xty = xty + (sigi %*% crossprod(yi,xi)) } } xty = matrix(xty,ncol=1) # then vec(t(D)) ~ N(V^{-1}(xty + Ad*deltabar),V^{-1}) V = (xtx+Ad) cov=chol2inv(chol(xtx+Ad)) return(cov%*%(xty+Ad%*%deltabar) + t(chol(cov))%*%rnorm(length(deltabar))) } #------------------------------------------------------------------------------------------------------- # # check arguments # pandterm=function(message) { stop(message,call.=FALSE) } 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$Z)) { cat("Z not specified",fill=TRUE); fsh() ; drawdelta=FALSE} else {if (nrow(Data$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)) {oldncol=ncol(lgtdata[[1]]$X)} for (i in 1:nlgt) { if(is.null(lgtdata[[i]]$y)) {pandterm(paste("Requires element y of lgtdata[[",i,"]]"))} if(is.null(lgtdata[[i]]$X)) {pandterm(paste("Requires element X of lgtdata[[",i,"]]"))} ypooled=c(ypooled,lgtdata[[i]]$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=c(.01,2) nulimdef=c(.01,3) vlimdef=c(.1,4) 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$Prioralpha)) {Prioralpha=list(Istarmin=1,Istarmax=min(50,0.1*nlgt),power=0.8)} else {Prioralpha=Prior$Prioralpha; if(is.null(Prioralpha$Istarmin)) {Prioralpha$Istarmin=1} 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=0.8} } gamma= .5772156649015328606 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$Ad) & drawdelta) {Ad=.01*diag(nvar*nz)} else {Ad=Prior$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$s)) {s=2.93/sqrt(nvar)} else {s=Mcmc$s} if(is.null(Mcmc$w)) {w=.1} else {w=Mcmc$w} if(is.null(Mcmc$keep)) {keep=1} else {keep=Mcmc$keep} if(is.null(Mcmc$maxuniq)) {maxuniq=200} else {keep=Mcmc$maxuniq} if(is.null(Mcmc$gridsize)) {gridsize=20} else {gridsize=Mcmc$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$power,fill=TRUE) cat(" ",fill=TRUE) if(drawdelta) { cat("deltabar",fill=TRUE) print(deltabar) cat("Ad",fill=TRUE) print(Ad) } cat(" ",fill=TRUE) cat("MCMC Parms: ",fill=TRUE) cat(paste("s=",round(s,3)," w= ",w," R= ",R," keep= ",keep," maxuniq= ",maxuniq, " gridsize for lambda hyperparms= ",gridsize),fill=TRUE) cat("",fill=TRUE) # # allocate space for draws # if(drawdelta) Deltadraw=matrix(double((floor(R/keep))*nz*nvar),ncol=nz*nvar) betadraw=array(double((floor(R/keep))*nlgt*nvar),dim=c(nlgt,nvar,floor(R/keep))) probdraw=matrix(double(floor(R/keep)),ncol=1) oldbetas=matrix(double(nlgt*nvar),ncol=nvar) oldll=double(nlgt) loglike=double(floor(R/keep)) thetaStar=NULL compdraw=NULL Istardraw=matrix(double(floor(R/keep)),ncol=1) alphadraw=matrix(double(floor(R/keep)),ncol=1) nudraw=matrix(double(floor(R/keep)),ncol=1) vdraw=matrix(double(floor(R/keep)),ncol=1) adraw=matrix(double(floor(R/keep)),ncol=1) # # intialize compute quantities for Metropolis # cat("initializing Metropolis candidate densities for ",nlgt," units ...",fill=TRUE) fsh() # # now go thru and computed fraction likelihood estimates and hessians # # Lbar=log(pooled likelihood^(n_i/N)) # # fraction loglike = (1-w)*loglike_i + w*Lbar # betainit=c(rep(0,nvar)) # # compute pooled optimum # out=optim(betainit,llmnl,method="BFGS",control=list( fnscale=-1,trace=0,reltol=1e-6), X=Xpooled,y=ypooled) betapooled=out$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]]$betafmle if(i%%50 ==0) cat(" completed unit #",i,fill=TRUE) fsh() } # # initialize delta # if (drawdelta) olddelta=rep(0,nz*nvar) # # initialize theta,thetaStar,ind # theta=vector("list",nlgt) for(i in 1:nlgt) {theta[[i]]=list(mu=rep(0,nvar),rooti=diag(nvar))} ind=double(nlgt) thetaStar=unique(theta) nunique=length(thetaStar) for(j in 1:nunique){ ind[which(sapply(theta,identical,thetaStar[[j]]))]=j } # # initialize alpha,lambda # alpha=1 lambda=list(mubar=rep(0,nvar),Amu=1,nu=nvar+1,V=(nvar+1)*diag(nvar)) # # fix oldprob (only one comp) # oldprob=1 # # start main iteration loop # itime=proc.time()[3] cat("MCMC Iteration (est time to end - min) ",fill=TRUE) fsh() for(rep in 1:R) { # first draw comps,ind,p | {beta_i}, delta # ind,p need initialization comps is drawn first in sub-Gibbs if(drawdelta) {mgout=rDPGibbs1(oldbetas-Z%*%t(matrix(olddelta,ncol=nz)),theta,thetaStar,ind, lambda,alpha,Prioralpha,lambda_hyper,maxuniq,gridsize)} else {mgout=rDPGibbs1(oldbetas,theta,thetaStar,ind, lambda,alpha,Prioralpha,lambda_hyper,maxuniq,gridsize)} ind=mgout$ind lambda=mgout$lambda alpha=mgout$alpha theta=mgout$theta thetaStar=mgout$thetaStar Istar=length(thetaStar) # now draw delta | {beta_i}, ind, comps if(drawdelta) {olddelta=drawDelta(Z,oldbetas,ind,thetaStar,deltabar,Ad)} # # loop over all lgt equations drawing beta_i | ind[i],z[i,],mu[ind[i]],rooti[ind[i]] # for (lgt in 1:nlgt) { rootpi=thetaStar[[ind[lgt]]]$rooti # note: beta_i = Delta*z_i + u_i Delta is nvar x nz if(drawdelta) { betabar=thetaStar[[ind[lgt]]]$mu+matrix(olddelta,ncol=nz)%*%as.vector(Z[lgt,])} else { betabar=thetaStar[[ind[lgt]]]$mu } if (rep == 1) { oldll[lgt]=llmnl(oldbetas[lgt,],lgtdata[[lgt]]$y,lgtdata[[lgt]]$X)} # compute inc.root inc.root=chol(chol2inv(chol(lgtdata[[lgt]]$hess+rootpi%*%t(rootpi)))) metropout=mnlRwMetropOnce(lgtdata[[lgt]]$y,lgtdata[[lgt]]$X,oldbetas[lgt,], oldll[lgt],s,inc.root,betabar,rootpi) oldbetas[lgt,]=metropout$betadraw oldll[lgt]=metropout$oldll } # # # print time to completion and draw # every 100th draw # if(((rep/100)*100) ==(floor(rep/100)*100)) {ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R+1-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh()} # # save every keepth draw # mkeep=rep/keep if((mkeep*keep) == (floor(mkeep)*keep)) { betadraw[,,mkeep]=oldbetas probdraw[mkeep,]=oldprob alphadraw[mkeep,]=alpha Istardraw[mkeep,]=Istar adraw[mkeep,]=lambda$Amu nudraw[mkeep,]=lambda$nu vdraw[mkeep,]=lambda$V[1,1]/lambda$nu loglike[mkeep]=sum(oldll) if(drawdelta) Deltadraw[mkeep,]=olddelta compdraw[[mkeep]]=list(list(mu=mgout$thetaNp1[[1]],rooti=mgout$thetaNp1[[2]])) } } ctime=proc.time()[3] cat(" Total Time Elapsed: ",round((ctime-itime)/60,2),fill=TRUE) if(drawdelta){ attributes(Deltadraw)$class=c("bayesm.mat","mcmc") attributes(Deltadraw)$mcpar=c(1,R,keep)} attributes(betadraw)$class=c("bayesm.hcoef") nmix=list(probdraw=probdraw,zdraw=NULL,compdraw=compdraw) attributes(nmix)$class="bayesm.nmix" attributes(adraw)$class=c("bayesm.mat","mcmc") attributes(nudraw)$class=c("bayesm.mat","mcmc") attributes(vdraw)$class=c("bayesm.mat","mcmc") attributes(Istardraw)$class=c("bayesm.mat","mcmc") attributes(alphadraw)$class=c("bayesm.mat","mcmc") if(drawdelta) {return(list(Deltadraw=Deltadraw,betadraw=betadraw,nmix=nmix,alphadraw=alphadraw,Istardraw=Istardraw, adraw=adraw,nudraw=nudraw,vdraw=vdraw,loglike=loglike))} else {return(list(betadraw=betadraw,nmix=nmix,alphadraw=alphadraw,Istardraw=Istardraw, adraw=adraw,nudraw=nudraw,vdraw=vdraw,loglike=loglike))} } bayesm/R/rhierLinearModel.R0000755000176000001440000002020010764073630015336 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 # # 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 # # 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$y) if(is.na(v)) return(1) if(v>0) return (v) else return (1)} # runiregG= function(y,X,XpX,Xpy,sigmasq,A,betabar,nu,ssq){ # # Purpose: # perform one Gibbs iteration for Univ Regression Model # only does one iteration so can be used in rhierLinearModel # # Model: # y = Xbeta + e e ~N(0,sigmasq) # y is n x 1 # X is n x k # beta is k x 1 vector of coefficients # # Priors: beta ~ N(betabar,A^-1) # sigmasq ~ (nu*ssq)/chisq_nu # n=length(y) k=ncol(XpX) sigmasq=as.vector(sigmasq) # # first draw beta | sigmasq # IR=backsolve(chol(XpX/sigmasq+A),diag(k)) btilde=crossprod(t(IR))%*%(Xpy/sigmasq+A%*%betabar) beta = btilde + IR%*%rnorm(k) # # now draw sigmasq | beta # res=y-X%*%beta s=t(res)%*%res sigmasq=(nu*ssq + s)/rchisq(1,nu+n) list(betadraw=beta,sigmasqdraw=sigmasq) } #------------------------------------------------------------------------------ # # # check arguments # pandterm=function(message) {stop(message,call.=FALSE)} if(missing(Data)) {pandterm("Requires Data argument -- list of regdata and Z")} if(is.null(Data$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 (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 # 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=0.01*diag(nz); nu.e=3; ssq=sapply(regdata,getvar) ; nu=nvar+3 ; 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$A)) {A=.01*diag(nz)} else {A=Prior$A} if(is.null(Prior$nu.e)) {nu.e=3} else {nu.e=Prior$nu.e} if(is.null(Prior$ssq)) {ssq=sapply(regdata,getvar)} else {ssq=Prior$ssq} if(is.null(Prior$nu)) {nu=nvar+3} else {nu=Prior$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$keep)) {keep=1} else {keep=Mcmc$keep} } # # 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,fill=TRUE) cat(" ",fill=TRUE) # # allocate space for the draws and set initial values of Vbeta and Delta # Vbetadraw=matrix(double(floor(R/keep)*nvar*nvar),ncol=nvar*nvar) Deltadraw=matrix(double(floor(R/keep)*nz*nvar),ncol=nz*nvar) taudraw=matrix(double(floor(R/keep)*nreg),ncol=nreg) betadraw=array(double(floor(R/keep)*nreg*nvar),dim=c(nreg,nvar,floor(R/keep))) tau=double(nreg) Delta=c(rep(0,nz*nvar)) Vbeta=as.vector(diag(nvar)) betas=matrix(double(nreg*nvar),ncol=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) # # start main iteration loop # itime=proc.time()[3] cat("MCMC Iteration (est time to end - min) ",fill=TRUE) fsh() for(rep in 1:R) { Abeta=chol2inv(chol(matrix(Vbeta,ncol=nvar))) betabar=Z%*%matrix(Delta,ncol=nvar) # # loop over all regressions # for (reg in 1:nreg) { regout=runiregG(regdata[[reg]]$y,regdata[[reg]]$X,regdata[[reg]]$XpX, regdata[[reg]]$Xpy,tau[reg],Abeta,betabar[reg,],nu.e,ssq[reg]) betas[reg,]=regout$betadraw tau[reg]=regout$sigmasqdraw } # # draw Vbeta, Delta | {beta_i} # rmregout=rmultireg(betas,Z,Deltabar,A,nu,V) Vbeta=as.vector(rmregout$Sigma) Delta=as.vector(rmregout$B) # # print time to completion and draw # every 100th draw # if(rep%%100 == 0) {ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh()} if(rep%%keep == 0) {mkeep=rep/keep Vbetadraw[mkeep,]=Vbeta Deltadraw[mkeep,]=Delta taudraw[mkeep,]=tau betadraw[,,mkeep]=betas} } ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') attributes(taudraw)$class=c("bayesm.mat","mcmc") attributes(taudraw)$mcpar=c(1,R,keep) 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) attributes(betadraw)$class=c("bayesm.hcoef") return(list(Vbetadraw=Vbetadraw,Deltadraw=Deltadraw,betadraw=betadraw,taudraw=taudraw)) } bayesm/R/rhierLinearMixture.R0000755000176000001440000002671011071420416015735 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 # # 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) # # 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 # # 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)} # runiregG= function(y,X,XpX,Xpy,sigmasq,rooti,betabar,nu,ssq){ # # Purpose: # perform one Gibbs iteration for Univ Regression Model # only does one iteration so can be used in both rhierLinearMixture & 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 # # Priors: beta ~ N(betabar,A^-1) # sigmasq ~ (nu*ssq)/chisq_nu # n=length(y) k=ncol(XpX) sigmasq=as.vector(sigmasq) A=crossprod(rooti) # # first draw beta | sigmasq # IR=backsolve(chol(XpX/sigmasq+A),diag(k)) btilde=crossprod(t(IR))%*%(Xpy/sigmasq+A%*%betabar) beta = btilde + IR%*%rnorm(k) # # now draw sigmasq | beta # res=y-X%*%beta s=t(res)%*%res sigmasq=(nu*ssq + s)/rchisq(1,nu+n) list(betadraw=beta,sigmasqdraw=sigmasq) } # drawDelta= function(x,y,z,comps,deltabar,Ad){ # Z,oldbetas,ind,oldcomp,deltabar,Ad # 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 betas: nreg x nvar # x is Z: nreg x nz # y = xD' + U , rows of U are indep with covs Sigma_i given by z and comps nvar=ncol(y) #p nz=ncol(x) #k xtx = matrix(0.0,nz*nvar,nz*nvar) xty = matrix(0.0,nvar,nz) #this is the unvecced version, have to vec after sum for(i in 1:length(comps)) { nobs=sum(z==i) if(nobs > 0) { if(nobs == 1) { yi = matrix(y[z==i,],ncol=nvar); xi = matrix(x[z==i,],ncol=nz)} else { yi = y[z==i,]; xi = x[z==i,]} yi = t(t(yi)-comps[[i]][[1]]) sigi = crossprod(t(comps[[i]][[2]])) xtx = xtx + crossprod(xi) %x% sigi xty = xty + (sigi %*% crossprod(yi,xi)) } } xty = matrix(xty,ncol=1) # then vec(t(D)) ~ N(V^{-1}(xty + Ad*deltabar),V^{-1}) V = (xtx+Ad) cov=chol2inv(chol(xtx+Ad)) return(cov%*%(xty+Ad%*%deltabar) + t(chol(cov))%*%rnorm(length(deltabar))) } #------------------------------------------------------------------------------------------------------- pandterm=function(message) { stop(message,call.=FALSE) } 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 (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 # 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$nu.e)) {nu.e=3} else {nu.e=Prior$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$Amu)) {Amu=matrix(.01,ncol=1)} else {Amu=matrix(Prior$Amu,ncol=1)} if(ncol(Amu) != 1 | nrow(Amu) != 1) {pandterm("Am must be a 1 x 1 array")} if(is.null(Prior$nu)) {nu=nvar+3} else {nu=Prior$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$Ad) & drawdelta) {Ad=.01*diag(nvar*nz)} else {Ad=Prior$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$a)) { a=rep(5,ncomp)} else {a=Prior$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$keep)) {keep=1} else {keep=Mcmc$keep} if(is.null(Mcmc$R)) {pandterm("Requires R argument in Mcmc list")} else {R=Mcmc$R} } # # print out problem # cat(" ",fill=TRUE) cat("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(paste(" R= ",R," keep= ",keep),fill=TRUE) cat("",fill=TRUE) # # allocate space for draws # taudraw=matrix(double(floor(R/keep)*nreg),ncol=nreg) if(drawdelta) Deltadraw=matrix(double((floor(R/keep))*nz*nvar),ncol=nz*nvar) betadraw=array(double((floor(R/keep))*nreg*nvar),dim=c(nreg,nvar,floor(R/keep))) probdraw=matrix(double((floor(R/keep))*ncomp),ncol=ncomp) oldbetas=matrix(double(nreg*nvar),ncol=nvar) oldcomp=NULL compdraw=NULL # # 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) # # initialize probs # oldprob=rep(1/ncomp,ncomp) # # initialize comps # tcomp=list(list(mu=rep(0,nvar),rooti=diag(nvar))) oldcomp=rep(tcomp,ncomp) # # start main iteration loop # itime=proc.time()[3] cat("MCMC Iteration (est time to end - min) ",fill=TRUE) fsh() for(rep in 1:R) { # first draw comps,ind,p | {beta_i}, delta # ind,p need initialization comps is drawn first in sub-Gibbs if(drawdelta) {mgout=rmixGibbs(oldbetas-Z%*%t(matrix(olddelta,ncol=nz)), mubar,Amu,nu,V,a,oldprob,ind,oldcomp)} else {mgout=rmixGibbs(oldbetas, mubar,Amu,nu,V,a,oldprob,ind,oldcomp)} oldprob=mgout[[1]] oldcomp=mgout[[3]] ind=mgout[[2]] # 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 (reg in 1:nreg) { rootpi=oldcomp[[ind[reg]]]$rooti # note: beta_i = Delta*z_i + u_i Delta is nvar x nz if(drawdelta) { betabar=oldcomp[[ind[reg]]]$mu+matrix(olddelta,ncol=nz)%*%as.vector(Z[reg,])} else { betabar=oldcomp[[ind[reg]]]$mu } regout=runiregG(regdata[[reg]]$y,regdata[[reg]]$X,regdata[[reg]]$XpX, regdata[[reg]]$Xpy,tau[reg],rootpi,betabar,nu.e,ssq[reg]) oldbetas[reg,]=regout$betadraw tau[reg]=regout$sigmasqdraw } # # print time to completion and draw # every 100th draw # if(((rep/100)*100) ==(floor(rep/100)*100)) {ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R+1-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh()} # # save every keepth draw # mkeep=rep/keep if((mkeep*keep) == (floor(mkeep)*keep)) { taudraw[mkeep,]=tau betadraw[,,mkeep]=oldbetas probdraw[mkeep,]=oldprob if(drawdelta) Deltadraw[mkeep,]=olddelta compdraw[[mkeep]]=oldcomp } } ctime=proc.time()[3] cat(" Total Time Elapsed: ",round((ctime-itime)/60,2),fill=TRUE) attributes(taudraw)$class=c("bayesm.mat","mcmc") attributes(taudraw)$mcpar=c(1,R,keep) if(drawdelta){ attributes(Deltadraw)$class=c("bayesm.mat","mcmc") attributes(Deltadraw)$mcpar=c(1,R,keep)} attributes(betadraw)$class=c("bayesm.hcoef") nmix=list(probdraw=probdraw,zdraw=NULL,compdraw=compdraw) attributes(nmix)$class="bayesm.nmix" if(drawdelta) {return(list(taudraw=taudraw,Deltadraw=Deltadraw,betadraw=betadraw,nmix=nmix))} else {return(list(taudraw=taudraw,betadraw=betadraw,nmix=nmix))} } bayesm/R/rhierBinLogit.R0000755000176000001440000001641210571564274014671 0ustar ripleyusers# # ----------------------------------------------------------------------------- # rhierBinLogit= function(Data,Prior,Mcmc){ # # revision history: # changed 5/12/05 by Rossi to add error checking # 1/07 removed init.rmultiregfp # 3/07 added classes # # purpose: run binary heterogeneous logit model # # Arguments: # Data contains a list of (lgtdata[[i]],Z) # lgtdata[[i]]=list(y,X) # y is index of brand chosen, y=1 is exp[X'beta]/(1+exp[X'beta]) # X is a matrix that is n_i x by nvar # Z is a matrix of demographic variables nlgt*nz that have been # mean centered so that the intercept is interpretable # Prior contains a list of (nu,V,Deltabar,ADelta) # beta_i ~ N(Z%*%Delta,Vbeta) # vec(Delta) ~ N(vec(Deltabar),Vbeta (x) ADelta^-1) # Vbeta ~ IW(nu,V) # Mcmc is a list of (sbeta,R,keep) # sbeta is scale factor for RW increment for beta_is # R is number of draws # keep every keepth draw # # Output: # a list of Deltadraw (R/keep x nvar x nz), Vbetadraw (R/keep x nvar**2), # llike (R/keep), betadraw is a nlgt x nvar x nz x R/keep array of draws of betas # nunits=length(lgtdata) # # define functions needed # # ------------------------------------------------------------------------ # loglike= function(y,X,beta) { # function computer log likelihood of data for binomial logit model # Pr(y=1) = 1 - Pr(y=0) = exp[X'beta]/(1+exp[X'beta]) prob = exp(X%*%beta)/(1+exp(X%*%beta)) prob = prob*y + (1-prob)*(1-y) sum(log(prob)) } # # # check arguments # pandterm=function(message) { stop(message,call.=FALSE) } if(missing(Data)) {pandterm("Requires Data argument -- list of m,lgtdata, and (possibly) Z")} if(is.null(Data$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 (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]]$X)) {oldncol=ncol(lgtdata[[1]]$X)} for (i in 1:nlgt) { if(is.null(lgtdata[[i]]$y)) {pandterm(paste("Requires element y of lgtdata[[",i,"]]"))} if(is.null(lgtdata[[i]]$X)) {pandterm(paste("Requires element X of lgtdata[[",i,"]]"))} 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/rDPGibbs.R0000755000176000001440000004624710763337575013602 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]) # # 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 # # 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 # # # # define needed functions # # ----------------------------------------------------------------------------------------- # q0=function(y,lambda,eta){ # # function to compute a vector of int f(y[i]|theta) p(theta|lambda)dlambda # here p(theta|lambda) is G0 the base prior # # implemented for a multivariate normal data density and standard conjugate # prior: # theta=list(mu,Sigma) # f(y|theta,eta) is N(mu,Sigma) # lambda=list(mubar,Amu,nu,V) # mu|Sigma ~ N(mubar,Sigma (x) Amu^-1) # Sigma ~ IW(nu,V) # # arguments: # Y is n x k matrix of observations # lambda=list(mubar,Amu,nu,V) # eta is not used # # output: # vector of q0 values for each obs (row of Y) # # p. rossi 12/05 # # here y is matrix of observations (each row is an obs) mubar=lambda$mubar; nu=lambda$nu ; Amu=lambda$Amu; V=lambda$V k=ncol(y) R=chol(V) logdetR=sum(log(diag(R))) if (k > 1) {lnk1k2=(k/2)*log(2)+log((nu-k)/2)+lgamma((nu-k)/2)-lgamma(nu/2)+sum(log(nu/2-(1:(k-1))/2))} else {lnk1k2=(k/2)*log(2)+log((nu-k)/2)+lgamma((nu-k)/2)-lgamma(nu/2)} constant=-(k/2)*log(2*pi)+(k/2)*log(Amu/(1+Amu)) + lnk1k2 + nu*logdetR # # note: here we are using the fact that |V + S_i | = |R|^2 (1 + v_i'v_i) # where v_i = sqrt(Amu/(1+Amu))*t(R^-1)*(y_i-mubar), R is chol(V) # # and S_i = Amu/(1+Amu) * (y_i-mubar)(y_i-mubar)' # mat=sqrt(Amu/(1+Amu))*t(backsolve(R,diag(ncol(y))))%*%(t(y)-mubar) vivi=colSums(mat^2) lnq0v=constant-((nu+1)/2)*(2*logdetR+log(1+vivi)) return(exp(lnq0v)) } # ---------------------------------------------------------------------------------------------- rmultinomF= function(p) { return(sum(runif(1) > cumsum(p))+1) } # ----------------------------------------------------------------------------------------------- alphaD=function(Prioralpha,Istar,gridsize){ # # function to draw alpha using prior, p(alpha)= (1-(alpha-alphamin)/(alphamax-alphamin))**power # power=Prioralpha$power alphamin=Prioralpha$alphamin alphamax=Prioralpha$alphamax n=Prioralpha$n alpha=seq(from=alphamin,to=(alphamax-0.000001),len=gridsize) lnprob=Istar*log(alpha) + lgamma(alpha) - lgamma(n+alpha) + power*log(1-(alpha-alphamin)/(alphamax-alphamin)) lnprob=lnprob-median(lnprob) probs=exp(lnprob) probs=probs/sum(probs) return(alpha[rmultinomF(probs)]) } # # ------------------------------------------------------------------------------------------ # yden=function(thetaStar,y,eta){ # # function to compute f(y | theta) # computes f for all values of theta in theta list of lists # # arguments: # thetaStar is a list of lists. thetaStar[[i]] is a list with components, mu, rooti # y |theta[[i]] ~ N(mu,(rooti %*% t(rooti))^-1) rooti is inverse of Chol root of Sigma # eta is not used # # output: # length(thetaStar) x n array of values of f(y[j,]|thetaStar[[i]] # nunique=length(thetaStar) n=nrow(y) ydenmat=matrix(double(n*nunique),ncol=n) k=ncol(y) for(i in 1:nunique){ # now compute vectorized version of lndMvn # compute y_i'RIRI'y_i for all i # mu=thetaStar[[i]]$mu; rooti=thetaStar[[i]]$rooti quads=colSums((crossprod(rooti,(t(y)-mu)))^2) ydenmat[i,]=exp(-(k/2)*log(2*pi) + sum(log(diag(rooti))) - .5*quads) } return(ydenmat) } # # ----------------------------------------------------------------------------------------- # GD=function(lambda){ # # function to draw from prior for Multivariate Normal Model # # mu|Sigma ~ N(mubar,Sigma x Amu^-1) # Sigma ~ IW(nu,V) # # note: we must insure that mu is a vector to use most efficient # lndMvn routine # nu=lambda$nu V=lambda$V mubar=lambda$mubar Amu=lambda$Amu k=length(mubar) Sigma=rwishart(nu,chol2inv(chol(lambda$V)))$IW root=chol(Sigma) mu=mubar+(1/sqrt(Amu))*t(root)%*%matrix(rnorm(k),ncol=1) return(list(mu=as.vector(mu),rooti=backsolve(root,diag(k)))) } # # ------------------------------------------------------------------------------------------- # thetaD=function(y,lambda,eta){ # # function to draw from posterior of theta given data y and base prior G0(lambda) # # here y ~ N(mu,Sigma) # theta = list(mu=mu,rooti=chol(Sigma)^-1) # mu|Sigma ~ N(mubar,Sigma (x) Amu-1) # Sigma ~ IW(nu,V) # # arguments: # y is n x k matrix of obs # lambda is list(mubar,Amu,nu,V) # eta is not used # output: # one draw of theta, list(mu,rooti) # Sigma=inv(rooti)%*%t(inv(rooti)) # # note: we assume that y is a matrix. if there is only one obs, y is a 1 x k matrix # rout=rmultireg(y,matrix(c(rep(1,nrow(y))),ncol=1),matrix(lambda$mubar,nrow=1),matrix(lambda$Amu,ncol=1), lambda$nu,lambda$V) return(list(mu=as.vector(rout$B),rooti=backsolve(chol(rout$Sigma),diag(ncol(y))))) } # # -------------------------------------------------------------------------------------------- # load a faster version of lndMvn # note: version of lndMvn below assumes x,mu is a vector! lndMvn=function (x, mu, rooti) { return(-(length(x)/2) * log(2 * pi) - 0.5 * sum(((x-mu)%*%rooti)**2) + sum(log(diag(rooti)))) } # ----------------------------------------------------------------------------------------- lambdaD=function(lambda,thetastar,alim=c(.01,2),nulim=c(.01,2),vlim=c(.1,5),gridsize=20){ # # revision history # p. rossi 7/06 # vectorized 1/07 # changed 2/08 to paramaterize V matrix of IW prior to nu*v*I; then mode of Sigma=nu/(nu+2)vI # this means that we have a reparameterization to v* = nu*v # # function to draw (nu, v, a) using uniform priors # # theta_j=(mu_j,Sigma_j) mu_j~N(0,Sigma_j/a) Sigma_j~IW(nu,vI) # recall E[Sigma]= vI/(nu-dim-1) # # define functions needed # ---------------------------------------------------------------------------------------------- rmultinomF= function(p) { return(sum(runif(1) > cumsum(p))+1) } echo=function(lst){return(t(lst[[2]]))} rootiz=function(lst){crossprod(lst[[2]],lst[[1]])} # # ------------------------------------------------------------------------------------------ d=length(thetastar[[1]]$mu) Istar=length(thetastar) aseq=seq(from=alim[1],to=alim[2],len=gridsize) nuseq=d-1+exp(seq(from=nulim[1],to=nulim[2],len=gridsize)) # log uniform grid vseq=seq(from=vlim[1],to=vlim[2],len=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 # out=double(Istar*d*d) out=sapply(thetastar,echo) dim(out)=c(d,Istar*d) # out has the rootis in form: [t(rooti_1), t(rooti_2), ...,t(rooti_Istar)] sumdiagriri=sum(colSums(out^2)) # sum_j tr(rooti_j%*%t(rooti_j)) # now get diagonals of rooti ind=cbind(c(1:(d*Istar)),rep((1:d),Istar)) out=t(out) sumlogdiag=sum(log(out[ind])) rimu=sapply(thetastar,rootiz) # columns of rimu contain t(rooti_j)%*%mu_j dim(rimu)=c(d,Istar) sumquads=sum(colSums(rimu^2)) # # draw a (conditionally indep of nu,v given theta_j) lnprob=double(length(aseq)) #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)*log(2*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)] # # draw nu given v # V=lambda$V lnprob=double(length(nuseq)) #for(i in seq(along=nuseq)){ #for(j in seq(along=thetastar)){ #Sigma_j=crossprod(backsolve(thetastar[[j]]$rooti,diag(d))) #lnprob[i]=lnprob[i]+lndIWishart(nuseq[i],V,Sigma_j)} arg=rep(c(1:d),gridsize) dim(arg)=c(d,gridsize) arg=t(arg) arg=(nuseq+1-arg)/2 lnprob=-Istar*log(2)*d/2*nuseq - Istar*rowSums(lgamma(arg)) + Istar*d*log(sqrt(V[1,1]))*nuseq + sumlogdiag*nuseq lnprob=lnprob-max(lnprob)+200 probs=exp(lnprob) probs=probs/sum(probs) nudraw=nuseq[rmultinomF(probs)] # # draw v given nu # lnprob=double(length(vseq)) #for(i in seq(along=vseq)){ #V=vseq[i]*diag(d) #for(j in seq(along=thetastar)){ #Sigma_j=crossprod(backsolve(thetastar[[j]]$rooti,diag(d))) #lnprob[i]=lnprob[i]+lndIWishart(nudraw,V,Sigma_j)} # lnprob=Istar*nudraw*d*log(sqrt(vseq))-.5*sumdiagriri*vseq lnprob=Istar*nudraw*d*log(sqrt(vseq*nudraw))-.5*sumdiagriri*vseq*nudraw lnprob=lnprob-max(lnprob)+200 probs=exp(lnprob) probs=probs/sum(probs) vdraw=vseq[rmultinomF(probs)] # # put back into lambda # return(list(mubar=c(rep(0,d)),Amu=adraw,nu=nudraw,V=nudraw*vdraw*diag(d))) } # ----------------------------------------------------------------------------------------- # check arguments # pandterm=function(message) {stop(message,call.=FALSE)} if(missing(Data)) {pandterm("Requires Data argument -- list of y")} if(is.null(Data$y)) {pandterm("Requires Data element y")} y=Data$y # # check data for validity # if(!is.matrix(y)) {pandterm("y must be a matrix")} nobs=nrow(y) dimy=ncol(y) # # check for Prior # alimdef=c(.01,10) nulimdef=c(.01,3) vlimdef=c(.1,4) if(missing(Prior)) {pandterm("requires Prior argument ")} else { if(is.null(Prior$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=1,Istarmax=min(50,0.1*nobs),power=0.8)} else {Prioralpha=Prior$Prioralpha; if(is.null(Prioralpha$Istarmin)) {Prioralpha$Istarmin=1} else {Prioralpha$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$power=0.8} } } gamma= .5772156649015328606 Prioralpha$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=1} else {keep=Mcmc$keep} if(is.null(Mcmc$maxuniq)) {maxuniq=200} else {maxuniq=Mcmc$maxuniq} if(is.null(Mcmc$SCALE)) {SCALE=TRUE} else {SCALE=Mcmc$SCALE} if(is.null(Mcmc$gridsize)) {gridsize=20} 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," maxuniq= ",maxuniq," gridsize for lambda hyperparms= ",gridsize, fill=TRUE) cat(" ",fill=TRUE) # initialize theta, thetastar, indic theta=vector("list",nobs) for(i in 1:nobs) {theta[[i]]=list(mu=rep(0,dimy),rooti=diag(dimy))} indic=double(nobs) thetaStar=unique(theta) nunique=length(thetaStar) for(j in 1:nunique){ indic[which(sapply(theta,identical,thetaStar[[j]]))]=j } # # initialize lambda # lambda=list(mubar=rep(0,dimy),Amu=.1,nu=dimy+1,V=(dimy+1)*diag(dimy)) # # initialize alpha # alpha=1 alphadraw=double(floor(R/keep)) Istardraw=double(floor(R/keep)) adraw=double(floor(R/keep)) nudraw=double(floor(R/keep)) vdraw=double(floor(R/keep)) thetaNp1draw=vector("list",floor(R/keep)) inddraw=matrix(double((floor(R/keep))*nobs),ncol=nobs) # # do scaling # if(SCALE){ dvec=sqrt(apply(y,2,var)) ybar=apply(y,2,mean) y=scale(y,center=ybar,scale=dvec) dvec=1/dvec # R function scale divides by scale } # # 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 # itime=proc.time()[3] cat("MCMC Iteration (est time to end -min) ",fill=TRUE) fsh() for(rep in 1:R) { n = length(theta) eta=NULL # note eta is not used thetaNp1=NULL q0v = q0(y,lambda,eta) # now that we draw lambda we need to recompute q0v each time p=c(rep(1/(alpha+(n-1)),n-1),alpha/(alpha+(n-1))) nunique=length(thetaStar) if(nunique > maxuniq ) { pandterm("maximum number of unique thetas exceeded")} ydenmat=matrix(double(maxuniq*n),ncol=n) ydenmat[1:nunique,]=yden(thetaStar,y,eta) # 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! # use .Call to draw theta list out= .Call("thetadraw",y,ydenmat,indic,q0v,p,theta,lambda,eta=eta, thetaD=thetaD,yden=yden,maxuniq,nunique,new.env()) # theta has been modified by thetadraw so we need to recreate thetaStar thetaStar=unique(theta) nunique=length(thetaStar) #thetaNp1 and remix probs=double(nunique+1) for(j in 1:nunique) { ind = which(sapply(theta,identical,thetaStar[[j]])) probs[j]=length(ind)/(alpha+n) new_utheta=thetaD(y[ind,,drop=FALSE],lambda,eta) for(i in seq(along=ind)) {theta[[ind[i]]]=new_utheta} indic[ind]=j thetaStar[[j]]=new_utheta } probs[nunique+1]=alpha/(alpha+n) ind=rmultinomF(probs) if(ind==length(probs)) { thetaNp1=GD(lambda) } else { thetaNp1=thetaStar[[ind]] } # draw alpha alpha=alphaD(Prioralpha,nunique,gridsize=gridsize) # draw lambda lambda=lambdaD(lambda,thetaStar,alim=lambda_hyper$alim,nulim=lambda_hyper$nulim, vlim=lambda_hyper$vlim,gridsize=gridsize) if(rep%%100==0) { ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh() } if(rep%%keep ==0) { mkeep=rep/keep alphadraw[mkeep]=alpha Istardraw[mkeep]=nunique adraw[mkeep]=lambda$Amu nudraw[mkeep]=lambda$nu vdraw[mkeep]=lambda$V[1,1]/lambda$nu if(SCALE){ thetaNp1[[1]]=thetaNp1[[1]]/dvec+ybar if(ncol(y)>1) {thetaNp1[[2]]=diag(dvec)%*%thetaNp1[[2]]} else {thetaNp1[[2]]=dvec*thetaNp1[[2]]} } thetaNp1draw[[mkeep]]=list(list(mu=thetaNp1[[1]],rooti=thetaNp1[[2]])) # here we put the draws into the list of lists of list format useful for # finite mixture of normals utilities inddraw[mkeep,]=indic } } ctime=proc.time()[3] cat("Total Time Elapsed= ",round((ctime-itime)/60,2),fill=TRUE) nmix=list(probdraw=matrix(c(rep(1,nrow(inddraw))),ncol=1),zdraw=inddraw,compdraw=thetaNp1draw) attributes(nmix)$class="bayesm.nmix" attributes(alphadraw)$class=c("bayesm.mat","mcmc") attributes(Istardraw)$class=c("bayesm.mat","mcmc") attributes(adraw)$class=c("bayesm.mat","mcmc") attributes(nudraw)$class=c("bayesm.mat","mcmc") attributes(vdraw)$class=c("bayesm.mat","mcmc") return(list(alphadraw=alphadraw,Istardraw=Istardraw,adraw=adraw,nudraw=nudraw, vdraw=vdraw,nmix=nmix)) } bayesm/R/rdirichlet.R0000755000176000001440000000026610225364076014253 0ustar ripleyusersrdirichlet = function(alpha) { # # Purpose: # draw from Dirichlet(alpha) # dim = length(alpha) y=rep(0,dim) for(i in 1:dim) y[i] = rgamma(1,alpha[i]) return(y/sum(y)) } bayesm/R/rbprobitGibbs.R0000755000176000001440000000776410576267145014736 0ustar ripleyusersrbprobitGibbs= function(Data,Prior,Mcmc) { # # revision history: # p. rossi 1/05 # 3/07 added validity check of values of y and classes # 3/07 fixed error with betabar supplied # # purpose: # draw from posterior for binary probit using Gibbs Sampler # # Arguments: # Data - list of X,y # X is nobs x nvar, y is nobs vector of 0,1 # Prior - list of A, betabar # A is nvar x nvar prior preci matrix # betabar is nvar x 1 prior mean # Mcmc # R is number of draws # keep is thinning parameter # # Output: # list of betadraws # # Model: y = 1 if w=Xbeta + e > 0 e ~N(0,1) # # Prior: beta ~ N(betabar,A^-1) # # # ---------------------------------------------------------------------- # define functions needed # breg1= function(root,X,y,Abetabar) { # # p.rossi 12/04 # # Purpose: draw from posterior for linear regression, sigmasq=1.0 # # Arguments: # root is chol((X'X+A)^-1) # Abetabar = A*betabar # # Output: draw from posterior # # Model: y = Xbeta + e e ~ N(0,I) # # Prior: beta ~ N(betabar,A^-1) # cov=crossprod(root,root) betatilde=cov%*%(crossprod(X,y)+Abetabar) betatilde+t(root)%*%rnorm(length(betatilde)) } pandterm=function(message) {stop(message,call.=FALSE)} # # ---------------------------------------------------------------------- # # check arguments # if(missing(Data)) {pandterm("Requires Data argument -- list of y and X")} if(is.null(Data$X)) {pandterm("Requires Data element X")} X=Data$X if(is.null(Data$y)) {pandterm("Requires Data element y")} y=Data$y nvar=ncol(X) nobs=length(y) # # check data for validity # if(length(y) != nrow(X) ) {pandterm("y and X not of same row dim")} if(sum(unique(y) %in% c(0:1)) < length(unique(y))) {pandterm("Invalid y, must be 0,1")} # # check for Prior # if(missing(Prior)) { betabar=c(rep(0,nvar)); A=.01*diag(nvar)} else { if(is.null(Prior$betabar)) {betabar=c(rep(0,nvar))} else {betabar=Prior$betabar} if(is.null(Prior$A)) {A=.01*diag(nvar)} else {A=Prior$A} } # # check dimensions of Priors # if(ncol(A) != nrow(A) || ncol(A) != nvar || nrow(A) != nvar) {pandterm(paste("bad dimensions for A",dim(A)))} if(length(betabar) != nvar) {pandterm(paste("betabar wrong length, length= ",length(betabar)))} # # check MCMC argument # if(missing(Mcmc)) {pandterm("requires Mcmc argument")} else { if(is.null(Mcmc$R)) {pandterm("requires Mcmc element R")} else {R=Mcmc$R} if(is.null(Mcmc$keep)) {keep=1} else {keep=Mcmc$keep} } # # print out problem # cat(" ", fill=TRUE) cat("Starting Gibbs Sampler for Binary Probit Model",fill=TRUE) cat(" with ",length(y)," observations",fill=TRUE) cat("Table of y Values",fill=TRUE) print(table(y)) cat(" ", fill=TRUE) cat("Prior Parms: ",fill=TRUE) cat("betabar",fill=TRUE) print(betabar) cat("A",fill=TRUE) print(A) cat(" ", fill=TRUE) cat("MCMC parms: ",fill=TRUE) cat("R= ",R," keep= ",keep,fill=TRUE) cat(" ",fill=TRUE) betadraw=matrix(double(floor(R/keep)*nvar),ncol=nvar) beta=c(rep(0,nvar)) sigma=c(rep(1,nrow(X))) root=chol(chol2inv(chol((crossprod(X,X)+A)))) Abetabar=crossprod(A,betabar) a=ifelse(y == 0,-100, 0) b=ifelse(y == 0, 0, 100) # # start main iteration loop # itime=proc.time()[3] cat("MCMC Iteration (est time to end - min) ",fill=TRUE) fsh() for (rep in 1:R) { # draw z given beta(i-1) mu=X%*%beta z=rtrun(mu,sigma,a,b) beta=breg1(root,X,z,Abetabar) # # print time to completion and draw # every 100th draw # if(rep%%100 == 0) {ctime=proc.time()[3] timetoend=((ctime-itime)/rep)*(R-rep) cat(" ",rep," (",round(timetoend/60,1),")",fill=TRUE) fsh()} if(rep%%keep == 0) {mkeep=rep/keep; betadraw[mkeep,]=beta} } ctime = proc.time()[3] cat(' Total Time Elapsed: ',round((ctime-itime)/60,2),'\n') attributes(betadraw)$class=c("bayesm.mat","mcmc") attributes(betadraw)$mcpar=c(1,R,keep) return(list(betadraw=betadraw)) } bayesm/R/rbiNormGibbs.R0000755000176000001440000000645010571562150014477 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) } # pandterm=function(message) {stop(message,call.=FALSE)} # # 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)$mcpar=c(1,R,1) return(draws) } bayesm/R/plot.bayesm.nmix.R0000755000176000001440000000773211754251324015335 0ustar ripleyusersplot.bayesm.nmix=function(x,names,burnin=trunc(.1*nrow(probdraw)),Grid,bi.sel,nstd=2,marg=TRUE, Data,ngrid=50,ndraw=200,...){ # # S3 method to plot normal mixture marginal and bivariate densities # nmixlist is a list of 3 components, nmixlist[[1]]: array of mix comp prob draws, # mmixlist[[2]] is not used, nmixlist[[3]] is list of draws of components # P. Rossi 2/07 # P. Rossi 3/07 fixed problem with dropping dimensions on probdraw (if ncomp=1) # P. Rossi 2/08 added marg flag to plot marginals # P. Rossi 3/08 added Data argument to paint histograms on the marginal plots # nmixlist=x if(mode(nmixlist) != "list") stop(" Argument must be a list \n") probdraw=nmixlist[[1]]; compdraw=nmixlist[[3]] if(!is.matrix(probdraw)) stop(" First element of list (probdraw) must be a matrix \n") if(mode(compdraw) != "list") stop(" Third element of list (compdraw) must be a list \n") op=par(no.readonly=TRUE) on.exit(par(op)) R=nrow(probdraw) if(R < 100) {cat(" fewer than 100 draws submitted \n"); return(invisible())} datad=length(compdraw[[1]][[1]]$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/plot.bayesm.mat.R0000755000176000001440000000433710650701116015132 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)) if(is.null(attributes(X)$dim)) X=as.matrix(X) nx=ncol(X) if(nrow(X) < 100 & CHECK_NDRAWS) {cat("fewer than 100 draws submitted \n"); return(invisible())} if(!missing(tvalues)){ if(mode(tvalues) !="numeric") {stop("tvalues must be a numeric vector \n")} else {if(length(tvalues)!=nx) stop("tvalues are wrong length \n")} } if(nx==1) par(mfrow=c(1,1)) if(nx==2) par(mfrow=c(2,1)) if(nx==3) par(mfrow=c(3,1)) if(nx==4) par(mfrow=c(2,2)) if(nx>=5) par(mfrow=c(3,2)) if(missing(names)) {names=as.character(1:nx)} if (DEN) ylabtxt="density" else ylabtxt="freq" for(index in 1:nx){ hist(X[(burnin+1):nrow(X),index],xlab="",ylab=ylabtxt,main=names[index],freq=!DEN,col="magenta",...) if(!missing(tvalues)) abline(v=tvalues[index],lwd=2,col="blue") if(INT){ quants=quantile(X[(burnin+1):nrow(X),index],prob=c(.025,.975)) mean=mean(X[(burnin+1):nrow(X),index]) semean=numEff(X[(burnin+1):nrow(X),index])$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") } par(ask=dev.interactive()) } 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/plot.bayesm.hcoef.R0000755000176000001440000000320111754302152015425 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)) nunits=d[1] nvar=d[2] R=d[3] if(R < 100) {cat("fewer than 100 draws submitted \n"); return(invisible())} # # plot posterior distributions of nvar coef for 30 rand units # if(missing(names)) {names=as.character(1:nvar)} rsam=sort(sample(c(1:nunits),30)) # randomly sample 30 cross-sectional units par(mfrow=c(1,1)) par(las=3) # horizontal labeling 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$stats=apply(ext,2,quantile,probs=c(0,.05,.95,1)) bxp(out,xlab="Cross-sectional Unit",main=paste("Coefficients on Var ",names[var],sep=""),boxfill="magenta",...) if(var==1) par(ask=dev.interactive()) } # # plot posterior means for each var # par(las=1) pmeans=matrix(0,nrow=nunits,ncol=nvar) for(i in 1:nunits) pmeans[i,]=apply(X[i,,(burnin+1):R],1,mean) names=as.character(1:nvar) attributes(pmeans)$class="bayesm.mat" for(i in 1:nvar) names[i]=paste("Posterior Means of Coef ",names[var],sep="") plot(pmeans,names,TRACEPLOT=FALSE,INT=FALSE,DEN=FALSE,CHECK_NDRAWS=FALSE,...) invisible() } 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$acf[-1]) stderr=sqrt(var(x)*f/length(x)) list(stderr=stderr,f=f,m=m) } bayesm/R/nmat.R0000755000176000001440000000042710225356251013054 0ustar ripleyusersnmat=function(vec) { # # function to take var-cov matrix in vector form and create correlation matrix # and store in vector form # p=as.integer(sqrt(length(vec))) sigma=matrix(vec,ncol=p) nsig=1/sqrt(diag(sigma)) return(as.vector(nsig*(t(nsig*sigma)))) } bayesm/R/momMix.R0000755000176000001440000000413110307453451013360 0ustar ripleyusersmomMix= function(probdraw,compdraw) { # # Revision History: # R. McCulloch 11/04 # P. Rossi 3/05 put in backsolve fixed documentation # P. Rossi 9/05 fixed error in mom -- return var not sigma # # purpose: compute moments of normal mixture averaged over MCMC draws # # arguments: # probdraw -- ith row is ith draw of probabilities of mixture comp # compdraw -- list of lists of draws of mixture comp moments (each sublist is from mixgibbs) # # output: # a list with the mean vector, covar matrix, vector of std deve, and corr matrix # # ---------------------------------------------------------------------------------- # define function needed mom=function(prob,comps){ # purpose: obtain mu and cov from list of normal components # # arguments: # prob: vector of mixture probs # comps: list, each member is a list comp with ith normal component ~N(comp[[1]],Sigma), # Sigma = t(R)%*%R, R^{-1} = comp[[2]] # returns: # a list with [[1]]=$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$sigma } mu=mu/length(compdraw) sigma=sigma/length(compdraw) sd=sd/length(compdraw) corr=corr/length(compdraw) return(list(mu=mu,sigma=sigma,sd=sd,corr=corr)) } bayesm/R/mnpProb.R0000755000176000001440000000325710316561164013540 0ustar ripleyusersmnpProb= function(beta,Sigma,X,r=100) { # # revision history: # written by Rossi 9/05 # # purpose: # function to MNP probabilities for a given X matrix (corresponding # to "one" observation # # arguments: # X is p-1 x k array of covariates (including intercepts) # note: X is from the "differenced" system # beta is k x 1 with k = ncol(X) # Sigma is p-1 x p-1 # r is the number of random draws to use in GHK # # output -- probabilities # for each observation w = Xbeta + e e ~N(0,Sigma) # if y=j (j max(w_-j) and w_j >0 # if y=p, w < 0 # # to use GHK we must transform so that these are rectangular regions # e.g. if y=1, w_1 > 0 and w_1 - w_-1 > 0 # # define Aj such that if j=1,..,p-1, Ajw = Ajmu + Aje > 0 is equivalent to y=j # implies Aje > -Ajmu # lower truncation is -Ajmu and cov = AjSigma t(Aj) # # for p, e < - mu # # # define functions needed # ghkvec = function(L,trunpt,above,r){ dim=length(above) n=length(trunpt)/dim .C('ghk_vec',as.integer(n),as.double(L),as.double(trunpt),as.integer(above),as.integer(dim), as.integer(r),res=double(n))$res} # 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/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/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/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/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/lndMvst.R0000755000176000001440000000114710354030136013536 0ustar ripleyuserslndMvst= function(x,nu,mu,rooti,NORMC=FALSE) { # # modified by Rossi 12/2005 to include normalizing constant # # 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) # dim=length(x) if(NORMC) {constant=(nu/2)*log(nu)+lgamma((nu+dim)/2)-(dim/2)*log(pi)-lgamma(nu/2)} else {constant=0} z=as.vector(t(rooti)%*%(x-mu)) return(constant -((dim+nu)/2)*log(nu+z%*%z)+sum(log(diag(rooti)))) } bayesm/R/lndMvn.R0000755000176000001440000000104610354030510013337 0ustar ripleyuserslndMvn= function(x,mu,rooti) { # # changed 12/05 by Rossi to include normalizing constant # # 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) # z=as.vector(t(rooti)%*%(x-mu)) return( -(length(x)/2)*log(2*pi) -.5*(z%*%z) + sum(log(diag(rooti)))) } bayesm/R/lndIWishart.R0000755000176000001440000000124610354034261014342 0ustar ripleyuserslndIWishart= function(nu,V,IW) { # # P. Rossi 12/04 # # purpose: evaluate log-density of inverted Wishart # includes normalizing constant # # arguments: # nu is d. f. parm # V is location matrix # IW is the value at which the density should be evaluated # # output: # value of log density # # note: in this parameterization, E[IW]=V/(nu-k-1) # k=ncol(V) Uiw=chol(IW) lndetVd2=sum(log(diag(chol(V)))) lndetIWd2=sum(log(diag(Uiw))) # # first evaluate constant # const=((nu*k)/2)*log(2)+((k*(k-1))/4)*log(pi) arg=(nu+1-c(1:k))/2 const=const+sum(lgamma(arg)) return(-const+nu*lndetVd2-(nu+k+1)*lndetIWd2-.5*sum(diag(V%*%chol2inv(Uiw)))) } bayesm/R/lndIChisq.R0000755000176000001440000000036310225325633013772 0ustar ripleyuserslndIChisq= function(nu,ssq,x) { # # P. Rossi 12/04 # # Purpose: evaluate log-density of scaled Inverse Chi-sq # density of r.var. 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/R/llnhlogit.R0000755000176000001440000000244110225321532014101 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 # root=function(c1,c2,tol,iterlim) { u=double(length(c1)) .C("callroot",as.integer(length(c1)),as.double(c1),as.double(c2),as.double(tol), as.integer(iterlim),r=as.double(u))$r} m=ncol(lnprices) n=length(choice) d=ncol(Xexpend) alpha=theta[1:m] k=theta[(m+1):(2*m)] gamma=theta[(2*m+1):(2*m+d)] tau=theta[length(theta)] iotam=c(rep(1,m)) c1=as.vector(Xexpend%*%gamma)%x%iotam-as.vector(t(lnprices))+alpha c2=c(rep(exp(k),n)) u=root(c1,c2,.0000001,20) v=alpha - u*exp(k)-as.vector(t(lnprices)) vmat=matrix(v,ncol=m,byrow=TRUE) vmat=tau*vmat ind=seq(1,n) vchosen=vmat[cbind(ind,choice)] lnprob=vchosen-log((exp(vmat))%*%iotam) return(sum(lnprob)) } bayesm/R/llmnp.R0000755000176000001440000000373010316322312013227 0ustar ripleyusersllmnp= function(beta,Sigma,X,y,r) { # # revision history: # edited by rossi 2/8/05 # adde 1.0e-50 before taking log to avoid -Inf 6/05 # changed order of arguments to put beta first 9/05 # # purpose: # function to evaluate MNP likelihood using GHK # # arguments: # X is n*(p-1) x k array of covariates (including intercepts) # note: X is from the "differenced" system # y is vector of n indicators of multinomial response # beta is k x 1 with k = ncol(X) # Sigma is p-1 x p-1 # r is the number of random draws to use in GHK # # output -- value of log-likelihood # for each observation w = Xbeta + e e ~N(0,Sigma) # if y=j (j max(w_-j) and w_j >0 # if y=p, w < 0 # # to use GHK we must transform so that these are rectangular regions # e.g. if y=1, w_1 > 0 and w_1 - w_-1 > 0 # # define Aj such that if j=1,..,p-1, Ajw = Ajmu + Aje > 0 is equivalent to y=j # implies Aje > -Ajmu # lower truncation is -Ajmu and cov = AjSigma t(Aj) # # for p, e < - mu # # # define functions needed # ghkvec = function(L,trunpt,above,r){ dim=length(above) n=length(trunpt)/dim .C('ghk_vec',as.integer(n),as.double(L),as.double(trunpt),as.integer(above),as.integer(dim), as.integer(r),res=double(n))$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 logl=logl + sum(log(ghkvec(Lj,trunpt,above,r)+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) logl=logl+sum(log(ghkvec(Lj,trunpt,above,r)+1.0e-50)) return(logl) } bayesm/R/llmnl.R0000755000176000001440000000110510316322344013222 0ustar ripleyusersllmnl= function(beta,y,X) { # p. rossi 2004 # changed order of arguments to put beta first 9/05 # # Purpose:evaluate log-like for MNL # # Arguments: # 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 # beta is k vector of coefs # # Output: value of loglike # n=length(y) j=nrow(X)/n Xbeta=X%*%beta Xbeta=matrix(Xbeta,byrow=T,ncol=j) ind=cbind(c(1:n),y) xby=Xbeta[ind] Xbeta=exp(Xbeta) iota=c(rep(1,j)) denom=log(Xbeta%*%iota) return(sum(xby-denom)) } bayesm/R/ghkvec.R0000755000176000001440000000053410226545065013367 0ustar ripleyusersghkvec = function(L,trunpt,above,r){ # # R interface to GHK code -- allows for a vector of truncation points # revision history- # P. Rossi 4/05 # dim=length(above) n=length(trunpt)/dim return(.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) } 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/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/createX.R0000755000176000001440000000522410224401102013471 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 # pandterm=function(message) {stop(message,call.=FALSE)} 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/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/clusterMix.R0000755000176000001440000000744510365770006014266 0ustar ripleyusersclusterMix= function(zdraw,cutoff=.9,SILENT=FALSE){ # # # 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. # # 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 # # ------------------------------------------------------------------------------------------ ztoSim=function(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) # # p.rossi 9/05 # n=length(z) zvec=c(rep(z,n)) zcomp=z%x%c(rep(1,n)) Sim=as.numeric((zvec==zcomp)) dim(Sim)=c(n,n) return(Sim) } Simtoz=function(Sim){ # # function to convert Similarity matrix to indicator vector # Sim is n x n matrix, Sim[i,j]=1 if pair(i,j) are in same group # z is vector of indicators from (1,...,p) of group memberships (dim n) # # # p.rossi 9/05 n=ncol(Sim) z=double(n) i=1 groupn=1 while (i <= n){ validind=z==0 if(sum(Sim[validind,i]==1)>=1) { z[validind]=as.numeric(Sim[validind,i]==1)*groupn groupn=groupn+1 } i=i+1 } return(z) } # ---------------------------------------------------------------------------------------- # # check arguments # pandterm=function(message) { stop(message,call.=FALSE) } if(missing(zdraw)) {pandterm("Requires zdraw argument -- R x n matrix of indicator draws")} # # 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))} # # compute posterior mean of Similarity matrix # # if(!SILENT){ cat("Computing Posterior Expectation of Similarity Matrix",fill=TRUE) cat("processing draws ...",fill=TRUE); fsh() } Pmean=matrix(0,nrow=nobs,ncol=nobs) R=nrow(zdraw) for (r in 1:R) { Pmean=Pmean+ztoSim(zdraw[r,]) if(!SILENT) {if(r%%100 == 0) {cat(" ",r,fill=TRUE); fsh()}} } Pmean=Pmean/R # # now find index for draw which minimizes discrepancy between # post exp of similarity and sim implied by that z if(!SILENT){ cat(" ",fill=TRUE) cat("Look for zdraw which minimizes loss",fill=TRUE) cat("processing draws ...",fill=TRUE); fsh() } loss=double(R) for (r in 1:R){ loss[r]=sum(abs(Pmean-ztoSim(zdraw[r,]))) if(!SILENT) {if(r%%100 == 0) {cat(" ",r,fill=TRUE);fsh()}} } index=which(loss==min(loss)) clustera=zdraw[index[1],] # # now due clustering by assigning Similarity to any (i,j) pair for which # Pmean > cutoff Sim=matrix(as.numeric(Pmean >= cutoff),ncol=nobs) clusterb=Simtoz(Sim) return(list(clustera=clustera,clusterb=clusterb)) } bayesm/R/cgetC.R0000755000176000001440000000062110224401103013120 0ustar ripleyuserscgetC = function(e,k) { # 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 temp = (1:(k-1))+.5 m1 = sum(temp) m2 = sum(temp^2) return(.C('getC',as.double(e),as.integer(k),as.double(m1),as.double(m2),cc=double(k+1))$cc) } bayesm/R/breg.R0000755000176000001440000000105610224412235013025 0ustar ripleyusersbreg= function(y,X,betabar,A) { # # P.Rossi 12/04 # revision history: # P. Rossi 3/27/05 -- changed to augment strategy # # Purpose: draw from posterior for linear regression, sigmasq=1.0 # # Output: draw from posterior # # Model: y = Xbeta + e e ~ N(0,I) # # Prior: beta ~ N(betabar,A^-1) # k=length(betabar) RA=chol(A) W=rbind(X,RA) z=c(y,as.vector(RA%*%betabar)) IR=backsolve(chol(crossprod(W)),diag(k)) # W'W=R'R ; (W'W)^-1 = IR IR' -- this is UL decomp return(crossprod(t(IR))%*%crossprod(W,z)+IR%*%rnorm(k)) } bayesm/NAMESPACE0000755000176000001440000000150611022776635013017 0ustar ripleyusersuseDynLib(bayesm) export(breg,cgetC,createX,eMixMargDen,mixDen,fsh,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,plot.bayesm.mat, plot.bayesm.hcoef,plot.bayesm.nmix,rordprobitGibbs,rivGibbs,rivDP,rDPGibbs, rhierMnlDP) ## 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/man/0000755000176000001440000000000011754551577012356 5ustar ripleyusersbayesm/man/tuna.Rd0000755000176000001440000001042711430350011013566 0ustar ripleyusers\name{tuna} \alias{tuna} \docType{data} \title{Data on Canned Tuna Sales} \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 University of Chicago \url{http://http://research.chicagogsb.edu/marketing/databases/dominicks/dataset.aspx}. 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 the following 30 variables. \describe{ \item{\code{WEEK}}{a numeric vector} \item{\code{MOVE1}}{unit sales of Star Kist 6 oz.} \item{\code{MOVE2}}{unit sales of Chicken of the Sea 6 oz.} \item{\code{MOVE3}}{unit sales of Bumble Bee Solid 6.12 oz.} \item{\code{MOVE4}}{unit sales of Bumble Bee Chunk 6.12 oz.} \item{\code{MOVE5}}{unit sales of Geisha 6 oz.} \item{\code{MOVE6}}{unit sales of Bumble Bee Large Cans.} \item{\code{MOVE7}}{unit sales of HH Chunk Lite 6.5 oz.} \item{\code{NSALE1}}{a measure of display activity of Star Kist 6 oz.} \item{\code{NSALE2}}{a measure of display activity of Chicken of the Sea 6 oz.} \item{\code{NSALE3}}{a measure of display activity of Bumble Bee Solid 6.12 oz.} \item{\code{NSALE4}}{a measure of display activity of Bumble Bee Chunk 6.12 oz.} \item{\code{NSALE5}}{a measure of display activity of Geisha 6 oz.} \item{\code{NSALE6}}{a measure of display activity of Bumble Bee Large Cans.} \item{\code{NSALE7}}{a measure of display activity of HH Chunk Lite 6.5 oz.} \item{\code{LPRICE1}}{log of price of Star Kist 6 oz.} \item{\code{LPRICE2}}{log of price of Chicken of the Sea 6 oz.} \item{\code{LPRICE3}}{log of price of Bumble Bee Solid 6.12 oz.} \item{\code{LPRICE4}}{log of price of Bumble Bee Chunk 6.12 oz.} \item{\code{LPRICE5}}{log of price of Geisha 6 oz.} \item{\code{LPRICE6}}{log of price of Bumble Bee Large Cans.} \item{\code{LPRICE7}}{log of price of HH Chunk Lite 6.5 oz.} \item{\code{LWHPRIC1}}{log of wholesale price of Star Kist 6 oz.} \item{\code{LWHPRIC2}}{log of wholesale price of Chicken of the Sea 6 oz.} \item{\code{LWHPRIC3}}{log of wholesale price of Bumble Bee Solid 6.12 oz.} \item{\code{LWHPRIC4}}{log of wholesale price of Bumble Bee Chunk 6.12 oz.} \item{\code{LWHPRIC5}}{log of wholesale price of Geisha 6 oz.} \item{\code{LWHPRIC6}}{log of wholesale price of Bumble Bee Large Cans.} \item{\code{LWHPRIC7}}{log of wholesale price of HH Chunk Lite 6.5 oz.} \item{\code{FULLCUST}}{total customers visits} } } \source{ Chevalier, A. Judith, Anil K. Kashyap and Peter E. 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 et al. \cr \url{hhttp://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$betadraw) if(0){ ## plotting examples plot(out$betadraw) } } } \keyword{datasets} bayesm/man/summary.bayesm.var.Rd0000755000176000001440000000340311430347765016404 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: .1*nrow(Vard) } \item{tvalues}{ optional vector of "true" values for use in simulation examples } \item{QUANTILES}{ logical for should quantiles be displayed, def: 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 summary(object) where object is of class 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 QUANTILES=TRUE, quantiles of marginal distirbutions in the columns of Vard are displayed. \cr \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{ ## ## not run # out=rmnpGibbs(Data,Prior,Mcmc) # summary(out$sigmadraw) # } \keyword{ univar } bayesm/man/summary.bayesm.nmix.Rd0000755000176000001440000000270511430571046016562 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 \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 "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: .1*nrow(probdraw)} \item{...}{ parms to send to summary} } \details{ an object of class "bayesm.nmix" is a list of three components: \describe{ \item{probdraw}{ a matrix of 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{ ## ## not run # out=rnmix(Data,Prior,Mcmc) # summary(out) # } \keyword{ plot } bayesm/man/summary.bayesm.mat.Rd0000755000176000001440000000370311754540355016377 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 "bayesm.mat" } \item{names}{ optional character vector of names for the columns of \code{X}} \item{burnin}{ number of draws to burn-in, def: .1*nrow(X) } \item{tvalues}{ optional vector of "true" values for use in simulation examples } \item{QUANTILES}{ logical for should quantiles be displayed, def: TRUE } \item{TRAILER}{ logical for should a trailer be displayed, def: 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 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 QUANTILES=TRUE, quantiles of marginal distirbutions in the columns of X are displayed. \cr \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{ ## ## not run # out=rmnpGibbs(Data,Prior,Mcmc) # summary(out$betadraw) # } \keyword{ univar } bayesm/man/simnhlogit.Rd0000755000176000001440000000232311430347656015015 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}{ n x p array of prices } \item{Xexpend}{ n x k array of values of expenditure variables} } \details{ For detail on parameterization, see \code{llnhlogit}. } \value{ a list containing: \item{y}{n x 1 vector of multinomial outcomes (1, \ldots, p)} \item{Xexpend}{expenditure variables} \item{lnprices}{ price array } \item{theta}{coefficients} \item{prob}{n x p array of choice probabilities} } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 4. \cr \url{http://www.perossi.org/home/bsm-1} } \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. } \seealso{ \code{\link{llnhlogit}} } \keyword{ models } bayesm/man/Scotch.Rd0000755000176000001440000000502011430347622014051 0ustar ripleyusers\name{Scotch} \alias{Scotch} \docType{data} \title{ Survey Data on Brands of Scotch Consumed} \description{ 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 the following 21 variables. All variables are coded 1 if consumed in last year, 0 if not. \describe{ \item{\code{Chivas.Regal}}{a numeric vector} \item{\code{Dewar.s.White.Label}}{a numeric vector} \item{\code{Johnnie.Walker.Black.Label}}{a numeric vector} \item{\code{J...B}}{a numeric vector} \item{\code{Johnnie.Walker.Red.Label}}{a numeric vector} \item{\code{Other.Brands}}{a numeric vector} \item{\code{Glenlivet}}{a numeric vector} \item{\code{Cutty.Sark}}{a numeric vector} \item{\code{Glenfiddich}}{a numeric vector} \item{\code{Pinch..Haig.}}{a numeric vector} \item{\code{Clan.MacGregor}}{a numeric vector} \item{\code{Ballantine}}{a numeric vector} \item{\code{Macallan}}{a numeric vector} \item{\code{Passport}}{a numeric vector} \item{\code{Black...White}}{a numeric vector} \item{\code{Scoresby.Rare}}{a numeric vector} \item{\code{Grants}}{a numeric vector} \item{\code{Ushers}}{a numeric vector} \item{\code{White.Horse}}{a numeric vector} \item{\code{Knockando}}{a numeric vector} \item{\code{the.Singleton}}{a numeric vector} } } \source{ Edwards, Y. and G. Allenby (2003), "Multivariate Analysis of Multiple Response Data," \emph{JMR} 40, 321-334. } \references{ Chapter 4, \emph{Bayesian Statistics and Marketing} by Rossi et al.\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(.01,.05,.5,.95,.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)$class="bayesm.var" cat(" Draws of Correlation Matrix ",fill=TRUE) summary(rdraw) } } \keyword{datasets} bayesm/man/rwishart.Rd0000755000176000001440000000254211430347576014507 0ustar ripleyusers\name{rwishart} \alias{rwishart} \concept{Wishart distribution} \concept{Inverted Wishart} \concept{simulation} \title{ Draw from Wishart and Inverted Wishart Distribution } \description{ \code{rwishart} draws from the Wishart and Inverted Wishart distributions. } \usage{ rwishart(nu, V) } \arguments{ \item{nu}{ d.f. parameter} \item{V}{ pds location matrix} } \details{ In the parameterization used here, \eqn{W} \eqn{\sim}{~} \eqn{W(nu,V)}, \eqn{E[W]=nuV}. \cr If you want to use an Inverted Wishart prior, you \emph{must invert the location matrix} before calling \code{rwishart}, e.g. \cr \eqn{Sigma} \eqn{\sim}{~} IW(nu,V); \eqn{Sigma^{-1}} \eqn{\sim}{~} \eqn{W(nu,V^{-1})}. } \value{ \item{W}{ Wishart draw } \item{IW }{Inverted Wishart draw} \item{C }{ Upper tri root of W} \item{CI }{ inv(C), \eqn{W^{-1}} = CICI'} } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 2. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \examples{ ## set.seed(66) rwishart(5,diag(3))$IW } \keyword{ multivariate } bayesm/man/runiregGibbs.Rd0000755000176000001440000000415211430347527015261 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)} } \details{ Model: \eqn{y = Xbeta + e}. \eqn{e} \eqn{\sim}{~} \eqn{N(0,sigmasq)}. \cr Priors: \eqn{beta} \eqn{\sim}{~} \eqn{N(betabar,A^{-1})}. \eqn{sigmasq} \eqn{\sim}{~} \eqn{(nu*ssq)/chisq_{nu}}. List arguments contain \itemize{ \item{\code{X}}{n x k Design Matrix} \item{\code{y}}{n x 1 vector of observations} \item{\code{betabar}}{k x 1 prior mean (def: 0)} \item{\code{A}}{k x k prior precision matrix (def: .01I)} \item{\code{nu}}{ d.f. parm for Inverted Chi-square prior (def: 3)} \item{\code{ssq}}{ scale parm for Inverted Chi-square prior (def:var(y))} \item{\code{R}}{ number of MCMC draws } \item{\code{keep}}{ thinning parameter - keep every keepth draw } } } \value{ list of MCMC draws \item{betadraw }{ R x k array of betadraws } \item{sigmasqdraw }{ R vector of sigma-sq draws} } \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} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \seealso{ \code{\link{runireg}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=1000} else {R=10} set.seed(66) n=100 X=cbind(rep(1,n),runif(n)); beta=c(1,2); sigsq=.25 y=X\%*\%beta+rnorm(n,sd=sqrt(sigsq)) Data1=list(y=y,X=X); Mcmc1=list(R=R) out=runiregGibbs(Data=Data1,Mcmc=Mcmc1) cat("Summary of beta and Sigma draws",fill=TRUE) summary(out$betadraw,tvalues=beta) summary(out$sigmasqdraw,tvalues=sigsq) if(0){ ## plotting examples plot(out$betadraw) } } \keyword{ regression } bayesm/man/runireg.Rd0000755000176000001440000000377711430347462014324 0ustar ripleyusers\name{runireg} \alias{runireg} \concept{bayes} \concept{regression} \title{ IID Sampler for Univariate Regression } \description{ \code{runireg} implements an iid sampler to draw from the posterior of a univariate regression with a conjugate prior. } \usage{ runireg(Data, Prior, Mcmc) } \arguments{ \item{Data}{ list(y,X)} \item{Prior}{ list(betabar,A, nu, ssq) } \item{Mcmc}{ list(R,keep)} } \details{ Model: \eqn{y = Xbeta + e}. \eqn{e} \eqn{\sim}{~} \eqn{N(0,sigmasq)}. \cr Priors: \eqn{beta} \eqn{\sim}{~} \eqn{N(betabar,sigmasq*A^{-1})}. \eqn{sigmasq} \eqn{\sim}{~} \eqn{(nu*ssq)/chisq_{nu}}. List arguments contain \itemize{ \item{\code{X}}{n x k Design Matrix} \item{\code{y}}{n x 1 vector of observations} \item{\code{betabar}}{k x 1 prior mean (def: 0)} \item{\code{A}}{k x k prior precision matrix (def: .01I)} \item{\code{nu}}{ d.f. parm for Inverted Chi-square prior (def: 3)} \item{\code{ssq}}{ scale parm for Inverted Chi-square prior (def: var(y))} \item{\code{R}}{ number of draws } \item{\code{keep}}{ thinning parameter - keep every keepth draw } } } \value{ list of iid draws \item{betadraw }{ R x k array of betadraws } \item{sigmasqdraw }{ R vector of sigma-sq draws} } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 2. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \seealso{ \code{\link{runiregGibbs}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) n=200 X=cbind(rep(1,n),runif(n)); beta=c(1,2); sigsq=.25 y=X\%*\%beta+rnorm(n,sd=sqrt(sigsq)) out=runireg(Data=list(y=y,X=X),Mcmc=list(R=R)) cat("Summary of beta/sigma-sq draws",fill=TRUE) summary(out$betadraw,tvalues=beta) summary(out$sigmasqdraw,tvalues=sigsq) if(0){ ## plotting examples plot(out$betadraw) } } \keyword{ regression } bayesm/man/rtrun.Rd0000755000176000001440000000220011430347414013774 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}{ sd } \item{a}{ lower bound } \item{b}{ upper bound } } \details{ Note that due to the vectorization of the rnorm,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) } \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} } \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) 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/rsurGibbs.Rd0000755000176000001440000000553311430574542014604 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{ Model: \eqn{y_i = X_ibeta_i + e_i}. i=1,\ldots,m. m regressions. \cr (e(1,k), \ldots, e(m,k)) \eqn{\sim}{~} \eqn{N(0,Sigma)}. k=1, \ldots, nobs. We can also write as the stacked model: \cr \eqn{y = Xbeta + e} where y is a nobs*m long vector and k=length(beta)=sum(length(betai)). Note: we must have the same number of observations in each equation but we can have different numbers of X variables Priors: \eqn{beta} \eqn{\sim}{~} \eqn{N(betabar,A^{-1})}. \eqn{Sigma} \eqn{\sim}{~} \eqn{IW(nu,V)}. List arguments contain \itemize{ \item{\code{regdata}}{list of lists, regdata[[i]]=list(y=yi,X=Xi)} \item{\code{betabar}}{k x 1 prior mean (def: 0)} \item{\code{A}}{k x k prior precision matrix (def: .01I)} \item{\code{nu}}{ d.f. parm for Inverted Wishart prior (def: m+3)} \item{\code{V}}{ scale parm for Inverted Wishart prior (def: nu*I)} \item{\code{R}}{ number of MCMC draws } \item{\code{keep}}{ thinning parameter - keep every keepth draw } } } \value{ list of MCMC draws \item{betadraw }{ R x k array of betadraws } \item{Sigmadraw }{ R x (m*m) array of Sigma draws} } \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} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \seealso{ \code{\link{rmultireg}} } \examples{ if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=1000} else {R=10} ## ## simulate data from SUR set.seed(66) 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(.5,.2,.2,.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) Mcmc1=list(R=R) out=rsurGibbs(Data=list(regdata=regdata),Mcmc=Mcmc1) 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)])) if(0){ plot(out$betadraw,tvalues=c(beta1,beta2)) } } \keyword{ regression} bayesm/man/rscaleUsage.Rd0000755000176000001440000000535411430347307015076 0ustar ripleyusers\name{rscaleUsage} \alias{rscaleUsage} \concept{MCMC} \concept{bayes} \concept{ordinal data} \concept{scale usage} \concept{hierarchical models} \title{ MCMC Algorithm for Multivariate Ordinal Data with Scale Usage Heterogeneity.} \description{ \code{rscaleUsage} implements an MCMC algorithm for multivariate ordinal data with scale usage heterogeniety. } \usage{ rscaleUsage(Data,Prior, Mcmc) } \arguments{ \item{Data}{ list(k,x)} \item{Prior}{ list(nu,V,mubar,Am,gsigma,gl11,gl22,gl12,Lambdanu,LambdaV,ge) (optional) } \item{Mcmc}{ list(R,keep,ndghk,printevery,e,y,mu,Sigma,sigma,tau,Lambda) (optional) } } \details{ Model: n=nrow(x) individuals respond to m=ncol(x) questions. all questions are on a scale 1, \ldots, k. for respondent i and question j, \cr \eqn{x_{ij} = d}, if \eqn{c_{d-1} \le y_{ij} \le c_d}. \cr d=1,\ldots,k. \eqn{c_d = a + bd +ed^2}. \cr \eqn{y_i = mu + tau_i*iota + sigma_i*z_i}. \eqn{z_i} \eqn{\sim}{~} \eqn{N(0,Sigma)}. \cr Priors:\cr \eqn{(tau_i,ln(sigma_i))} \eqn{\sim}{~} \eqn{N(phi,Lamda)}. \eqn{phi=(0,lambda_{22})}. \cr mu \eqn{\sim}{~} \eqn{N(mubar, Am{^-1})}.\cr Sigma \eqn{\sim}{~} IW(nu,V).\cr Lambda \eqn{\sim}{~} IW(Lambdanu,LambdaV).\cr e \eqn{\sim}{~} unif on a grid. \cr } \value{ a list containing: \item{Sigmadraw}{R/keep x m*m array of Sigma draws} \item{mudraw}{R/keep x m array of mu draws} \item{taudraw}{R/keep x n array of tau draws} \item{sigmadraw}{R/keep x n array of sigma draws} \item{Lambdadraw}{R/keep x 4 array of Lamda draws} \item{edraw}{R/keep x 1 array of e draws} } \note{ It is \strong{highly} recommended that the user choose the default settings. This means not specifying the argument \code{Prior} and setting \code{R} in Mcmc and \code{Data} only. If you wish to change prior settings and/or the grids used, please read the case study in Allenby et al carefully. } \section{Warning}{ \eqn{tau_i}, \eqn{sigma_i} are identified from the scale usage patterns in the m questions asked per respondent (\# cols of x). Do not attempt to use this on data sets with only a small number of total questions! } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch, Case Study on Scale Usage Heterogeneity. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Rob McCulloch and Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \examples{ ## if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=1000} else {R=1} { data(customerSat) surveydat = list(k=10,x=as.matrix(customerSat)) Mcmc1 = list(R=R) set.seed(66) out=rscaleUsage(Data=surveydat,Mcmc=Mcmc1) summary(out$mudraw) } } \keyword{ models } bayesm/man/rordprobitGibbs.Rd0000755000176000001440000000651611430347214015773 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. } \usage{ rordprobitGibbs(Data, Prior, Mcmc) } \arguments{ \item{Data}{ list(X, y, k)} \item{Prior}{ list(betabar, A, dstarbar, Ad)} \item{Mcmc}{ list(R, keep, s, change, draw) } } \details{ Model: \eqn{z = X\beta + e}. \eqn{e} \eqn{\sim}{~} \eqn{N(0,I)}. y=1,..,k. cutoff=c( c [1] ,..c [k+1] ). \cr y=k, if c [k] <= z < c [k+1] . Prior: \eqn{\beta} \eqn{\sim}{~} \eqn{N(betabar,A^{-1})}. \eqn{dstar} \eqn{\sim}{~} \eqn{N(dstarbar,Ad^{-1})}. List arguments contain \describe{ \item{\code{X}}{n x nvar Design Matrix} \item{\code{y}}{n x 1 vector of observations, (1,...,k)} \item{\code{k}}{the largest possible value of y} \item{\code{betabar}}{nvar x 1 prior mean (def: 0)} \item{\code{A}}{nvar x nvar prior precision matrix (def: .01I)} \item{\code{dstarbar}}{ndstar x 1 prior mean, ndstar=k-2 (def: 0)} \item{\code{Ad}}{ndstar x ndstar prior precision matrix (def:I)} \item{\code{s}}{ scaling parm for RW Metropolis (def: 2.93/sqrt(nvar))} \item{\code{R}}{ number of MCMC draws } \item{\code{keep}}{ thinning parameter - keep every keepth draw (def: 1)} } } \value{ \item{betadraw }{R/keep x k matrix of betadraws} \item{cutdraw }{R/keep x (k-1) matrix of cutdraws} \item{dstardraw }{R/keep x (k-2) matrix of dstardraws} \item{accept }{a value of acceptance rate in RW Metropolis} } \note{ set c[1]=-100. 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]), c[4]=c[3]+exp(dstar[2]),..., c[k] = c[k-1] + exp(datsr[k-2]) Be careful in assessing prior parameter, Ad. .1 is too small for many applications. } \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{ ## ## rordprobitGibbs example ## if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} ## 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 )) } set.seed(66) 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$cutdraw,tvalues=cutoff[2:k]) if(0){ ## plotting examples plot(out$cutdraw) } } \keyword{ models } bayesm/man/rnmixGibbs.Rd0000755000176000001440000001021011430570565014733 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) (only ncomp required)} \item{Mcmc}{ list(R,keep,Loglike) (R required) } } \details{ Model: \cr \eqn{y_i} \eqn{\sim}{~} \eqn{N(mu_{ind_i},Sigma_{ind_i})}. \cr ind \eqn{\sim}{~} iid multinomial(p). p is a ncomp x 1 vector of probs. Priors:\cr \eqn{mu_j} \eqn{\sim}{~} \eqn{N(mubar,Sigma_j (x) A^{-1})}. \eqn{mubar=vec(Mubar)}. \cr \eqn{Sigma_j} \eqn{\sim}{~} IW(nu,V).\cr note: this is the natural conjugate prior -- a special case of multivariate regression.\cr \eqn{p} \eqn{\sim}{~} Dirchlet(a). Output of the components is in the form of a list of lists. \cr compsdraw[[i]] is ith draw -- list of ncomp lists. \cr compsdraw[[i]][[j]] is list of parms for jth normal component. \cr jcomp=compsdraw[[i]][j]]. Then jth comp \eqn{\sim}{~} \eqn{N(jcomp[[1]],Sigma)}, \eqn{Sigma} = t(R)\%*\%R, \eqn{R^{-1}} = jcomp[[2]]. List arguments contain: \itemize{ \item{y}{ n x k array of data (rows are obs) } \item{Mubar}{ 1 x k array with prior mean of normal comp means (def: 0)} \item{A}{ 1 x 1 precision parameter for prior on mean of normal comp (def: .01)} \item{nu}{ d.f. parameter for prior on Sigma (normal comp cov matrix) (def: k+3)} \item{V}{ k x k location matrix of IW prior on Sigma (def: nuI)} \item{a}{ ncomp x 1 vector of Dirichlet prior parms (def: rep(5,ncomp))} \item{ncomp}{ number of normal components to be included } \item{R}{ number of MCMC draws } \item{keep}{ MCMC thinning parm: keep every keepth draw (def: 1)} \item{LogLike}{ logical flag for compute log-likelihood (def: FALSE)} } } \value{ \item{nmix}{a list containing: probdraw,zdraw,compdraw} \item{ll}{vector of log-likelihood values} } \note{ more details on contents of nmix: \cr \describe{ \item{probdraw}{R/keep x ncomp array of mixture prob draws} \item{zdraw}{R/keep x nobs array of indicators of mixture comp identity for each obs} \item{compdraw}{R/keep lists of lists of comp parm draws} } 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 Allenby et al, chapter 5 for details. Use \code{eMixMargDen} or \code{momMix} to compute posterior expectation or distribution of various identified parameters. } \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} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \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) comps = list() # change to "rooti" scale 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$x) ncomp=9 Prior1=list(ncomp=ncomp) Mcmc1=list(R=R,keep=1) out=rnmixGibbs(Data=Data1,Prior=Prior1,Mcmc=Mcmc1) cat("Summary of Normal Mixture Distribution",fill=TRUE) summary(out) tmom=momMix(matrix(pvec,nrow=1),list(comps)) mat=rbind(tmom$mu,tmom$sd) cat(" True Mean/Std Dev",fill=TRUE) print(mat) if(0){ ## ## plotting examples ## plot(out$nmix,Data=dm$x) } } \keyword{ multivariate } bayesm/man/rnegbinRw.Rd0000755000176000001440000000673311430574375014606 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. beta | alpha and 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,s\_beta,s\_alpha,beta0 } } \details{ Model: \eqn{y} \eqn{\sim}{~} \eqn{NBD(mean=lambda, over-dispersion=alpha)}. \cr \eqn{lambda=exp(x'beta)} Prior: \eqn{beta} \eqn{\sim}{~} \eqn{N(betabar,A^{-1})} \cr \eqn{alpha} \eqn{\sim}{~} \eqn{Gamma(a,b)}. \cr note: prior mean of \eqn{alpha = a/b}, \eqn{variance = a/(b^2)} list arguments contain: \itemize{ \item{\code{y}}{ nobs vector of counts (0,1,2,\ldots)} \item{\code{X}}{nobs x nvar matrix} \item{\code{betabar}}{ nvar x 1 prior mean (def: 0)} \item{\code{A}}{ nvar x nvar pds prior prec matrix (def: .01I)} \item{\code{a}}{ Gamma prior parm (def: .5)} \item{\code{b}}{ Gamma prior parm (def: .1)} \item{\code{R}}{ number of MCMC draws} \item{\code{keep}}{ MCMC thinning parm: keep every keepth draw (def: 1)} \item{\code{s\_beta}}{ scaling for beta| alpha RW inc cov matrix (def: 2.93/sqrt(nvar)} \item{\code{s\_alpha}}{ scaling for alpha | beta RW inc cov matrix (def: 2.93)} } } \value{ a list containing: \item{betadraw}{R/keep x nvar array of beta draws} \item{alphadraw}{R/keep vector of alpha draws} \item{llike}{R/keep 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.\cr 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. } \seealso{ \code{\link{rhierNegbinRw}} } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, McCulloch. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Sridhar Narayanam & Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \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=Mcmc1) cat("Summary of alpha/beta draw",fill=TRUE) summary(out$alphadraw,tvalues=alpha) summary(out$betadraw,tvalues=beta) if(0){ ## plotting examples plot(out$betadraw) } } \keyword{ models } bayesm/man/rmvst.Rd0000755000176000001440000000174511430347045014012 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 } \references{ For further discussion, see \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}. } \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \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{ distribution } bayesm/man/rmvpGibbs.Rd0000755000176000001440000000661411430346771014577 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(p,y,X)} \item{Prior}{ list(betabar,A,nu,V) (optional)} \item{Mcmc}{ list(beta0,sigma0,R,keep) (R required) } } \details{ model: \cr \eqn{w_i = X_i beta + e}. \eqn{e} \eqn{\sim}{~} N(0,Sigma). note: \eqn{w_i} is p x 1.\cr \eqn{y_{ij} = 1}, if \eqn{w_{ij} > 0}, else \eqn{y_i=0}. j=1,\ldots,p. \cr priors:\cr \eqn{beta} \eqn{\sim}{~} \eqn{N(betabar,A^{-1})}\cr \eqn{Sigma} \eqn{\sim}{~} IW(nu,V)\cr to make up X matrix use \code{createX} List arguments contain \itemize{ \item{\code{p}}{dimension of multivariate probit} \item{\code{X}}{n*p x k Design Matrix} \item{\code{y}}{n*p x 1 vector of 0,1 outcomes} \item{\code{betabar}}{k x 1 prior mean (def: 0)} \item{\code{A}}{k x k prior precision matrix (def: .01I)} \item{\code{nu}}{ d.f. parm for IWishart prior (def: (p-1) + 3)} \item{\code{V}}{ pds location parm for IWishart prior (def: nu*I)} \item{\code{beta0}}{ initial value for beta} \item{\code{sigma0}}{ initial value for sigma } \item{\code{R}}{ number of MCMC draws } \item{\code{keep}}{ thinning parameter - keep every keepth draw (def: 1)} } } \value{ a list containing: \item{betadraw }{R/keep x k array of betadraws} \item{sigmadraw}{R/keep x p*p array of sigma draws -- each row is in vector form} } \note{ beta and Sigma are not identifed. Correlation matrix and the betas divided by the appropriate standard deviation are. See Allenby et al for details or example below. } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 4. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \seealso{ \code{\link{rmnpGibbs}} } \examples{ ## if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) p=3 n=500 beta=c(-2,0,2) Sigma=matrix(c(1,.5,.5,.5,1,.5,.5,.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 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)) } 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) if(0){ plot(betatilde,tvalues=beta/sqrt(diag(Sigma))) } } \keyword{ models } \keyword{ multivariate } bayesm/man/rmultireg.Rd0000755000176000001440000000475611430346554014662 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}{ n x m matrix of observations on m dep vars } \item{X}{ n x k matrix of observations on indep vars (supply intercept) } \item{Bbar}{ k x m matrix of prior mean of regression coefficients } \item{A}{ k x k Prior precision matrix } \item{nu}{ d.f. parameter for Sigma } \item{V}{ m x m pdf location parameter for prior on Sigma } } \details{ Model: \eqn{Y=XB+U}. \eqn{cov(u_i) = Sigma}. \eqn{B} is k x m matrix of coefficients. \eqn{Sigma} is m x m covariance. Priors: \eqn{beta} given \eqn{Sigma} \eqn{\sim}{~} \eqn{N(betabar,Sigma (x) A^{-1})}. \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 } } \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} } \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{ ## 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,.5,.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(.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(.01,.05,.5,.95,.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(.01,.05,.5,.95,.99)) mat=rbind(as.vector(Sigma),mat); rownames(mat)[1]="Sigma" print(mat) } \keyword{ regression } bayesm/man/rmnpGibbs.Rd0000755000176000001440000000707011430346500014552 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(p, y, X)} \item{Prior}{ list(betabar,A,nu,V) (optional)} \item{Mcmc}{ list(beta0,sigma0,R,keep) (R required) } } \details{ model: \cr \eqn{w_i = X_i\beta + e}. \eqn{e} \eqn{\sim}{~} \eqn{N(0,Sigma)}. note: \eqn{w_i, e} are (p-1) x 1.\cr \eqn{y_i = j}, if \eqn{w_{ij} > max(0,w_{i,-j})} j=1,\ldots,p-1. \eqn{w_{i,-j}} means elements of \eqn{w_i} other than the jth. \cr \eqn{y_i = p}, if all \eqn{w_i < 0}.\cr priors:\cr \eqn{beta} \eqn{\sim}{~} \eqn{N(betabar,A^{-1})} \cr \eqn{Sigma} \eqn{\sim}{~} IW(nu,V)\cr to make up X matrix use \code{\link{createX}} with \code{DIFF=TRUE}. List arguments contain \itemize{ \item{\code{p}}{number of choices or possible multinomial outcomes} \item{\code{y}}{n x 1 vector of multinomial outcomes} \item{\code{X}}{n*(p-1) x k Design Matrix} \item{\code{betabar}}{k x 1 prior mean (def: 0)} \item{\code{A}}{k x k prior precision matrix (def: .01I)} \item{\code{nu}}{ d.f. parm for IWishart prior (def: (p-1) + 3)} \item{\code{V}}{ pds location parm for IWishart prior (def: nu*I)} \item{\code{beta0}}{ initial value for beta} \item{\code{sigma0}}{ initial value for sigma } \item{\code{R}}{ number of MCMC draws } \item{\code{keep}}{ thinning parameter - keep every keepth draw (def: 1)} } } \value{ a list containing: \item{betadraw }{R/keep x k array of betadraws} \item{sigmadraw}{R/keep x (p-1)*(p-1) array of sigma draws -- each row is in vector form} } \note{ beta is not identified. beta/sqrt(\eqn{sigma_{11}}) and Sigma/\eqn{sigma_{11}} are. See Allenby et al or example below for details. } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 4. \cr \url{http://www.perossi.org/home/bsm-1l} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \seealso{ \code{\link{rmvpGibbs}} } \examples{ ## if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) p=3 n=500 beta=c(-1,1,1,2) Sigma=matrix(c(1,.5,.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) 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)) } 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)])) if(0){ ## plotting examples plot(betatilde,tvalues=beta) } } \keyword{ models } bayesm/man/rmnlIndepMetrop.Rd0000755000176000001440000000526011430346436015755 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{rmnIndepMetrop} implements Independence Metropolis for the MNL. } \usage{ rmnlIndepMetrop(Data, Prior, Mcmc) } \arguments{ \item{Data}{ list(p,y,X)} \item{Prior}{ list(A,betabar) optional} \item{Mcmc}{ list(R,keep,nu) } } \details{ Model: y \eqn{\sim}{~} MNL(X,beta). \eqn{Pr(y=j) = exp(x_j'beta)/\sum_k{e^{x_k'beta}}}. \cr Prior: \eqn{beta} \eqn{\sim}{~} \eqn{N(betabar,A^{-1})} \cr list arguments contain: \itemize{ \item{\code{p}}{number of alternatives} \item{\code{y}}{ nobs vector of multinomial outcomes (1,\ldots, p)} \item{\code{X}}{nobs*p x nvar matrix} \item{\code{A}}{ nvar x nvar pds prior prec matrix (def: .01I)} \item{\code{betabar}}{ nvar x 1 prior mean (def: 0)} \item{\code{R}}{ number of MCMC draws} \item{\code{keep}}{ MCMC thinning parm: keep every keepth draw (def: 1)} \item{\code{nu}}{ degrees of freedom parameter for independence t density (def: 6) } } } \value{ a list containing: \item{betadraw}{R/keep x nvar array of beta draws} \item{loglike}{R/keep vector of loglike values for each draw} \item{acceptr}{acceptance rate of Metropolis draws} } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 5. \cr \url{http://www.perossi.org/home/bsm-1l} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \seealso{ \code{\link{rhierMnlRwMixture}} } \examples{ ## if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) n=200; p=3; beta=c(1,-1,1.5,.5) 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)) } 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) if(0){ ## plotting examples plot(out$betadraw) } } \keyword{ models } bayesm/man/rmixture.Rd0000755000176000001440000000223011430346365014510 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}{ ncomp x 1 vector of prior probabilities for each mixture component } \item{comps}{ list of mixture component parameters } } \details{ comps is a list of length, ncomp = length(pvec). comps[[j]][[1]] is mean vector for the jth component. comps[[j]][[2]] is the inverse of the cholesky root of Sigma for that component } \value{ A list containing \ldots \item{x}{ An n x length(comps[[1]][[1]]) array of iid draws } \item{z}{ A n x 1 vector of indicators of which component each draw is taken from } } \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. } \seealso{ \code{\link{rnmixGibbs}} } \keyword{ distribution } \keyword{ multivariate } bayesm/man/rmixGibbs.Rd0000755000176000001440000000302111430346331014547 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. } \usage{ rmixGibbs(y, Bbar, A, nu, V, a, p, z, comps) } \arguments{ \item{y}{ data array - 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 priro } \item{a}{ Dirichlet prior parms } \item{p}{ prior prob of each mixture component } \item{z}{ component identities for each observation -- "indicators"} \item{comps}{ list of components for the normal mixture } } \details{ \code{rmixGibbs} is not designed to be called directly. Instead, use \code{rnmixGibbs} wrapper function. } \value{ a list containing: \item{p}{draw mixture probabilities } \item{z}{draw of indicators of each component} \item{comps}{new draw of normal component parameters } } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Allenby, McCulloch, and Rossi, Chapter 5. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Rob McCulloch and 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. } \seealso{ \code{\link{rnmixGibbs}} } \keyword{ multivariate } bayesm/man/rivGibbs.Rd0000755000176000001440000000634611430346240014404 0ustar ripleyusers\name{rivGibbs} \alias{rivGibbs} \concept{Instrumental Variables} \concept{Gibbs Sampler} \concept{bayes} \concept{endogeneity} \concept{simultaneity} \concept{MCMC} \title{ Gibbs Sampler for Linear "IV" Model} \description{ \code{rivGibbs} is a Gibbs Sampler for a linear structural equation with an arbitrary number of instruments. } \usage{ rivGibbs(Data, Prior, Mcmc) } \arguments{ \item{Data}{ list(z,w,x,y) } \item{Prior}{ list(md,Ad,mbg,Abg,nu,V) (optional) } \item{Mcmc}{ list(R,keep) (R required) } } \details{ Model:\cr \eqn{x=z'delta + e1}. \cr \eqn{y=beta*x + w'gamma + e2}. \cr \eqn{e1,e2} \eqn{\sim}{~} \eqn{N(0,Sigma)}. Note: if intercepts are desired in either equation, include vector of ones in z or w Priors:\cr \eqn{delta} \eqn{\sim}{~} \eqn{N(md,Ad^{-1})}. \eqn{vec(beta,gamma)} \eqn{\sim}{~} \eqn{N(mbg,Abg^{-1})} \cr \eqn{Sigma} \eqn{\sim}{~} IW(nu,V) List arguments contain: \itemize{ \item{\code{z}}{ matrix of obs on instruments} \item{\code{y}}{ vector of obs on lhs var in structural equation} \item{\code{x}}{ "endogenous" var in structural eqn} \item{\code{w}}{ matrix of obs on "exogenous" vars in the structural eqn} \item{\code{md}}{ prior mean of delta (def: 0)} \item{\code{Ad}}{ pds prior prec for prior on delta (def: .01I)} \item{\code{mbg}}{ prior mean vector for prior on beta,gamma (def: 0)} \item{\code{Abg}}{ pds prior prec for prior on beta,gamma (def: .01I)} \item{\code{nu}}{ d.f. parm for IW prior on Sigma (def: 5)} \item{\code{V}}{ pds location matrix for IW prior on Sigma (def: nuI)} \item{\code{R}}{ number of MCMC draws} \item{\code{keep}}{ MCMC thinning parm: keep every keepth draw (def: 1)} } } \value{ a list containing: \item{deltadraw}{R/keep x dim(delta) array of delta draws} \item{betadraw}{R/keep x 1 vector of beta draws} \item{gammadraw}{R/keep x dim(gamma) array of gamma draws } \item{Sigmadraw}{R/keep x 4 array of Sigma draws} } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 5. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Rob McCulloch and Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \examples{ ## if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) simIV = function(delta,beta,Sigma,n,z,w,gamma) { eps = matrix(rnorm(2*n),ncol=2) \%*\% chol(Sigma) x = z \%*\% delta + eps[,1]; y = beta*x + eps[,2] + w\%*\%gamma list(x=as.vector(x),y=as.vector(y)) } n = 200 ; p=1 # number of instruments z = cbind(rep(1,n),matrix(runif(n*p),ncol=p)) w = matrix(1,n,1) rho=.8 Sigma = matrix(c(1,rho,rho,1),ncol=2) delta = c(1,4); beta = .5; gamma = c(1) simiv = simIV(delta,beta,Sigma,n,z,w,gamma) Mcmc1=list(); Data1 = list() Data1$z = z; Data1$w=w; Data1$x=simiv$x; Data1$y=simiv$y Mcmc1$R = R Mcmc1$keep=1 out=rivGibbs(Data=Data1,Mcmc=Mcmc1) cat("Summary of Beta draws",fill=TRUE) summary(out$betadraw,tvalues=beta) cat("Summary of Sigma draws",fill=TRUE) summary(out$Sigmadraw,tvalues=as.vector(Sigma[upper.tri(Sigma,diag=TRUE)])) if(0){ ## plotting examples plot(out$betadraw) } } \keyword{ models } bayesm/man/rivDP.Rd0000755000176000001440000001267511430346175013672 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 equation implemented with a Dirichlet Process Prior. } \usage{ rivDP(Data, Prior, Mcmc) } \arguments{ \item{Data}{ list(z,w,x,y) } \item{Prior}{ list(md,Ad,mbg,Abg,lambda,Prioralpha) (optional) } \item{Mcmc}{ list(R,keep,SCALE) (R required) } } \details{ Model:\cr \eqn{x=z'delta + e1}. \cr \eqn{y=beta*x + w'gamma + e2}. \cr \eqn{e1,e2} \eqn{\sim}{~} \eqn{N(theta_{i})}. \eqn{theta_{i}} represents \eqn{mu_{i},Sigma_{i}} Note: Error terms have non-zero means. DO NOT include intercepts in the z or w matrices. This is different from \code{rivGibbs} which requires intercepts to be included explicitly. Priors:\cr \eqn{delta} \eqn{\sim}{~} \eqn{N(md,Ad^{-1})}. \eqn{vec(beta,gamma)} \eqn{\sim}{~} \eqn{N(mbg,Abg^{-1})} \cr \eqn{theta_{i}\sim{~}G} \cr \eqn{G} \eqn{\sim}{~} \eqn{DP(alpha,G_{0})} \cr \eqn{G_{0}} is the natural conjugate prior for \eqn{(mu,Sigma)}: \cr \eqn{Sigma} \eqn{\sim}{~} \eqn{IW(nu,vI)} and \eqn{mu | Sigma} \eqn{\sim}{~} \eqn{N(0,1/amu Sigma)} \cr These parameters are collected together in the list \code{lambda}. It is highly recommended that you use the default settings for these hyper-parameters.\cr \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 List arguments contain: \itemize{ \item{\code{z}}{ matrix of obs on instruments} \item{\code{y}}{ vector of obs on lhs var in structural equation} \item{\code{x}}{ "endogenous" var in structural eqn} \item{\code{w}}{ matrix of obs on "exogenous" vars in the structural eqn} \item{\code{md}}{ prior mean of delta (def: 0)} \item{\code{Ad}}{ pds prior prec for prior on delta (def: .01I)} \item{\code{mbg}}{ prior mean vector for prior on beta,gamma (def: 0)} \item{\code{Abg}}{ pds prior prec for prior on beta,gamma (def: .01I)} \item{\code{lambda}}{ list of hyperparameters for theta prior- use default settings } \item{\code{Prioralpha}}{ list of hyperparameters for theta prior- use default settings } \item{\code{R}}{ number of MCMC draws} \item{\code{keep}}{ MCMC thinning parm: keep every keepth draw (def: 1)} \item{\code{SCALE}}{ scale data, def: TRUE} \item{\code{gridsize}}{ gridsize parm for alpha draws (def: 20)} } output includes object \code{nmix} of class "bayesm.nmix" which contains draws of predictive distribution of errors (a Bayesian analogue of a density estimate for the error terms).\cr nmix:\cr \itemize{ \item{\code{probdraw}}{ not used} \item{\code{zdraw}}{ not used} \item{\code{compdraw}}{ list R/keep of draws from bivariate predictive for the errors} } note: in compdraw list, there is only one component per draw } \value{ a list containing: \item{deltadraw}{R/keep x dim(delta) array of delta draws} \item{betadraw}{R/keep x 1 vector of beta draws} \item{gammadraw}{R/keep x dim(gamma) array of gamma draws } \item{Istardraw}{R/keep x 1 array of drawsi of the number of unique normal components} \item{alphadraw}{R/keep x 1 array of draws of Dirichlet Process tightness parameter} \item{nmix}{R/keep x list of draws for predictive distribution of errors} } \references{ For further discussion, see "A Semi-Parametric Bayesian Approach to the Instrumental Variable Problem," by Conley, Hansen, McCulloch and Rossi, Journal of Econometrics (2008).\cr } \seealso{\code{rivGibbs}} \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \examples{ ## if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} ## ## simulate scaled log-normal errors and run ## set.seed(66) k=10 delta=1.5 Sigma=matrix(c(1,.6,.6,1),ncol=2) N=1000 tbeta=4 set.seed(66) scalefactor=.6 root=chol(scalefactor*Sigma) mu=c(1,1) ## ## compute interquartile ranges ## ninterq=qnorm(.75)-qnorm(.25) error=matrix(rnorm(100000*2),ncol=2)%*%root error=t(t(error)+mu) Err=t(t(exp(error))-exp(mu+.5*scalefactor*diag(Sigma))) lnNinterq=quantile(Err[,1],prob=.75)-quantile(Err[,1],prob=.25) ## ## simulate data ## error=matrix(rnorm(N*2),ncol=2)\%*\%root error=t(t(error)+mu) Err=t(t(exp(error))-exp(mu+.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] # set intial values for MCMC Data = list(); Mcmc=list() Data$z = z; Data$x=x; Data$y=y # start MCMC and keep results Mcmc$maxuniq=100 Mcmc$R=R end=Mcmc$R begin=100 out=rivDP(Data=Data,Mcmc=Mcmc) cat("Summary of Beta draws",fill=TRUE) summary(out$betadraw,tvalues=tbeta) if(0){ ## plotting examples plot(out$betadraw,tvalues=tbeta) plot(out$nmix) ## plot "fitted" density of the errors ## } } \keyword{ models } bayesm/man/rhierNegbinRw.Rd0000755000176000001440000001202711430346143015375 0ustar ripleyusers\name{rhierNegbinRw} \alias{rhierNegbinRw} \concept{MCMC} \concept{hierarchical NBD regression} \concept{Negative Binomial regression} \concept{Poisson regression} \concept{Metropolis algorithm} \concept{bayes} \title{ MCMC Algorithm for Negative Binomial Regression } \description{ \code{rhierNegbinRw} implements an MCMC strategy for the hierarchical Negative Binomial (NBD) regression model. Metropolis steps for each unit level set of regression parameters are automatically tuned by optimization. Over-dispersion parameter (alpha) is common across units. } \usage{ rhierNegbinRw(Data, Prior, Mcmc) } \arguments{ \item{Data}{ list(regdata,Z) } \item{Prior}{ list(Deltabar,Adelta,nu,V,a,b) } \item{Mcmc}{ list(R,keep,s\_beta,s\_alpha,c,Vbeta0,Delta0) } } \details{ Model: \eqn{y_i} \eqn{\sim}{~} NBD(mean=lambda, over-dispersion=alpha). \cr \eqn{lambda=exp(X_ibeta_i)} Prior: \eqn{beta_i} \eqn{\sim}{~} \eqn{N(Delta'z_i,Vbeta)}. \eqn{vec(Delta|Vbeta)} \eqn{\sim}{~} \eqn{N(vec(Deltabar),Vbeta (x) Adelta)}. \cr \eqn{Vbeta} \eqn{\sim}{~} \eqn{IW(nu,V)}. \cr \eqn{alpha} \eqn{\sim}{~} \eqn{Gamma(a,b)}. \cr note: prior mean of \eqn{alpha = a/b}, \eqn{variance = a/(b^2)} list arguments contain: \itemize{ \item{\code{regdata}}{ list of lists with data on each of nreg units} \item{\code{regdata[[i]]$X}}{ nobs\_i x nvar matrix of X variables} \item{\code{regdata[[i]]$y}}{ nobs\_i x 1 vector of count responses} \item{\code{Z}}{nreg x nz mat of unit chars (def: vector of ones)} \item{\code{Deltabar}}{ nz x nvar prior mean matrix (def: 0)} \item{\code{Adelta}}{ nz x nz pds prior prec matrix (def: .01I)} \item{\code{nu}}{ d.f. parm for IWishart (def: nvar+3)} \item{\code{V}}{location matrix of IWishart prior (def: nuI)} \item{\code{a}}{ Gamma prior parm (def: .5)} \item{\code{b}}{ Gamma prior parm (def: .1)} \item{\code{R}}{ number of MCMC draws} \item{\code{keep}}{ MCMC thinning parm: keep every keepth draw (def: 1)} \item{\code{s\_beta}}{ scaling for beta| alpha RW inc cov (def: 2.93/sqrt(nvar))} \item{\code{s\_alpha}}{ scaling for alpha | beta RW inc cov (def: 2.93)} \item{\code{c}}{ fractional likelihood weighting parm (def:2)} \item{\code{Vbeta0}}{ starting value for Vbeta (def: I)} \item{\code{Delta0}}{ starting value for Delta (def: 0)} } } \value{ a list containing: \item{llike}{R/keep vector of values of log-likelihood} \item{betadraw}{nreg x nvar x R/keep array of beta draws} \item{alphadraw}{R/keep 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.\cr 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 Z variables. } \seealso{ \code{\link{rnegbinRw}} } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 5. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Sridhar Narayanam & Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \examples{ ## if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} 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) } 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$alpha,tvalues=alpha) if(0){ ## plotting examples plot(out$betadraw) plot(out$alpha,tvalues=alpha) plot(out$Deltadraw,tvalues=as.vector(Delta)) } } \keyword{models} bayesm/man/rhierMnlRwMixture.Rd0000755000176000001440000001465311745642047016321 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(p,lgtdata,Z) ( Z is optional) } \item{Prior}{ list(a,deltabar,Ad,mubar,Amu,nu,V,ncomp) (all but ncomp are optional)} \item{Mcmc}{ list(s,w,R,keep) (R required)} } \details{ Model: \cr \eqn{y_i} \eqn{\sim}{~} \eqn{MNL(X_i,beta_i)}. i=1,\ldots, length(lgtdata). \eqn{theta_i} is nvar x 1. \eqn{beta_i}= ZDelta[i,] + \eqn{u_i}. \cr Note: here ZDelta refers to Z\%*\%D, ZDelta[i,] is ith row of this product.\cr Delta is an nz x nvar array. \eqn{u_i} \eqn{\sim}{~} \eqn{N(mu_{ind},Sigma_{ind})}. \eqn{ind} \eqn{\sim}{~} multinomial(pvec). \cr Priors: \cr \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}{~} IW(nu,V) \cr Lists contain: \itemize{ \item{\code{p}}{ p is number of choice alternatives} \item{\code{lgtdata}}{list of lists with each cross-section unit MNL data} \item{\code{lgtdata[[i]]$y}}{ \eqn{n_i} vector of multinomial outcomes (1,\ldots,m)} \item{\code{lgtdata[[i]]$X}}{ \eqn{n_i}*p by nvar design matrix for ith unit} \item{\code{a}}{vector of length ncomp of Dirichlet prior parms (def: rep(5,ncomp))} \item{\code{deltabar}}{nz*nvar vector of prior means (def: 0)} \item{\code{Ad}}{ prior prec matrix for vec(D) (def: .01I)} \item{\code{mubar}}{ nvar x 1 prior mean vector for normal comp mean (def: 0)} \item{\code{Amu}}{ prior precision for normal comp mean (def: .01I)} \item{\code{nu}}{ d.f. parm for IW prior on norm comp Sigma (def: nvar+3)} \item{\code{V}}{ pds location parm for IW prior on norm comp Sigma (def: nuI)} \item{\code{ncomp}}{ number of components used in normal mixture } \item{\code{s}}{ scaling parm for RW Metropolis (def: 2.93/sqrt(nvar))} \item{\code{w}}{ fractional likelihood weighting parm (def: .1)} \item{\code{R}}{ number of MCMC draws} \item{\code{keep}}{ MCMC thinning parm: keep every keepth draw (def: 1)} } } \value{ a list containing: \item{Deltadraw}{R/keep x nz*nvar matrix of draws of Delta, first row is initial value} \item{betadraw}{ nlgt x nvar x R/keep array of draws of betas} \item{nmix}{ list of 3 components, probdraw, NULL, compdraw } \item{loglike}{ log-likelihood for each kept draw (length R/keep)} } \note{ More on \code{probdraw} component of nmix list:\cr R/keep x ncomp matrix of draws of probs of mixture components (pvec) \cr More on \code{compdraw} component of return value list: \cr \itemize{ \item{compdraw[[i]]}{ the ith draw of components for mixtures} \item{compdraw[[i]][[j]]}{ ith draw of the jth normal mixture comp} \item{compdraw[[i]][[j]][[1]]}{ ith draw of jth normal mixture comp mean vector} \item{compdraw[[i]][[j]][[2]]}{ ith draw of jth normal mixture cov parm (rooti) } } Note: Z should \strong{not} include an intercept and is centered for ease of interpretation.\cr Be careful in assessing prior parameter, Amu. .01 is too small for many applications. See Rossi et al, chapter 5 for full discussion.\cr Note: as of version 2.0-2 of \code{bayesm}, the fractional weight parameter has been changed to a weight between 0 and 1. 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 R values may be required (>20,000). } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 5. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \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 # 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(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(.4,.2,.4) simmnlwX= function(n,X,beta) { ## simulate from MNL model conditional on X matrix 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){ ## set if(1) above to produce plots bmat=matrix(0,nlgt,ncoef) for(i in 1:nlgt) {bmat[i,]=simlgtdata[[i]]$beta} par(mfrow=c(ncoef,1)) for(i in 1:ncoef) hist(bmat[,i],breaks=30,col="magenta") } ## set parms for priors and Z Prior1=list(ncomp=5) keep=5 Mcmc1=list(R=R,keep=keep) Data1=list(p=p,lgtdata=simlgtdata,Z=Z) out=rhierMnlRwMixture(Data=Data1,Prior=Prior1,Mcmc=Mcmc1) cat("Summary of Delta draws",fill=TRUE) summary(out$Deltadraw,tvalues=as.vector(Delta)) cat("Summary of Normal Mixture Distribution",fill=TRUE) summary(out$nmix) if(0) { ## plotting examples plot(out$betadraw) plot(out$nmix) } } \keyword{models} bayesm/man/rhierMnlDP.Rd0000755000176000001440000002231611430345717014644 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(p,lgtdata,Z) ( Z is optional) } \item{Prior}{ list(deltabar,Ad,Prioralpha,lambda\_hyper) (all are optional)} \item{Mcmc}{ list(s,w,R,keep) (R required)} } \details{ Model: \cr \eqn{y_i} \eqn{\sim}{~} \eqn{MNL(X_i,beta_i)}. i=1,\ldots, length(lgtdata). \eqn{theta_i} is nvar x 1. \eqn{beta_i}= ZDelta[i,] + \eqn{u_i}. \cr Note: here ZDelta refers to Z\%*\%D, ZDelta[i,] is ith row of this product.\cr Delta is an nz x nvar array. \eqn{beta_i} \eqn{\sim}{~} \eqn{N(mu_i,Sigma_i)}. \cr Priors: \cr \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[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 = Istarmin \cr alpha= alphamax then expected number of components = Istarmax \cr Lists contain: \cr Data:\cr \itemize{ \item{\code{p}}{ p is number of choice alternatives} \item{\code{lgtdata}}{list of lists with each cross-section unit MNL data} \item{\code{lgtdata[[i]]$y}}{ \eqn{n_i} vector of multinomial outcomes (1,\ldots,m)} \item{\code{lgtdata[[i]]$X}}{ \eqn{n_i} by nvar design matrix for ith unit} } Prior: \cr \itemize{ \item{\code{deltabar}}{nz*nvar vector of prior means (def: 0)} \item{\code{Ad}}{ prior prec matrix for vec(D) (def: .01I)} } Prioralpha:\cr \itemize{ \item{\code{Istarmin}}{expected number of components at lower bound of support of alpha def(1)} \item{\code{Istarmax}}{expected number of components at upper bound of support of alpha (def: min(50,.1*nlgt))} \item{\code{power}}{power parameter for alpha prior (def: .8)} } lambda\_hyper:\cr \itemize{ \item{\code{alim}}{defines support of a distribution,def:c(.01,2) } \item{\code{nulim}}{defines support of nu distribution, def:c(.01,3)} \item{\code{vlim}}{defines support of v distribution, def:c(.1,4)} } Mcmc:\cr \itemize{ \item{\code{R}}{number of mcmc draws} \item{\code{keep}}{thinning parm, keep every keepth draw} \item{\code{maxuniq}}{storage constraint on the number of unique components} \item{\code{gridsize}}{number of discrete points for hyperparameter priors,def: 20} } } \value{ a list containing: \item{Deltadraw}{R/keep x nz*nvar matrix of draws of Delta, first row is initial value} \item{betadraw}{ nlgt x nvar x R/keep array of draws of betas} \item{nmix}{ list of 3 components, probdraw, NULL, compdraw } \item{adraw}{R/keep draws of hyperparm a} \item{vdraw}{R/keep draws of hyperparm v} \item{nudraw}{R/keep draws of hyperparm nu} \item{Istardraw}{R/keep draws of number of unique components} \item{alphadraw}{R/keep draws of number of DP tightness parameter} \item{loglike}{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. More on nmix list:\cr contains the draws from the predictive distribution of a "new" observations parameters. These are simply the parameters of one normal distribution. We enforce compatibility with a mixture of k components in order to utilize generic summary plotting functions. Therefore,\code{probdraw} is a vector of ones. \code{zdraw} (indicator draws) is omitted as it is not necessary for density estimation. \code{compdraw} contains the draws of the \eqn{theta_{n+1}} as a list of list of lists. More on \code{compdraw} component of return value list: \itemize{ \item{compdraw[[i]]}{ith draw of components for mixtures} \item{compdraw[[i]][[1]]}{ith draw of the thetanp1} \item{compdraw[[i]][[1]][[1]]}{ith draw of mean vector} \item{compdraw[[i]][[1]][[2]]}{ith draw of parm (rooti)} } 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. Note: Z should \strong{not} include an intercept and is centered for ease of interpretation.\cr Large R values may be required (>20,000). } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 5. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \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(.4,.2,.4) simmnlwX= function(n,X,beta) { ## simulate from MNL model conditional on X matrix 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$y,X=X,beta=betai) } ## plot betas if(1){ ## set if(1) above to produce plots bmat=matrix(0,nlgt,ncoef) for(i in 1:nlgt) {bmat[i,]=simlgtdata[[i]]$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$Deltadraw,tvalues=as.vector(Delta)) if(0) { ## plotting examples plot(out$betadraw) plot(out$nmix) } } \keyword{models} bayesm/man/rhierLinearModel.Rd0000755000176000001440000000741711430345647016074 0ustar ripleyusers\name{rhierLinearModel} \alias{rhierLinearModel} \concept{bayes} \concept{MCMC} \concept{Gibbs Sampling} \concept{hierarchical models} \concept{linear model} \title{ Gibbs Sampler for Hierarchical Linear Model } \description{ \code{rhierLinearModel} implements a Gibbs Sampler for hierarchical linear models with a normal prior. } \usage{ rhierLinearModel(Data, Prior, Mcmc) } \arguments{ \item{Data}{ list(regdata,Z) (Z optional). } \item{Prior}{ list(Deltabar,A,nu.e,ssq,nu,V) (optional).} \item{Mcmc}{ list(R,keep) (R required).} } \details{ Model: length(regdata) regression equations. \cr \eqn{y_i = X_ibeta_i + e_i}. \eqn{e_i} \eqn{\sim}{~} \eqn{N(0,tau_i)}. nvar X vars in each equation. Priors:\cr \eqn{tau_i} \eqn{\sim}{~} nu.e*\eqn{ssq_i/\chi^2_{nu.e}}. \eqn{tau_i} is the variance of \eqn{e_i}.\cr \eqn{beta_i} \eqn{\sim}{~} N(ZDelta[i,],\eqn{V_{beta}}). \cr Note: ZDelta is the matrix Z * Delta; [i,] refers to ith row of this product. \eqn{vec(Delta)} given \eqn{V_{beta}} \eqn{\sim}{~} \eqn{N(vec(Deltabar),V_{beta} (x) A^{-1})}.\cr \eqn{V_{beta}} \eqn{\sim}{~} \eqn{IW(nu,V)}. \cr \eqn{Delta, Deltabar} are nz x nvar. \eqn{A} is nz x nz. \eqn{V_{beta}} is nvar x nvar. Note: if you don't have any z vars, set Z=iota (nreg x 1). List arguments contain: \itemize{ \item{\code{regdata}}{ list of lists with X,y matrices for each of length(regdata) regressions} \item{\code{regdata[[i]]$X}}{ X matrix for equation i } \item{\code{regdata[[i]]$y}}{ y vector for equation i } \item{\code{Deltabar}}{ nz x nvar matrix of prior means (def: 0)} \item{\code{A}}{ nz x nz matrix for prior precision (def: .01I)} \item{\code{nu.e}}{ d.f. parm for regression error variance prior (def: 3)} \item{\code{ssq}}{ scale parm for regression error var prior (def: var(\eqn{y_i}))} \item{\code{nu}}{ d.f. parm for Vbeta prior (def: nvar+3)} \item{\code{V}}{ Scale location matrix for Vbeta prior (def: nu*I)} \item{\code{R}}{ number of MCMC draws} \item{\code{keep}}{ MCMC thinning parm: keep every keepth draw (def: 1)} } } \value{ a list containing \item{betadraw}{nreg x nvar x R/keep array of individual regression coef draws} \item{taudraw}{R/keep x nreg array of error variance draws} \item{Deltadraw}{R/keep x nz x nvar array of Deltadraws} \item{Vbetadraw}{R/keep x nvar*nvar array of Vbeta draws} } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 3. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.comu}. } \seealso{ \code{\link{rhierLinearMixture}} } \examples{ ## if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} nreg=100; nobs=100; nvar=3 Vbeta=matrix(c(1,.5,0,.5,2,.7,0,.7,1),ncol=3) Z=cbind(c(rep(1,nreg)),3*runif(nreg)); Z[,2]=Z[,2]-mean(Z[,2]) nz=ncol(Z) Delta=matrix(c(1,-1,2,0,1,0),ncol=2) Delta=t(Delta) # first row of Delta is means of betas Beta=matrix(rnorm(nreg*nvar),nrow=nreg)\%*\%chol(Vbeta)+Z\%*\%Delta tau=.1 iota=c(rep(1,nobs)) regdata=NULL for (reg in 1:nreg) { X=cbind(iota,matrix(runif(nobs*(nvar-1)),ncol=(nvar-1))) y=X\%*\%Beta[reg,]+sqrt(tau)*rnorm(nobs); regdata[[reg]]=list(y=y,X=X) } Data1=list(regdata=regdata,Z=Z) Mcmc1=list(R=R,keep=1) out=rhierLinearModel(Data=Data1,Mcmc=Mcmc1) cat("Summary of Delta draws",fill=TRUE) summary(out$Deltadraw,tvalues=as.vector(Delta)) cat("Summary of Vbeta draws",fill=TRUE) summary(out$Vbetadraw,tvalues=as.vector(Vbeta[upper.tri(Vbeta,diag=TRUE)])) if(0){ ## plotting examples plot(out$betadraw) plot(out$Deltadraw) } } \keyword{ regression } bayesm/man/rhierLinearMixture.Rd0000755000176000001440000001270311430570246016456 0ustar ripleyusers\name{rhierLinearMixture} \alias{rhierLinearMixture} \concept{bayes} \concept{MCMC} \concept{Gibbs Sampling} \concept{mixture of normals} \concept{normal mixture} \concept{heterogeneity} \concept{regresssion} \concept{hierarchical models} \concept{linear model} \title{ Gibbs Sampler for Hierarchical Linear Model } \description{ \code{rhierLinearMixture} implements a Gibbs Sampler for hierarchical linear models with a mixture of normals prior. } \usage{ rhierLinearMixture(Data, Prior, Mcmc) } \arguments{ \item{Data}{ list(regdata,Z) (Z optional). } \item{Prior}{ list(deltabar,Ad,mubar,Amu,nu,V,nu.e,ssq,ncomp) (all but ncomp are optional).} \item{Mcmc}{ list(R,keep) (R required).} } \details{ Model: length(regdata) regression equations. \cr \eqn{y_i = X_ibeta_i + e_i}. \eqn{e_i} \eqn{\sim}{~} \eqn{N(0,tau_i)}. nvar X vars in each equation. Priors:\cr \eqn{tau_i} \eqn{\sim}{~} nu.e*\eqn{ssq_i/\chi^2_{nu.e}}. \eqn{tau_i} is the variance of \eqn{e_i}.\cr \eqn{beta_i}= ZDelta[i,] + \eqn{u_i}. \cr Note: here ZDelta refers to Z\%*\%D, ZDelta[i,] is ith row of this product.\cr Delta is an nz x nvar array. \eqn{u_i} \eqn{\sim}{~} \eqn{N(mu_{ind},Sigma_{ind})}. \eqn{ind} \eqn{\sim}{~} multinomial(pvec). \cr \eqn{pvec} \eqn{\sim}{~} dirichlet (a)\cr \eqn{delta= vec(Delta)} \eqn{\sim}{~} \eqn{N(deltabar,A_d^{-1})}\cr \eqn{mu_j} \eqn{\sim}{~} \eqn{N(mubar,Sigma_j (x) Amu^{-1})}\cr \eqn{Sigma_j} \eqn{\sim}{~} IW(nu,V) \cr List arguments contain: \itemize{ \item{\code{regdata}}{ list of lists with X,y matrices for each of length(regdata) regressions} \item{\code{regdata[[i]]$X}}{ X matrix for equation i } \item{\code{regdata[[i]]$y}}{ y vector for equation i } \item{\code{deltabar}}{nz*nvar vector of prior means (def: 0)} \item{\code{Ad}}{ prior prec matrix for vec(Delta) (def: .01I)} \item{\code{mubar}}{ nvar x 1 prior mean vector for normal comp mean (def: 0)} \item{\code{Amu}}{ prior precision for normal comp mean (def: .01I)} \item{\code{nu}}{ d.f. parm for IW prior on norm comp Sigma (def: nvar+3)} \item{\code{V}}{ pds location parm for IW prior on norm comp Sigma (def: nuI)} \item{\code{nu.e}}{ d.f. parm for regression error variance prior (def: 3)} \item{\code{ssq}}{ scale parm for regression error var prior (def: var(\eqn{y_i}))} \item{\code{ncomp}}{ number of components used in normal mixture } \item{\code{R}}{ number of MCMC draws} \item{\code{keep}}{ MCMC thinning parm: keep every keepth draw (def: 1)} } } \value{ a list containing \item{taudraw}{R/keep x nreg array of error variance draws} \item{betadraw}{nreg x nvar x R/keep array of individual regression coef draws} \item{Deltadraw}{R/keep x nz x nvar array of Deltadraws} \item{nmix}{list of three elements, (probdraw, NULL, compdraw)} } \note{ More on \code{probdraw} component of nmix return value list: \cr this is an R/keep by ncomp array of draws of mixture component probs (pvec)\cr More on \code{compdraw} component of nmix return value list: \describe{ \item{compdraw[[i]]}{the ith draw of components for mixtures} \item{compdraw[[i]][[j]]}{ith draw of the jth normal mixture comp} \item{compdraw[[i]][[j]][[1]]}{ith draw of jth normal mixture comp mean vector} \item{compdraw[[i]][[j]][[2]]}{ith draw of jth normal mixture cov parm (rooti)} } Note: Z should \strong{not} include an intercept and should be centered for ease of interpretation.\cr Be careful in assessing the prior parameter, Amu. .01 can be too small for some applications. See Rossi et al, chapter 5 for full discussion.\cr } \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} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \seealso{ \code{\link{rhierLinearModel}} } \examples{ ## if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) nreg=300; nobs=500; nvar=3; nz=2 Z=matrix(runif(nreg*nz),ncol=nz) Z=t(t(Z)-apply(Z,2,mean)) Delta=matrix(c(1,-1,2,0,1,0),ncol=nz) tau0=.1 iota=c(rep(1,nobs)) ## create arguments for rmixture tcomps=NULL a=matrix(c(1,0,0,0.5773503,1.1547005,0,-0.4082483,0.4082483,1.2247449),ncol=3) tcomps[[1]]=list(mu=c(0,-1,-2),rooti=a) tcomps[[2]]=list(mu=c(0,-1,-2)*2,rooti=a) tcomps[[3]]=list(mu=c(0,-1,-2)*4,rooti=a) tpvec=c(.4,.2,.4) regdata=NULL # simulated data with Z betas=matrix(double(nreg*nvar),ncol=nvar) tind=double(nreg) for (reg in 1:nreg) { tempout=rmixture(1,tpvec,tcomps) betas[reg,]=Delta\%*\%Z[reg,]+as.vector(tempout$x) tind[reg]=tempout$z X=cbind(iota,matrix(runif(nobs*(nvar-1)),ncol=(nvar-1))) tau=tau0*runif(1,min=0.5,max=1) y=X\%*\%betas[reg,]+sqrt(tau)*rnorm(nobs) regdata[[reg]]=list(y=y,X=X,beta=betas[reg,],tau=tau) } ## run rhierLinearMixture Data1=list(regdata=regdata,Z=Z) Prior1=list(ncomp=3) Mcmc1=list(R=R,keep=1) out1=rhierLinearMixture(Data=Data1,Prior=Prior1,Mcmc=Mcmc1) cat("Summary of Delta draws",fill=TRUE) summary(out1$Deltadraw,tvalues=as.vector(Delta)) cat("Summary of Normal Mixture Distribution",fill=TRUE) summary(out1$nmix) if(0){ ## plotting examples plot(out1$betadraw) plot(out1$nmix) plot(out1$Deltadraw) } } \keyword{ regression } bayesm/man/rhierBinLogit.Rd0000755000176000001440000001055311430345466015402 0ustar ripleyusers\name{rhierBinLogit} \alias{rhierBinLogit} \concept{bayes} \concept{MCMC} \concept{hierarchical models} \concept{binary logit} \title{ MCMC Algorithm for Hierarchical Binary Logit } \description{ \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) (note: Z is optional) } \item{Prior}{ list(Deltabar,ADelta,nu,V) (note: all are optional)} \item{Mcmc}{ list(sbeta,R,keep) (note: all but R are optional)} } \details{ Model: \cr \eqn{y_{hi} = 1} with \eqn{pr=exp(x_{hi}'beta_h)/(1+exp(x_{hi}'beta_h)}. \eqn{beta_h} is nvar x 1.\cr 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 Z\%*\%Delta, ZDelta[h,] is hth row of this product.\cr Delta is an nz x nvar array. \eqn{u_h} \eqn{\sim}{~} \eqn{N(0,V_{beta})}. \cr Priors: \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)} Lists contain: \itemize{ \item{\code{lgtdata}}{list of lists with each cross-section unit MNL data} \item{\code{lgtdata[[h]]$y}}{ \eqn{n_h} vector of binary outcomes (0,1)} \item{\code{lgtdata[[h]]$X}}{ \eqn{n_h} by nvar design matrix for hth unit} \item{\code{Deltabar}}{nz x nvar matrix of prior means (def: 0)} \item{\code{ADelta}}{ prior prec matrix (def: .01I)} \item{\code{nu}}{ d.f. parm for IW prior on norm comp Sigma (def: nvar+3)} \item{\code{V}}{ pds location parm for IW prior on norm comp Sigma (def: nuI)} \item{\code{sbeta}}{ scaling parm for RW Metropolis (def: .2)} \item{\code{R}}{ number of MCMC draws} \item{\code{keep}}{ MCMC thinning parm: keep every keepth draw (def: 1)} } } \value{ a list containing: \item{Deltadraw}{R/keep x nz*nvar matrix of draws of Delta} \item{betadraw}{ nlgt x nvar x R/keep array of draws of betas} \item{Vbetadraw}{ R/keep x nvar*nvar matrix of draws of Vbeta} \item{llike}{R/keep vector of log-like values} \item{reject}{R/keep vector of reject rates over nlgt units} } \note{ Some experimentation with the Metropolis scaling paramter (sbeta) may be required. } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 5. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \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 ## set hyper-parameters ## B=ZDelta + U 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,-.5,.5,0),nrow=nz,ncol=nvar) iota=matrix(1,nrow=nvar,ncol=1) Vbeta=diag(nvar)+.5*iota\%*\%t(iota) ## simulate data 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 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 alim,nulim, and 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 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 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. } \value{ \item{nmix}{a list containing: probdraw,zdraw,compdraw} \item{alphadraw}{vector of draws of DP process tightness parameter} \item{nudraw}{vector of draws of base prior hyperparameter} \item{adraw}{vector of draws of base prior hyperparameter} \item{vdraw}{vector of draws of base prior hyperparameter} } \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} ## simulate univariate data from Chi-Sq set.seed(66) 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=.8) Prior1=list(Prioralpha=Prioralpha) Mcmc=list(R=R,keep=1,maxuniq=200) out1=rDPGibbs(Prior=Prior1,Data=Data1,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$nmix,Grid=grid,Data=y1) ## plot true density with historgram plot(range(grid[,1]),1.5*range(dchisq(grid[,1],df=chisqdf)),type="n",xlab=paste("Chisq ; ",N," obs",sep=""), ylab="") hist(y1,xlim=rgi,freq=FALSE,col="yellow",breaks=20,add=TRUE) lines(grid[,1],dchisq(grid[,1],df=chisqdf)/(sum(dchisq(grid[,1],df=chisqdf))*deltax),col="blue",lwd=2) } ## simulate bivariate data from the "Banana" distribution (Meng and Barnard) banana=function(A,B,C1,C2,N,keep=10,init=10) { R=init*keep+N*keep x1=x2=0 bimat=matrix(double(2*N),ncol=2) for (r in 1:R) { x1=rnorm(1,mean=(B*x2+C1)/(A*(x2^2)+1),sd=sqrt(1/(A*(x2^2)+1))) x2=rnorm(1,mean=(B*x2+C2)/(A*(x1^2)+1),sd=sqrt(1/(A*(x1^2)+1))) if (r>init*keep && r\%\%keep==0) {mkeep=r/keep; bimat[mkeep-init,]=c(x1,x2)} } return(bimat) } set.seed(66) nvar2=2 A=0.5; B=0; C1=C2=3 y2=banana(A=A,B=B,C1=C1,C2=C2,1000) Data2=list(y=y2) Prioralpha=list(Istarmin=1,Istarmax=10,power=.8) Prior2=list(Prioralpha=Prioralpha) Mcmc=list(R=R,keep=1,maxuniq=200) out2=rDPGibbs(Prior=Prior2,Data=Data2,Mcmc) if(0){ ## plotting examples rx1=range(y2[,1]); rx2=range(y2[,2]) x1=seq(from=rx1[1],to=rx1[2],length.out=50) x2=seq(from=rx2[1],to=rx2[2],length.out=50) grid=cbind(x1,x2) plot(out2$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/rdirichlet.Rd0000755000176000001440000000152411430345261014761 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 } \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} } \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) rdirichlet(c(rep(3,5))) } \keyword{ distribution } bayesm/man/rbprobitGibbs.Rd0000755000176000001440000000375611430345202015426 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(X,y)} \item{Prior}{ list(betabar,A)} \item{Mcmc}{ list(R,keep) } } \details{ Model: \eqn{z = X\beta + e}. \eqn{e} \eqn{\sim}{~} \eqn{N(0,I)}. y=1, if z> 0. Prior: \eqn{\beta} \eqn{\sim}{~} \eqn{N(betabar,A^{-1})}. List arguments contain \describe{ \item{\code{X}}{Design Matrix} \item{\code{y}}{n x 1 vector of observations, (0 or 1)} \item{\code{betabar}}{k x 1 prior mean (def: 0)} \item{\code{A}}{k x k prior precision matrix (def: .01I)} \item{\code{R}}{ number of MCMC draws } \item{\code{keep}}{ thinning parameter - keep every keepth draw (def: 1)} } } \value{ \item{betadraw }{R/keep x k array of betadraws} } \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} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \seealso{ \code{\link{rmnpGibbs}} } \examples{ ## ## rbprobitGibbs example ## if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) simbprobit= function(X,beta) { ## function to simulate from binary probit including x variable 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$betadraw,tvalues=beta) if(0){ ## plotting example plot(out$betadraw,tvalues=beta) } } \keyword{ models } bayesm/man/rbiNormGibbs.Rd0000755000176000001440000000240611430345140015203 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 shown and the output is contrasted with the iid sampler. i 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{ (theta1,theta2) ~ N((0,0), Sigma=matrix(c(1,rho,rho,1),ncol=2)) } \value{ R x 2 array of draws } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapters 2 and 3. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \examples{ ## \dontrun{ out=rbiNormGibbs(rho=.95) } } \keyword{ distribution} bayesm/man/plot.bayesm.nmix.Rd0000755000176000001440000000446211430345072016043 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 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: .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: list(c(1,2))} \item{nstd}{number of standard deviations for default Grid, def: 2} \item{marg}{logical, if TRUE display marginals, def: 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(out,bi.sel=list(c(1,2),c(3,4),c(1,3))) # # plot bivariate distributions for dimension 1,2; 3,4; and 1,3 # } \keyword{ hplot } bayesm/man/plot.bayesm.mat.Rd0000755000176000001440000000376711430345040015653 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, bayesm.mat, or S3 class, mcmc } \item{names}{optional character vector of names for coefficients} \item{burnin}{number of draws to discard for burn-in, def: .1*nrow(X)} \item{tvalues}{vector of true values} \item{TRACEPLOT}{ logical, TRUE provide sequence plots of draws and acfs, def: TRUE } \item{DEN}{ logical, TRUE use density scale on histograms, def: TRUE } \item{INT}{ logical, TRUE put various intervals and points on graph, def: TRUE } \item{CHECK_NDRAWS}{ logical, TRUE check that there are at least 100 draws, def: 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 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{ ## ## not run # out=runiregGibbs(Data,Prior,Mcmc) # plot(out$betadraw) # } \keyword{ hplot } bayesm/man/plot.bayesm.hcoef.Rd0000755000176000001440000000312011754544760016160 0ustar ripleyusers\name{plot.bayesm.hcoef} \alias{plot.bayesm.hcoef} \concept{MCMC} \concept{S3 method} \concept{plot} \concept{hierarchical model} \title{Plot Method for Hierarchical Model Coefs } \description{ \code{plot.bayesm.hcoef} is an S3 method to plot 3 dim arrays of hierarchical coefficients. Arrays are of class bayesm.hcoef with dimensions: cross-sectional unit x coef x MCMC draw. } \usage{ \method{plot}{bayesm.hcoef}(x,names,burnin,...) } \arguments{ \item{x}{ An object of S3 class, bayesm.hcoef } \item{names}{ a list of names for the variables in the hierarchical model} \item{burnin}{ no draws to burnin, def: .1*R } \item{...}{ standard graphics parameters } } \details{ Typically, \code{plot.bayesm.hcoef} will be invoked by a call to the generic plot function as in \code{plot(object)} where object is of class bayesm.hcoef. All of the \code{bayesm} hierarchical routines return draws of hierarchical coefficients in this class (see example below). One can also simply invoke \code{plot.bayesm.hcoef} on any valid 3-dim array as in \code{plot.bayesm.hcoef(betadraws)} \cr \cr \code{plot.bayesm.hcoef} is also exported for use as a standard function, as in \code{plot.bayesm.hcoef(array)}. } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \seealso{ \code{\link{rhierMnlRwMixture}},\code{\link{rhierLinearModel}}, \code{\link{rhierLinearMixture}},\code{\link{rhierNegbinRw}} } \examples{ ## ## not run # out=rhierLinearModel(Data,Prior,Mcmc) # plot(out$betadraws) # } \keyword{ hplot } bayesm/man/orangeJuice.Rd0000755000176000001440000001514111430344743015067 0ustar ripleyusers\name{orangeJuice} \alias{orangeJuice} \docType{data} \title{Store-level Panel Data on Orange Juice Sales} \description{ yx, weekly sales of refrigerated orange juice at 83 stores. \cr storedemo, contains demographic information on those stores. \cr } \usage{data(orangeJuice)} \format{ This R object is a list of two data frames, list(yx,storedemo).\cr List of 2 \cr \$ yx :'data.frame': 106139 obs. of 19 variables:\cr \ldots \$ store : int [1:106139] 2 2 2 2 2 2 2 2 2 2 \cr \ldots \$ brand : int [1:106139] 1 1 1 1 1 1 1 1 1 1 \cr \ldots \$ week : int [1:106139] 40 46 47 48 50 51 52 53 54 57 \cr \ldots \$ logmove : num [1:106139] 9.02 8.72 8.25 8.99 9.09 \cr \ldots \$ constant: int [1:106139] 1 1 1 1 1 1 1 1 1 1 \cr \ldots \$ price1 : num [1:106139] 0.0605 0.0605 0.0605 0.0605 0.0605 \cr \ldots \$ price2 : num [1:106139] 0.0605 0.0603 0.0603 0.0603 0.0603 \cr \ldots \$ price3 : num [1:106139] 0.0420 0.0452 0.0452 0.0498 0.0436 \cr \ldots \$ price4 : num [1:106139] 0.0295 0.0467 0.0467 0.0373 0.0311 \cr \ldots \$ price5 : num [1:106139] 0.0495 0.0495 0.0373 0.0495 0.0495 \cr \ldots \$ price6 : num [1:106139] 0.0530 0.0478 0.0530 0.0530 0.0530 \cr \ldots \$ price7 : num [1:106139] 0.0389 0.0458 0.0458 0.0458 0.0466 \cr \ldots \$ price8 : num [1:106139] 0.0414 0.0280 0.0414 0.0414 0.0414 \cr \ldots \$ price9 : num [1:106139] 0.0289 0.0430 0.0481 0.0423 0.0423 \cr \ldots \$ price10 : num [1:106139] 0.0248 0.0420 0.0327 0.0327 0.0327 \cr \ldots \$ price11 : num [1:106139] 0.0390 0.0390 0.0390 0.0390 0.0382 \cr \ldots \$ deal : int [1:106139] 1 0 0 0 0 0 1 1 1 1 \cr \ldots \$ feat : num [1:106139] 0 0 0 0 0 0 0 0 0 0 \cr \ldots \$ profit : num [1:106139] 38.0 30.1 30.0 29.9 29.9 \cr 1 Tropicana Premium 64 oz; 2 Tropicana Premium 96 oz; 3 Florida's Natural 64 oz; \cr 4 Tropicana 64 oz; 5 Minute Maid 64 oz; 6 Minute Maid 96 oz; \cr 7 Citrus Hill 64 oz; 8 Tree Fresh 64 oz; 9 Florida Gold 64 oz; \cr 10 Dominicks 64 oz; 11 Dominicks 128 oz. \cr \$ storedemo:'data.frame': 83 obs. of 12 variables:\cr \ldots \$ STORE : int [1:83] 2 5 8 9 12 14 18 21 28 32 \cr \ldots \$ AGE60 : num [1:83] 0.233 0.117 0.252 0.269 0.178 \cr \ldots \$ EDUC : num [1:83] 0.2489 0.3212 0.0952 0.2222 0.2534 \cr \ldots \$ ETHNIC : num [1:83] 0.1143 0.0539 0.0352 0.0326 0.3807 \cr \ldots \$ INCOME : num [1:83] 10.6 10.9 10.6 10.8 10.0 \cr \ldots \$ HHLARGE : num [1:83] 0.1040 0.1031 0.1317 0.0968 0.0572 \cr \ldots \$ WORKWOM : num [1:83] 0.304 0.411 0.283 0.359 0.391 \cr \ldots \$ HVAL150 : num [1:83] 0.4639 0.5359 0.0542 0.5057 0.3866 \cr \ldots \$ SSTRDIST: num [1:83] 2.11 3.80 2.64 1.10 9.20 \cr \ldots \$ SSTRVOL : num [1:83] 1.143 0.682 1.500 0.667 1.111 \cr \ldots \$ CPDIST5 : num [1:83] 1.93 1.60 2.91 1.82 0.84 \cr \ldots \$ CPWVOL5 : num [1:83] 0.377 0.736 0.641 0.441 0.106 \cr } \details{ \describe{ \item{\code{store}}{store number} \item{\code{brand}}{brand indicator} \item{\code{week}}{week number} \item{\code{logmove}}{log of the number of units sold} \item{\code{constant}}{a vector of 1} \item{\code{price1}}{price of brand 1} \item{\code{deal}}{in-store coupon activity} \item{\code{feature}}{feature advertisement} \item{\code{STORE}}{store number} \item{\code{AGE60}}{percentage of the population that is aged 60 or older} \item{\code{EDUC}}{percentage of the population that has a college degree} \item{\code{ETHNIC}}{percent of the population that is black or Hispanic} \item{\code{INCOME}}{median income} \item{\code{HHLARGE}}{percentage of households with 5 or more persons} \item{\code{WORKWOM}}{percentage of women with full-time jobs} \item{\code{HVAL150}}{percentage of households worth more than \$150,000} \item{\code{SSTRDIST}}{distance to the nearest warehouse store} \item{\code{SSTRVOL}}{ratio of sales of this store to the nearest warehouse store} \item{\code{CPDIST5}}{average distance in miles to the nearest 5 supermarkets} \item{\code{CPWVOL5}}{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 et al.\cr \url{http://www.perossi.org/home/bsm-1} } \examples{ ## Example ## 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) ## Example 2 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$Vbetadraw) if(0){ ## plotting examples plot(out$betadraw) } } } \keyword{datasets} bayesm/man/numEff.Rd0000755000176000001440000000246611430344715014061 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}{ R x 1 vector of draws } \item{m}{ number of lags for autocorrelations } } \details{ default for number of lags is chosen so that if R = 5000, m =100 and increases as the sqrt(R). } \value{ \item{stderr }{standard error of the mean of x} \item{f }{ variance ratio (relative numerical efficiency) } } \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} } \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{ numEff(rnorm(1000),m=20) numEff(rnorm(1000)) } \keyword{ ts } \keyword{ utilities } bayesm/man/nmat.Rd0000755000176000001440000000167411430344656013604 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}{ k x k Cov matrix stored as a k*k x 1 vector (col by col) } } \details{ This routine is often used with apply to convert an R x (k*k) array of covariance MCMC draws to correlations. As in \code{corrdraws=apply(vardraws,1,nmat)} } \value{ 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/momMix.Rd0000755000176000001440000000322311430344631014074 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}{ R x ncomp list of draws of mixture probs } \item{compdraw}{ list of length R of draws of mixture component moments } } \details{ R is the number of MCMC draws in argument list above. \cr ncomp is the number of mixture components fitted.\cr compdraw is a list of lists of lists with mixture components. \cr compdraw[[i]] is ith draw. \cr compdraw[[i]][[j]][[1]] is the mean parameter vector for the jth component, ith MCMC draw. \cr compdraw[[i]][[j]][[2]] is the UL decomposition of \eqn{Sigma^{-1}} for the jth component, ith MCMC draw. } \value{ a list of the following items \dots \item{mu }{Posterior Expectation of Mean} \item{sigma }{Posterior Expecation of Covariance Matrix} \item{sd }{Posterior Expectation of Vector of Standard Deviations} \item{corr }{Posterior Expectation of Correlation Matrix} } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 5. \cr \url{http://www.perossi.org/home/bsm-1} } \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. } \seealso{ \code{\link{rmixGibbs}}} \keyword{ multivariate } bayesm/man/mnpProb.Rd0000755000176000001440000000334011430344565014251 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 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}{ 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, Sigma parameters. Uses the GHK method to compute choice probabilities. To simulate a distribution of probabilities, loop over the beta, Sigma draws from \code{rmnpGibbs} output. } \value{ p x 1 vector of choice probabilites } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi,Allenby and McCulloch, Chapters 2 and 4. \cr \url{http://www.perossi.org/home/bsm-1} } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \seealso{ \code{\link{rmnpGibbs}}, \code{\link{createX}} } \examples{ ## ## example of computing MNP probabilites ## here I'm thinking of Xa as having 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,.5,.5,1),ncol=2) mnpProb(beta,Sigma,X) } \keyword{ models } bayesm/man/mnlHess.Rd0000755000176000001440000000216211430344522014237 0ustar ripleyusers\name{mnlHess} \alias{mnlHess} \concept{multinomial logit} \concept{hessian} \title{ Computes -Expected Hessian for Multinomial Logit} \description{ \code{mnlHess} computes -Expected[Hessian] for Multinomial Logit Model } \usage{ mnlHess(beta,y, X) } \arguments{ \item{beta}{ k x 1 vector of coefficients } \item{y}{ n x 1 vector of choices, (1, \ldots,p) } \item{X}{ 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{ k x k matrix } \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-1l} } \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. } \seealso{ \code{\link{llmnl}}, \code{\link{createX}}, \code{\link{rmnlIndepMetrop}} } \examples{ ## \dontrun{mnlHess(beta,y,X)} } \keyword{ models } bayesm/man/mixDenBi.Rd0000755000176000001440000000307511430344451014332 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{ length(comps) is the number of mixture components. comps[[j]] is a list of parameters of the jth component. comps[[j]]\$mu is mean vector; comps[[j]]\$rooti is the UL decomp of \eqn{Sigma^{-1}}. } \value{ an array (length(xi)=length(xj) x 2) with density value } \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} } \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. } \seealso{ \code{\link{rnmixGibbs}}, \code{\link{mixDen}} } \examples{ \dontrun{ ## ## see examples in rnmixGibbs documentation ## } } \keyword{ models } \keyword{ multivariate } bayesm/man/mixDen.Rd0000755000176000001440000000266311430344400014053 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 component of a normal mixture at each of the points on a user-specifed grid. } \usage{ mixDen(x, pvec, comps) } \arguments{ \item{x}{ array - ith column gives grid points for ith variable } \item{pvec}{ vector of mixture component probabilites } \item{comps}{ list of lists of components for normal mixture } } \details{ length(comps) is the number of mixture components. comps[[j]] is a list of parameters of the jth component. comps[[j]]\$mu is mean vector; comps[[j]]\$rooti is the UL decomp of \eqn{Sigma^{-1}}. } \value{ an array of the same dimension as grid with density values. } \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} } \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. } \seealso{ \code{\link{rnmixGibbs}} } \examples{ \dontrun{ ## ## see examples in rnmixGibbs documentation ## } } \keyword{ models } \keyword{ multivariate } bayesm/man/margarine.Rd0000755000176000001440000001042611430344260014574 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{ This is an R object that is a list of two data frames, list(choicePrice,demos) List of 2 \cr \$ choicePrice:`data.frame': 4470 obs. of 12 variables:\cr \ldots \$ hhid : int [1:4470] 2100016 2100016 2100016 2100016 \cr \ldots \$ choice : num [1:4470] 1 1 1 1 1 4 1 1 4 1 \cr \ldots \$ PPk\_Stk : num [1:4470] 0.66 0.63 0.29 0.62 0.5 0.58 0.29 \cr \ldots \$ PBB\_Stk : num [1:4470] 0.67 0.67 0.5 0.61 0.58 0.45 0.51 \cr \ldots \$ PFl\_Stk : num [1:4470] 1.09 0.99 0.99 0.99 0.99 0.99 0.99 \cr \ldots \$ PHse\_Stk: num [1:4470] 0.57 0.57 0.57 0.57 0.45 0.45 0.29 \cr \ldots \$ PGen\_Stk: num [1:4470] 0.36 0.36 0.36 0.36 0.33 0.33 0.33 \cr \ldots \$ PImp\_Stk: num [1:4470] 0.93 1.03 0.69 0.75 0.72 0.72 0.72 \cr \ldots \$ PSS\_Tub : num [1:4470] 0.85 0.85 0.79 0.85 0.85 0.85 0.85 \cr \ldots \$ PPk\_Tub : num [1:4470] 1.09 1.09 1.09 1.09 1.07 1.07 1.07 \cr \ldots \$ PFl\_Tub : num [1:4470] 1.19 1.19 1.19 1.19 1.19 1.19 1.19 \cr \ldots \$ PHse\_Tub: num [1:4470] 0.33 0.37 0.59 0.59 0.59 0.59 0.59 \cr Pk is Parkay; BB is BlueBonnett, Fl is Fleischmanns, Hse is house, Gen is generic, Imp is Imperial, SS is Shed Spread. \_Stk indicates stick, \_Tub indicates Tub form. \$ demos :`data.frame': 516 obs. of 8 variables:\cr \ldots \$ hhid : num [1:516] 2100016 2100024 2100495 2100560 \cr \ldots \$ Income : num [1:516] 32.5 17.5 37.5 17.5 87.5 12.5 \cr \ldots \$ Fs3\_4 : int [1:516] 0 1 0 0 0 0 0 0 0 0 \cr \ldots \$ Fs5 : int [1:516] 0 0 0 0 0 0 0 0 1 0 \cr \ldots \$ Fam\_Size : int [1:516] 2 3 2 1 1 2 2 2 5 2 \cr \ldots \$ college : int [1:516] 1 1 0 0 1 0 1 0 1 1 \cr \ldots \$ whtcollar: int [1:516] 0 1 0 1 1 0 0 0 1 1 \cr \ldots \$ retired : int [1:516] 1 1 1 0 0 1 0 1 0 0 \cr Fs3\_4 is dummy (family size 3-4). Fs5 is dummy for family size >= 5. college,whtcollar,retired are dummies reflecting these statuses. } \details{ choice is a multinomial indicator of one of the 10 brands (in order listed under format). All prices are in \$. } \source{ Allenby and 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 et al.\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) if(0){ ## plotting examples plot(out$nmix) plot(out$Deltadraw)} } } \keyword{datasets} bayesm/man/logMargDenNR.Rd0000755000176000001440000000206211430344232015102 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.\cr Note: this approximation can be influenced by outliers in the vector of log-likelihoods. Use with \strong{care} . } \usage{ logMargDenNR(ll) } \arguments{ \item{ll}{ vector of log-likelihoods evaluated at length(ll) MCMC draws } } \value{ approximation to log marginal density value. } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapter 6. \cr \url{http://www.perossi.org/home/bsm-1l} } \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. } \keyword{ distribution } bayesm/man/lndMvst.Rd0000755000176000001440000000233111430344164014255 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 Sigma } \item{NORMC}{ include normalizing constant, def: FALSE } } \details{ \eqn{z} \eqn{\sim}{~} \eqn{MVst(mu,nu,\Sigma)} } \value{ log density value } \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} } \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. } \seealso{ \code{\link{lndMvn}} } \examples{ ## Sigma=matrix(c(1,.5,.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/lndMvn.Rd0000755000176000001440000000212511430344120014055 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 Sigma } } \details{ \eqn{z} \eqn{\sim}{~} \eqn{N(mu,\Sigma)} } \value{ log density value } \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} } \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. } \seealso{ \code{\link{lndMvst}} } \examples{ ## Sigma=matrix(c(1,.5,.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/lndIWishart.Rd0000755000176000001440000000227511430344044015062 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}, V is a k x k matrix \code{lndIWishart} computes the complete log-density, including normalizing constants. } \value{ log density value } \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} } \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. } \seealso{ \code{\link{rwishart}} } \examples{ ## lndIWishart(5,diag(3),(diag(3)+.5)) } \keyword{ distribution } bayesm/man/lndIChisq.Rd0000755000176000001440000000216211430343740014505 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 } } \details{ \eqn{Z= \nu*ssq/\chi^2_{\nu}}, \eqn{Z} \eqn{\sim}{~} Inverted Chi-Squared. \cr \code{lndIChisq} computes the complete log-density, including normalizing constants. } \value{ log density value } \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} } \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. } \seealso{ \code{\link{dchisq}} } \examples{ ## lndIChisq(3,1,2) } \keyword{ distribution } bayesm/man/llnhlogit.Rd0000755000176000001440000000300211430343630014613 0ustar ripleyusers\name{llnhlogit} \alias{llnhlogit} \concept{multinomial logit} \concept{non-homothetic utility} \title{ Evaluate Log Likelihood for non-homothetic Logit Model } \description{ \code{llmnp} 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}{ n x 1 vector of choice (1, \ldots, p) } \item{lnprices}{ n x p array of log-prices} \item{Xexpend}{ n x d array of vars predicting expenditure } } \details{ Non-homothetic logit model with: \eqn{ln(psi_i(U)) = alpha_i - e^{k_i}U} \cr Structure of theta vector \cr alpha: (p x 1) vector of utility intercepts.\cr k: (p x 1) vector of utility rotation parms. \cr gamma: (k x 1) -- expenditure variable coefs.\cr tau: (1 x 1) -- logit scale parameter.\cr } \value{ value of log-likelihood (sum of log prob of observed multinomial outcomes). } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch,Chapter 4. \cr \url{http://www.perossi.org/home/bsm-1} } \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. } \seealso{ \code{\link{simnhlogit}} } \examples{ ## \dontrun{ll=llnhlogit(theta,choice,lnprices,Xexpend)} } \keyword{ models } bayesm/man/llmnp.Rd0000755000176000001440000000376011430343350013753 0ustar ripleyusers\name{llmnp} \alias{llmnp} \concept{multinomial probit} \concept{GHK method} \concept{likelihood} \title{ Evaluate Log Likelihood for Multinomial Probit Model } \description{ \code{llmnp} evaluates the log-likelihood for the multinomial probit model. } \usage{ llmnp(beta, Sigma, X, y, r) } \arguments{ \item{beta}{ k x 1 vector of coefficients } \item{Sigma}{ (p-1) x (p-1) Covariance matrix of errors } \item{X}{ X is n*(p-1) x k array. X is from differenced system. } \item{y}{ y is vector of n indicators of multinomial response (1, \ldots, p). } \item{r}{ number of draws used in GHK } } \details{ X is (p-1)*n x k matrix. Use \code{\link{createX}} with \code{DIFF=TRUE} to create X. \cr Model for each obs: \eqn{w = Xbeta + e}. \eqn{e} \eqn{\sim}{~} \eqn{N(0,Sigma)}. censoring mechanism: if \eqn{y=j (j 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 j=1,\ldots,p-1, \eqn{A_jw = A_jmu + A_je > 0} is equivalent to \eqn{y=j}. Thus, if 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). } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch, Chapters 2 and 4. \cr \url{http://www.perossi.org/home/bsm-1} } \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. } \seealso{ \code{\link{createX}}, \code{\link{rmnpGibbs}} } \examples{ ## \dontrun{ll=llmnp(beta,Sigma,X,y,r)} } \keyword{ models } bayesm/man/llmnl.Rd0000755000176000001440000000245611430572356013762 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}{ k x 1 coefficient vector } \item{y}{ n x 1 vector of obs on y (1,\ldots, p) } \item{X}{ n*p x k Design matrix (use \code{createX} to make) } } \details{ Let \eqn{mu_i=X_i \beta}, then \eqn{Pr(y_i=j) = exp(mu_{i,j})/\sum_kexp(mu_{i,k})}.\cr \eqn{X_i} is the submatrix of X corresponding to the ith observation. X has n*p rows. Use \code{\link{createX}} to create X. } \value{ value of log-likelihood (sum of log prob of observed multinomial outcomes). } \references{ For further discussion, see \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}. } \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \seealso{ \code{\link{createX}}, \code{\link{rmnlIndepMetrop}} } \examples{ ## \dontrun{ll=llmnl(beta,y,X)} } \keyword{ models } bayesm/man/ghkvec.Rd0000755000176000001440000000266411430343140014077 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) } \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 } } \value{ approximation to integral } \note{ \code{ghkvec} can accept a vector of truncations and compute more than one integral. That is, length(trunpt)/length(above) number of different integrals, each with the same Sigma and mean 0 but different truncation points. See example below for an example with two integrals at different truncation points. } \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} } \author{ Peter Rossi,Anderson School, UCLA, \email{perossichi@gmail.com}. } \examples{ ## Sigma=matrix(c(1,.5,.5,1),ncol=2) L=t(chol(Sigma)) trunpt=c(0,0,1,1) above=c(1,1) ghkvec(L,trunpt,above,100) } \keyword{ distribution } bayesm/man/fsh.Rd0000755000176000001440000000052211430343005013377 0ustar ripleyusers\name{fsh} \alias{fsh} \title{ Flush Console Buffer } \description{ Flush contents of console buffer. This function only has an effect on the Windows GUI. } \usage{ fsh() } \value{ No value is returned. } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \keyword{ utilities } bayesm/man/eMixMargDen.Rd0000755000176000001440000000334511754316444015005 0ustar ripleyusers\name{eMixMargDen} \alias{eMixMargDen} \concept{normal mixtures} \concept{bayes} \concept{MCMC} \title{ Compute Marginal Densities of A Normal Mixture Averaged over MCMC Draws } \description{ \code{eMixMargDen} assumes that a multivariate mixture of normals has been fitted via MCMC (using \code{rnmixGibbs}). For each MCMC draw, the marginal densities for each component in the multivariate mixture are computed on a user-supplied grid and then averaged over draws. } \usage{ eMixMargDen(grid, probdraw, compdraw) } \arguments{ \item{grid}{ array of grid points, grid[,i] are ordinates for ith dimension of the density } \item{probdraw}{ array - each row of which contains a draw of probabilities of mixture comp } \item{compdraw}{ list of lists of draws of mixture comp moments } } \details{ length(compdraw) is number of MCMC draws. \cr compdraw[[i]] is a list draws of mu and inv Chol root for each of mixture components. \cr compdraw[[i]][[j]] is jth component. compdraw[[i]][[j]]\$mu is mean vector; compdraw[[i]][[j]]\$rooti is the UL decomp of \eqn{Sigma^{-1}}. } \value{ an array of the same dimension as grid with density values. } \references{ For further discussion, see \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}. } \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. To avoid errors, call with output from \code{\link{rnmixGibbs}}. } \seealso{ \code{\link{rnmixGibbs}} } \keyword{ models } \keyword{ multivariate } bayesm/man/detailing.Rd0000755000176000001440000000657410573337024014607 0ustar ripleyusers\name{detailing} \alias{detailing} \docType{data} \title{ Physician Detailing Data from Manchanda et al (2004)} \description{ Monthly data on detailing (sales calls) on 1000 physicians. 23 mos of data for each Physician. Includes physician covariates. Dependent Variable (\code{scripts}) is the number of new prescriptions ordered by the physician for the drug detailed. } \usage{data(detailing)} \format{ This R object is a list of two data frames, list(counts,demo). List of 2: \$ counts:`data.frame': 23000 obs. of 4 variables:\cr \ldots\$ id : int [1:23000] 1 1 1 1 1 1 1 1 1 1 \cr \ldots\$ scripts : int [1:23000] 3 12 3 6 5 2 5 1 5 3 \cr \ldots\$ detailing : int [1:23000] 1 1 1 2 1 0 2 2 1 1 \cr \ldots\$ lagged\_scripts: int [1:23000] 4 3 12 3 6 5 2 5 1 5 \$ demo :`data.frame': 1000 obs. of 4 variables:\cr \ldots\$ id : int [1:1000] 1 2 3 4 5 6 7 8 9 10 \cr \ldots\$ generalphys : int [1:1000] 1 0 1 1 0 1 1 1 1 1 \cr \ldots\$ specialist: int [1:1000] 0 1 0 0 1 0 0 0 0 0 \cr \ldots\$ mean\_samples: num [1:1000] 0.722 0.491 0.339 3.196 0.348 } \details{ generalphys is dummy for if doctor is a "general practitioner," specialist is dummy for if the physician is a specialist in the theraputic class for which the drug is intended, mean\_samples is the mean number of free drug samples given the doctor over the sample. } \source{ Manchanda, P., P. K. Chintagunta and P. E. 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) } nvar=ncol(X) # Number of X variables nz=ncol(Z) # Number of Z variables rm(detailing,counts) cat("Finished Reading data",fill=TRUE) fsh() Data = list(regdata=regdata, Z=Z) 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$alphadraw) if(0){ ## plotting examples plot(out$betadraw) plot(out$alphadraw) plot(out$Deltadraw) } } } \keyword{datasets} bayesm/man/customerSat.Rd0000755000176000001440000000235011430342503015133 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 (10 is "Excellent" and 1 is "Poor") } \usage{data(customerSat)} \format{ A data frame with 1811 observations on the following 10 variables. \describe{ \item{\code{q1}}{Overall Satisfaction} \item{\code{q2}}{Setting Competitive Prices} \item{\code{q3}}{Holding Price Increase to a Minimum} \item{\code{q4}}{Appropriate Pricing given Volume} \item{\code{q5}}{Demonstrating Effectiveness of Purchase} \item{\code{q6}}{Reach a Large \# of Customers} \item{\code{q7}}{Reach of Advertising} \item{\code{q8}}{Long-term Exposure} \item{\code{q9}}{Distribution} \item{\code{q10}}{Distribution to Right Geographic Areas} } } \source{ Rossi et al (2001), "Overcoming Scale Usage Heterogeneity," \emph{JASA} 96, 20-31. } \references{ Case Study 3, \emph{Bayesian Statistics and Marketing} by Rossi et al.\cr \url{http://www.perossi.org/home/bsm-1*} } \examples{ data(customerSat) apply(as.matrix(customerSat),2,table) } \keyword{datasets} bayesm/man/createX.Rd0000755000176000001440000000424511566563253014243 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 Xa } \item{nd}{ integer - number of non-alternative specific vars } \item{Xa}{ n x p*na matrix of alternative-specific vars } \item{Xd}{ 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: na,nd,Xa,Xd can be NULL to indicate lack of Xa or Xd variables. } \value{ X matrix -- n*(p-DIFF) x [(INT+nd)*(p-1) + na] matrix. } \references{ For further discussion, see \emph{Bayesian Statistics and Marketing} by Rossi, Allenby and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1} } \note{ \code{\link{rmnpGibbs}} assumes that the base alternative is the default. } \author{ Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}. } \seealso{ \code{\link{rmnlIndepMetrop}}, \code{\link{rmnpGibbs}} } \examples{ na=2; nd=1; p=3 vec=c(1,1.5,.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/condMom.Rd0000755000176000001440000000254511566563047014246 0ustar ripleyusers\name{condMom} \alias{condMom} \concept{normal distribution} \concept{conditional distribution} \title{ Computes Conditional Mean/Var of One Element of MVN given All Others } \description{ \code{condMom} compute moments of conditional distribution of ith element of normal given all others. } \usage{ condMom(x, mu, sigi, i) } \arguments{ \item{x}{ vector of values to condition on - ith element not used } \item{mu}{ length(x) mean vector } \item{sigi}{ length(x) dim inverse of covariance matrix } \item{i}{ conditional distribution of ith element } } \details{ \eqn{x} \eqn{\sim}{~} \eqn{MVN(mu,Sigma)}. \code{condMom} computes moments of \eqn{x_i} given \eqn{x_{-i}}. } \value{ a list containing: \item{cmean }{ cond mean } \item{cvar }{ cond variance} } \references{ For further discussion, see \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}. } \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. } \examples{ ## sig=matrix(c(1,.5,.5,.5,1,.5,.5,.5,1),ncol=3) sigi=chol2inv(chol(sig)) mu=c(1,2,3) x=c(1,1,1) condMom(x,mu,sigi,2) } \keyword{ distribution } bayesm/man/clusterMix.Rd0000755000176000001440000000511211430341727014767 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) } \arguments{ \item{zdraw}{ R x nobs array of draws of indicators } \item{cutoff}{ cutoff probability for similarity (def=.9)} \item{SILENT}{ logical flag for silent operation (def= FALSE) } } \details{ define a similarity matrix, Sim, Sim[i,j]=1 if observations i and 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, loss(E[Sim]-Sim(z)), where loss is absolute deviation. Method B: Define a Similarity matrix by setting any element of E[Sim] = 1 if E[Sim] > cutoff. Compute the clustering scheme associated with this "windsorized" Similarity matrix. } \value{ \item{clustera}{indicator function for clustering based on method A above} \item{clusterb}{indicator function for clustering based on method B above} } \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} } \author{ Peter Rossi, Graduate School of Business, University of Chicago \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. } \seealso{ \code{\link{rnmixGibbs}} } \keyword{ models } \keyword{ multivariate } \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,.5,.5,1),ncol=2) Sigma2=matrix(c(1,.5,.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 R=2000 Data=list(y=dm$x) ncomp=2 Prior=list(ncomp=ncomp,a=c(rep(100,ncomp))) Mcmc=list(R=R,keep=1) out=rnmixGibbs(Data=Data,Prior=Prior,Mcmc=Mcmc) begin=500 end=R ## find clusters outclusterMix=clusterMix(out$zdraw[begin:end,]) ## ## check on clustering versus "truth" ## note: there could be switched labels ## table(outclusterMix$clustera,dm$z) table(outclusterMix$clusterb,dm$z) } ## } bayesm/man/cheese.Rd0000755000176000001440000000407711430341322014064 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. \describe{ \item{\code{RETAILER}}{a list of 88 retailers} \item{\code{VOLUME}}{unit sales} \item{\code{DISP}}{a measure of display activity -- per cent ACV on display} \item{\code{PRICE}}{in \$} } } \source{ Boatwright et al (1999), "Account-Level Modeling for Trade Promotion," \emph{JASA} 94, 1063-1073. } \references{ Chapter 3, \emph{Bayesian Statistics and Marketing} by Rossi et al. \cr \url{http://www.perossi.org/home/bsm-1l} } \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$Vbetadraw) if(0){ # # plot hier coefs plot(out$betadraw) } } } \keyword{datasets} bayesm/man/cgetC.Rd0000755000176000001440000000206011430341276013653 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 1, ..., k with different scale usage patterns. } \usage{ cgetC(e, k) } \arguments{ \item{e}{ quadratic parameter (>0 and less than 1) } \item{k}{ items are on a scale from 1, \ldots, k } } \section{Warning}{ This is a utility function which implements \strong{no} error-checking. } \value{ A vector of k+1 cut-offs. } \references{ Rossi et al (2001), \dQuote{Overcoming Scale Usage Heterogeneity,} \emph{JASA}96, 20-31. } \author{ Rob McCulloch and Peter Rossi, Graduate School of Business, University of Chicago. \email{perossichi@gmail.com}. } \seealso{ \code{\link{rscaleUsage}} } \examples{ ## cgetC(.1,10) } \keyword{ utilities } bayesm/man/breg.Rd0000755000176000001440000000361711430341136013551 0ustar ripleyusers\name{breg} \alias{breg} \concept{bayes} \concept{regression} \title{Posterior Draws from a Univariate Regression with Unit Error Variance} \description{ \code{breg} makes one draw from the posterior of a univariate regression (scalar dependent variable) given the error variance = 1.0. A natural conjugate, normal prior is used. } \usage{ breg(y, X, betabar, A) } \arguments{ \item{y}{ vector of values of dep variable. } \item{X}{ n (length(y)) x k Design matrix. } \item{betabar}{ k x 1 vector. Prior mean of regression coefficients. } \item{A}{ Prior precision matrix. } } \details{ model: \eqn{y=x'\beta + e}. \eqn{e} \eqn{\sim}{~} \eqn{N(0,1)}. \cr prior: \eqn{\beta} \eqn{\sim}{~} \eqn{N(betabar,A^{-1})}. } \value{ k x 1 vector containing a draw from the posterior distribution. } \references{ For further discussion, see \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}. } \section{Warning}{ This routine is a utility routine that does \strong{not} check the input arguments for proper dimensions and type. In particular, X must be a matrix. If you have a vector for X, coerce it into a matrix with one column } \examples{ ## if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=1000} else {R=10} ## simulate data set.seed(66) n=100 X=cbind(rep(1,n),runif(n)); beta=c(1,2) y=X\%*\%beta+rnorm(n) ## ## set prior A=diag(c(.05,.05)); betabar=c(0,0) ## ## make draws from posterior betadraw=matrix(double(R*2),ncol=2) for (rep in 1:R) {betadraw[rep,]=breg(y,X,betabar,A)} ## ## summarize draws mat=apply(betadraw,2,quantile,probs=c(.01,.05,.5,.95,.99)) mat=rbind(beta,mat); rownames(mat)[1]="beta"; print(mat) } \keyword{models} \keyword{regression} \keyword{distribution} bayesm/man/bank.Rd0000755000176000001440000001013311430337215013537 0ustar ripleyusers\name{bank} \alias{bank} \docType{data} \title{ Bank Card Conjoint Data of Allenby and Ginter (1995)} \description{ Data from a conjoint experiment in which two partial profiles of credit cards were presented to 946 respondents. The variable bank\$choiceAtt\$choice indicates which profile was chosen. The profiles are coded as the difference in attribute levels. Thus, 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. data on age,income and gender (female=1) are also recorded in bank\$demo } \usage{data(bank)} \format{ This R object is a list of two data frames, list(choiceAtt,demo). List of 2 \$ choiceAtt:`data.frame': 14799 obs. of 16 variables:\cr \ldots\$ id : int [1:14799] 1 1 1 1 1 1 1 1 1 1 \cr \ldots\$ choice : int [1:14799] 1 1 1 1 1 1 1 1 0 1 \cr \ldots\$ Med\_FInt : int [1:14799] 1 1 1 0 0 0 0 0 0 0 \cr \ldots\$ Low\_FInt : int [1:14799] 0 0 0 0 0 0 0 0 0 0 \cr \ldots\$ Med\_VInt : int [1:14799] 0 0 0 0 0 0 0 0 0 0 \cr \ldots\$ Rewrd\_2 : int [1:14799] -1 1 0 0 0 0 0 1 -1 0 \cr \ldots\$ Rewrd\_3 : int [1:14799] 0 -1 1 0 0 0 0 0 1 -1 \cr \ldots\$ Rewrd\_4 : int [1:14799] 0 0 -1 0 0 0 0 0 0 1 \cr \ldots\$ Med\_Fee : int [1:14799] 0 0 0 1 1 -1 -1 0 0 0 \cr \ldots\$ Low\_Fee : int [1:14799] 0 0 0 0 0 1 1 0 0 0 \cr \ldots\$ Bank\_B : int [1:14799] 0 0 0 -1 1 -1 1 0 0 0 \cr \ldots\$ Out\_State : int [1:14799] 0 0 0 0 -1 0 -1 0 0 0 \cr \ldots\$ Med\_Rebate : int [1:14799] 0 0 0 0 0 0 0 0 0 0 \cr \ldots\$ High\_Rebate : int [1:14799] 0 0 0 0 0 0 0 0 0 0 \cr \ldots\$ High\_CredLine: int [1:14799] 0 0 0 0 0 0 0 -1 -1 -1 \cr \ldots\$ Long\_Grace : int [1:14799] 0 0 0 0 0 0 0 0 0 0 \$ demo :`data.frame': 946 obs. of 4 variables:\cr \ldots\$ id : int [1:946] 1 2 3 4 6 7 8 9 10 11 \cr \ldots\$ age : int [1:946] 60 40 75 40 30 30 50 50 50 40 \cr \ldots\$ income: int [1:946] 20 40 30 40 30 60 50 100 50 40 \cr \ldots\$ gender: int [1:946] 1 1 0 0 0 0 1 0 0 0 \cr } \details{ Each respondent was presented with between 13 and 17 paired comparisons. Thus, this dataset has a panel structure. } \source{ Allenby and Ginter (1995), "Using Extremes to Design Products and Segment Markets," \emph{JMR}, 392-403. } \references{ Appendix A, \emph{Bayesian Statistics and Marketing} by Rossi,Allenby and McCulloch. \cr \url{http://www.perossi.org/home/bsm-1l} } \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) fsh() 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 end=10000/20 summary(out$Deltadraw,burnin=begin) summary(out$Vbetadraw,burnin=begin) if(0){ ## plotting examples ## 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/inst/0000755000176000001440000000000011337150373012542 5ustar ripleyusersbayesm/inst/doc/0000755000176000001440000000000011754551447013321 5ustar ripleyusersbayesm/inst/doc/Tips_On_Using_bayesm.pdf0000755000176000001440000015273210231722074020072 0ustar ripleyusers%PDF-1.4 % 6 0 obj <> endobj xref 6 17 0000000016 00000 n 0000000792 00000 n 0000000636 00000 n 0000000868 00000 n 0000000995 00000 n 0000001112 00000 n 0000001703 00000 n 0000002081 00000 n 0000002229 00000 n 0000002601 00000 n 0000005034 00000 n 0000032762 00000 n 0000033015 00000 n 0000050020 00000 n 0000050284 00000 n 0000050505 00000 n 0000050737 00000 n trailer <<53d113926400af43b9b31ac07ff2d3b9>]>> startxref 0 %%EOF 8 0 obj<>stream xb``c``:%P30p4A1?C  ^,ް0&s>iad`8H3@% " endstream endobj 7 0 obj<> endobj 9 0 obj<> endobj 10 0 obj<>/ProcSet[/PDF/Text]/ExtGState<>>> endobj 11 0 obj<> endobj 12 0 obj<> endobj 13 0 obj<> endobj 14 0 obj<> endobj 15 0 obj<>stream HWے}߯% .WتՊzHy%`)3"U&sRlJHLӧ}.dOo B܅l4 Cu b}ybױfm_E&)`l~D\@\*M}Fx{N3?%l!BG[@Gu^?>>pOY/whzVK3հe#OLm%ۉxlu`}7&~SYZغ*Q)0{+8%{)s?JY ~6X$6B7Fܟe#  R_60؋Z)r &ϼ|cpw|Ag^}<I 8_/4qYQ[*Sj4E1,DZõkMQJF{k z~'o)\7{V-?޳VJP)*${M_G)j%462Wv򐤅x+:^88t3c4$9*c5z*`^jUgyĚS>?ILΧ}'OSUl_Z×r4LNGH[Fo8pIw$P]VbZu7#/# ri༡p읨v%0oKUMUVbUwAuVu^NQ~WsMCQpto6ijQlg/RȽ?~UhamBGsrc~HH8O= Vr^ӈ~wX:!:Bd%vV!Ώc\>.ҹǩ8&8솚>ܼBcH}kw%\λsG 8[w!R}6b~6@[(LSI?! uw8"jܹgB464=]`8UCܚɼ B<>=wޅ5B U\*'mL٫b h|Ghb,f۶hn9*,Y׷$il |ϻmDd[JK7٧]~`J+ 59Za2xxURm{55]Πz+xO :M#!PĎ,)ҧ*jkdy`W{ҍo(T~ڨז' 0/X'b߹!R[p3{SW,\[\-y}j_:_,>Ԣ<\YZ}֤gt$] ޑ֞3DYat]GRWYUa(hiI=דl& r0~XwDy endstream endobj 16 0 obj<>stream HW TSWY!lM./P*K/ ( !$f#Aq"nȸqFPE*2:2L.U:Au9g̙=4+( '2:@2,6SZ[ӕL֣/ aI݊&Y9\s_n^;rM9g- L@ffr.`5QpMq ϫ~`&j51=4U'"_U2klNY>C֌6y 9UFmvX@ 6xSO @O\ԃ9,6'bb=;tM슍`;I,6IsӘX&|S  ;ԍ1>E'iX;~UɅW6yՋ+[G*՟b.OҘRQ؛lFRvҘk*{>AT,gGbDAH,ĂÖF3l3Zr8LZI,|H;$Uxy\>H4,AAc{`>#]bpl,LDF#Ŀ(_li,(_^E//Ea0TTs#o˔NeG~шgz9S|gD_z+wԵ,6GN,&s7Q39Д{՜ӄ=&`͏W9e՛~Ms}ט*Z&%-ټ!l?'tsj: %@b<|zղ%g7l-g/xc>^HI*]Ʋ={NWr5|Yʬ`mL u+[%MGUk/2mkh|}j]|ܲ~U ߺ{q`ǪN ߇U7YEU< ra<9)' >W(Yn!q'_"TI7jo47-N1x[f=4<uM Ee< SCTc(mFYHEiJѾGk_we]ͥ~xwiOnl8wX SC Q欇+?['Ny?y!|iWE"Lm\鹴 PH"˓SόS=~Ѐ՗4!sRAw ޭ#vneϾ#m!% bt^Sk}7K]K3,b:*hoDC ~ZRٌF *9d֎ô|Hp;GaӒLA!N EȐ@"&0V{q4MIaDPW kQ*(;!? \#6'@IK0n%ajɘ%V ,0e3b>A|-a@GZ-bwu(Nxj`!v/EAO众Q]䠹w;h4\}MyD>絉^Unt+ `Qc5worᏬj5^m[)Xe =b!+niy+/$Cs[^ pLWL?3FҾ#&G>2'{msBsfM>G1 :+( [^RÊ9 `ћW!K!ah#1F} y1Neepl gǪgtأFHFĄX`-w0U#4Z '9q!Z$`>Hv4s|L\OB*Ax4VOR&7"$A\" mR5:yoZ2RefAC EOϩGFG4jфbͷZJm (0z 6& =[ݘk !)z S!"LƳEP*KWI)tIJ.SR,$59,O1,RکԤ(JT$WrНDGv),|2@ DA2B.pbxǡ^ϰ=dac[D k8-e7˫ӷn.z7wOޟwjgos_}a9f<ʭ=.vkq}a Cil{?aA+޾vZ6ؙF)$%'L}{|}R̓ly>m6ϓk\W-JdݱynVo5a˜[!S\@ro(=85+BCӺ/ W_?)W\`}f$=E{4gEޅ6^w\qeա#Lxv#NPɉQgϩcҟI[>uo}w1A F.5G,~w\yؾ*,]U-M>x:06`,(x⸦?ij7?Wc-P W*|'1'RM,D H))#{Ii #'c$xB/FS1NTJ??)81,d ),'ϞfM}! 밿 g _F^"X{їWv0K tS%|+B;F{0f)d?;_P-A6y!xxA,hO~eI .̇]fʆ/Řwh2đ0 ٿs=SסkA~LEaܷW"R@l=d1>S}'{zHxw7WINDvqcmnj5 Ç bfjbl$-LUNHd'rWXAf CQȫ:\A{U35Sihip2Wy%XUgj经UAV,hX$$EXP]cAhD'jgZW3+1$}(3ӹ6L;?2ɴS3L2QFMӀ :ڙ6v/ӗosw@V5R*uP623,3BVуP -[Zkv.--ˠ.f՛=C~RZ;'VYf]j0K-uX"|?ZZbfEF++ PswO[UMr  bw-. 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BE ĚiU 2/dx-ݳd0j[Z;9(/FWg?6=,[DZc(Oaw՞1[krge VN ARsFl54]N Rc Vq稫1d?ͨau< e 7E-5{&t3?/|S"?"{;"n?'e5E欛u; 3NZCN%ɛV9;cREkPwk(4ݵlvRMoցBe0 gV JZZGq9p5 PifI!m^3굫|sjF)MFhW[ }P-wODǀ^M0㉍7imi D ?bL9 I& T\0V{GKRtc@d~&.JRbSg𪫘ab2&l=kڀ`']czKyFLhx?)qB \TQTW W+I"w/G@n1+JEʐk!>TGBЇ\X!:J&B4{,߹{픦GnyaJYDf{) NVͯǾ#^)懺ֽYe_V;x~ l$y"c9:EN~-z^cԃ)ϥ]|y=_|qy3YZ;_^LjyDqk`2$wv3[GhROZ~f!t[#wy%"O.z,5hC#6 rb- >Z ߄9X>M< eYq>)Qbm}\趂$L}A*>=c|lxv 2 B2$G]`%TJZr&c!xөZ!Bءmڃofhc]M)Iۂ%g)i @5o' n~8uӁMO]sK v7Jb^؞*'PQ󩬓f}yxS<8}*YTm` @b@e餀z+xHznW{ٌm$f5K!w_Tlu`fXnu*~z|fA|wH{xIz;5o|uǸPݽb5yU7KRpͿY jcg|aFp\TRBڬ |("xg Oj'+amey"H$+Vn"up2vԅQ,HއI$%#q٭I}(_miw1v\> stream xYKkGW1{8aeY1+ɿW#mLiB 몯H)0R 0h,#UP1btB{#$_pZ 2S+-'ct"Q^*`SE-$b-E2HCI%1`4Lk@PZ8#T 2`#)>‡Myʤ ,g3m˙7@rXXBO%R%Ep, f@^aAhN G irJhKTƇ',;ee/I˞*`1ˁ`9PuaBGgQ3$a9QV=U6,("pTu+=XSMa% ʹh'cq/7C&P1z"0c(&H уԐau4 : '#QpBI~4(/ x-i > 8Io^/Hqj/~wtlAF#~WpcNJi@Kx%\&x ܦeg#OKW%%Ĩ7G7Nq}ec3kVX&rKg;k4m ZLx&4|&omd9rbV칓S,Ogw@ 86wb_J>L:9<;S j3ZӲNN_SU ˧_NtߡN=cOCx9XwSNݶcҷf_\w'Q+yq޶<1\C͸} 1dɅK=|=ܜ϶ eÙ͸,Tŭ?(ЬoWf)/3BV9g&,x,|=߾vW\DqvuW|UU~_ҌVgǫ4:n{5Fo bWg0 *v%NEWx[`1aߴ?wۑfw\nf7c2ߞV}m]9#boՖX~T᪻ ﻫ=r&|$?t,e+Ͱ}zcÁCMO4LVuCˌW?4J߯7 ߇غigwd35٩@3ڌIHꮉ7~Erz8q|,g˳vҏ&8q,i1ˎIwy>yL%(;vǎ1x3F)ngendstream endobj 396 0 obj << /Type /ObjStm /Length 1483 /Filter /FlateDecode /N 96 /First 838 >> stream xY=7+XR<)p[^I'J6K6%r;;5>OF' hZT1:`#j1z#V'`!.欉s&F;1yޤj&`&rLVq2ymmR "o`¡Hp0[#>O `X Ps]L{XNB0,H0,O`X"l.C`EDb`6aBtqj:KyHP " XW,_p,r #i ~`9Fؑ 7v"pa9Sp$G1Rp(mbpKnƄTI%{8Ԅc("񤩰`9 ,L0,GRE1Ȋ">1M  *se=8CTNԐE6G;0Sz<*lM(4E΢gRK{;ּ6/~7|rNFU^ӈn⑌+|:Ze t^5$6/LлG6v+YM|>(?61356JlO|O/SC_ANɏسa<wk?owvڇvڅ2(KU$}I={ׅt@ζIv=QfSY\KTU:Y4 ݥ`쪓s\W:l'AgB]wyyž}{ܶ/Z}/r]gC]_8c9wNt#_Ҕ/~Ei۞xaqX?wϛC &|+'J`=G$PPzgg\˜u$nﶧf0 lX& 7S`cXtj4%CS~(}zJYPzlI3ImrCDvPZvTh圤]g٭v/<ѓ;FV~I׭"[Yi5 \/39.uy!XfַЍ*IP%u;9޶Q&ek22ZZ7zc7byk<Z8O|-LΧ'rZ(S)"S!Pˤכϼ#gnMErCRI%)TʤJ4ϪNOBjiE2i12q5$PXs )Mŏ۷t?p!ǰq2>ŝq4 ˣ-,| i lVendstream endobj 493 0 obj << /Type /ObjStm /Length 1502 /Filter /FlateDecode /N 96 /First 838 >> stream x?6 ~ uGHJLZt?A I $=GMuu_!MS?Ѷ«MC ,c$W5HŕB)X!QBN1\24E(%xkpX&1,k"4đҞChbU UPIġ :$ђ`∊˒!n Cdd#L""  Ȟ0#Ẅ\𗁉2"WD5Z0#r:ÝRs ) /ULU 9'1, hSAJDQ&IGYGMI&', "J>ȕ| rSC9#$GLP,,H [Q@bTDFW;&w|bB>YV8fg k(+ r$5 /|R VPQoC{J*K&^bڨ& APLQ{>w}exmǧ⧟ ,wŭy.^7*7>+(VQ(K+EꚘhoD[[ڣW}-,{LkbRļTQʑo%kOK+M)QQi.Ew8s>>uy3s=Y#Eqhح]V.&\L=;3WcګLhȞenWSbp^v{`/pǿnïǶLt=5v4s{JM%dmKCfOkrt!w/akG]Ht[;ښ[;Uډ@Ѻ~j[I-m,֎q}K1-Ay툗״߿}G߯|[n߿lczXt뭁b[ z`KzCM癸VAnޤ,`I[_ uyVmm֛"cxzleꑸrVtňq>,䣐BJ.R#ғM۬xN !2ZRіiV޲|NZ_D[X9dܮJJ2B%%3rc=+oZ#&Tbet1Ɉm;ujkEO2CPb*#1-LL2bjӘ#<Ƈ?7D)F2ҸҡyvSk7LepL˽{G;z8vh&OfH7s#=8ֻ$$=L":z_x>O}69G9Б 뉸 9eb;'Ha$'NۓH\Oxb=*!}Qtry(~Nv9ORǟhX11^f7“E3<1~NN:&WgK[ DoNn) n}7endstream endobj 590 0 obj << /Type /ObjStm /Length 1705 /Filter /FlateDecode /N 96 /First 838 >> stream xY?$5im ]D8 ?zg9]韴#{\UuI\1H?ZHjFE1ƒ0"Yk֊2a$x<1Xqçyx<ֱYJqjĕ9P8sj %9&>bSD4Bs¹3cb3<qgᔂ3<};Dr3rG'DtMlCV :p(Ii`AtIXAǧ ϧ P%A(z1#n< rS#Y+4 n2jK NVjroݫJ&O ge[~)p\?:$VdžY'e V6'xqg&E~a3(. y6ERL\7&1NuK"EUq l W" |MI\b pVPAiikEd%ik`n54oIDiY@y~(N^K\@a8uQBq]P\)ו[(~q7دI',[.qZCq]P9P#XɁq`_ mQCq[PVʡ-=K$pe5j}<oܗ:Xk aO!Eo }[Bo_W!Bo_TK ڞ)N}'t9Bq<ɕOi_DW=KFD_~_Oo{/{>1co}{enOchX麗}(Ja|@lj~اVԧlBC=\qt_C }'8 endstream endobj 687 0 obj << /Type /ObjStm /Length 1641 /Filter /FlateDecode /N 96 /First 838 >> stream xY$56 ]K 0xgldMtҪKYV]{yطhd aZMtm –Z'g}uh1h6:ɾnx d(P&i#*JSaU&_ .UؕN~0,z),G` I I),7ܝ`X`Xlz8odlYFUwN#Az%S:@uʋPi@4*50|⭍t;Xm(_Z: 4X7a,٠JpC73҉NΙCVF,E \I2H2i:&|G5 5ܘ=σ曏G` 7Wq fKGF 4rkGHz۷ۛ/3jv{? 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G(k骟rOxwy|;qa#)!.?x0 5bP/.' cδ<*r Γ3yv;*M:6eE  sS 7Hnq3^*A I( k}F /&'L%cOyՕ+AfY8#냈1m\8 n( 1G{>'cβ%ScKb-b0!s' 4F(e*B G]Fiqdda\1)}Do|dh.$[z}zJx~c W@ Eʋȗ6㗬EvUZԲZ:&a% $a#U!HSz a kN |թ2r8:zuG6۸z0.(Aq.t/rrJuc*)$Ptx@?mO3ԊDHGHGLxH#w#u"܅Ɠk,.m'<*W>ql}SeYˍw4[[PJD44#"~:@oӁ#˳wL=S4#Z$ˎCI?]VߣCR#endstream endobj 1955 0 obj << /Type /XRef /Length 618 /Filter /FlateDecode /DecodeParms << /Columns 5 /Predictor 12 >> /W [ 1 3 1 ] /Info 97 0 R /Root 96 0 R /Size 1956 /ID [<0b84d85650a5b86eec6b29a43df2670f><99be13c53e4319436dd8ffb48d50f87d>] >> stream xKHaǿ;Ti솥M=VhHIAEP " EA-$)M(X)ns~v\sg{90G}#?gLb|)xJ?hjIĥѳݥl>hQ-R[I>n(.\V'QopUAWqt63UVoĢKjݢN]Hnќ#b/HnQvP,|A-R[Tu\,P"HnQ}K>vX, ^Y)/xsQ&?Z8œ{aJImaB/7)GXy 2ps4n|0q_=W:{&w§jݢ&h(TE"EĢjݢ;bQoZthfJ-R[eL,>,f?t$xZO';`'Cw&#_#$ȃ\TPoL-yXJ4l9 W<tΧs{9lgd>i _d6e!Ol9N洶BX[k&l_NOq)$J*~;%Št^fV*{Űp{ endstream endobj startxref 358873 %%EOF bayesm/DESCRIPTION0000755000176000001440000000323411754656016013310 0ustar ripleyusersPackage: bayesm Version: 2.2-5 Date: 2012-05-15 Title: Bayesian Inference for Marketing/Micro-econometrics Author: Peter Rossi . Maintainer: Peter Rossi Depends: R (>= 2.10) Description: bayesm 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, and Analysis of Multivariate Ordinal survey data with scale usage heterogeneity (as in Rossi et al, JASA (01)). For further reference, consult our book, Bayesian Statistics and Marketing by Rossi, Allenby and McCulloch. 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