Nothing
R/DPMolmm.R
In DPpackage: Bayesian Nonparametric Modeling in R
### DPMolmm.R
### Fit a ordinal linear mixed model with a Dirichlet Process mixture of
### normals prior for the random effect distribution.
###
### Copyright: Alejandro Jara, 2006-2012.
###
### Last modification: 17-08-2009.
###
### This program is free software; you can redistribute it and/or modify
### it under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2 of the License, or (at
### your option) any later version.
###
### This program is distributed in the hope that it will be useful, but
### WITHOUT ANY WARRANTY; without even the implied warranty of
### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
### General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with this program; if not, write to the Free Software
### Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
###
### The author's contact information:
###
### Alejandro Jara
### Department of Statistics
### Facultad de Matematicas
### Pontificia Universidad Catolica de Chile
### Casilla 306, Correo 22
### Santiago
### Chile
### Voice: +56-2-3544506 URL : http://www.mat.puc.cl/~ajara
### Fax : +56-2-3547729 Email: atjara@uc.cl
###
"DPMolmm"<-
function(fixed,random,prior,mcmc,state,status,data=sys.frame(sys.parent()),na.action=na.fail)
UseMethod("DPMolmm")
"DPMolmm.default"<-
function(fixed,
random,
prior,
mcmc,
state,
status,
data=sys.frame(sys.parent()),
na.action=na.fail)
{
#########################################################################################
# call parameters
#########################################################################################
m <- mcall <- cl <- match.call()
nm <- names(m)[-1]
keep <- is.element(nm, c("data", "na.action"))
for (i in nm[!keep]) m[[i]] <- NULL
allvars <- c(all.vars(fixed), all.vars(random))
Terms <- if (missing(data))
terms(fixed)
else terms(fixed, data = data)
cl$fixed <- eval(fixed)
cl$random <- eval(random)
m$formula <- as.formula(paste("~", paste(allvars, collapse = "+")))
environment(m$formula) <- environment(fixed)
m$drop.unused.levels <- TRUE
m[[1]] <- as.name("model.frame")
mf <- eval.parent(m)
#########################################################################################
# data structure
#########################################################################################
nrec <- dim(mf)[1]
resp <- mf[,1]
if(!is.factor(resp)) stop("the response must be a factor")
categ<-levels(resp)
ncateg<-length(categ)
if(ncateg <= 2) stop("the response must have 3 or more levels")
yr <- unclass(resp)
if(min(yr)==0)yr<-yr+1
if(min(yr)>1)yr<-yr+min(yr)+1
categn<-seq(1,ncateg)
crandom <- all.vars(random)
namesre <- (names(mf)==crandom[length(crandom)])
oldid <- mf[,namesre]
freqsub<-table(oldid)
namesre <- names(freqsub)
nsubject <- length(namesre)
newid <- seq(1,nrec)
for(i in 1:nsubject)
{
newid[oldid==namesre[i]] <- i
}
maxni <- max(freqsub)
idrec <- seq(1,nrec)
datastr <- matrix(0,nrow=nsubject,ncol=maxni+1)
datastr[,1] <- freqsub
for(i in 1:nsubject)
{
for(j in 1:freqsub[i])
{
datastr[i,(j+1)] <- idrec[newid==i][j]
}
}
#########################################################################################
# model structure
#########################################################################################
q <- length(crandom)
z <- matrix(1,nrow=nrec,ncol=1)
colnames(z) <- "(Intercept)"
nvarrand <- "(Intercept)"
if(q>1)
{
for(i in 1:(q-1))
{
zwork <- (names(mf)==crandom[i])
zwork <- matrix(mf[,zwork],nrow=nrec,ncol=1)
colnames(zwork) <- crandom[i]
nvarrand <- c(nvarrand,crandom[i])
z <- cbind(z,zwork)
}
}
cfixed <- all.vars(fixed)
cfixed <- cfixed[-1]
for(i in 1:q)
{
if(sum(nvarrand[i]==cfixed) != 0)
{
stop("Covariates cannot be included in the random and fixed part of the model")
}
}
x <- model.matrix(fixed,data=mf)
p <- dim(x)[2]
x <- x[,-1]
p <- p-1
nfixed <- p
if(p==0)
{
nfixed <- 0
p <- 1
x <- matrix(0,nrow=nrec,ncol=1)
}
xtx <- t(x)%*%x
#########################################################################################
# elements for Pseudo Countour Probabilities' computation
#########################################################################################
possiP <- NULL
if(nfixed>0)
{
mat <- attr(Terms,"factors")
namfact <- colnames(mat)
nvar <- dim(mat)[1]
nfact <- dim(mat)[2]
possiP <- matrix(0,ncol=2,nrow=nfact)
if (missing(data)) dataF <- model.frame(formula=fixed,xlev=NULL)
dataF <- model.frame(formula=fixed,data,xlev=NULL)
namD <- names(dataF)
isF <- sapply(dataF, function(x) is.factor(x) || is.logical(x))
nlevel <- rep(0,nvar)
for(i in 1:nvar)
{
if(isF[i])
{
nlevel[i]<-length(table(dataF[[i]]))
}
else
{
nlevel[i]<-1
}
}
startp<-1+q
for(i in 1:nfact)
{
tmp1<-1
for(j in 1:nvar)
{
if(mat[j,i]==1 && isF[j])
{
tmp1<-tmp1*(nlevel[j]-1)
}
}
endp<-startp+tmp1-1
possiP[i,1]<-startp
possiP[i,2]<-endp
startp<-endp+1
}
dimnames(possiP)<-list(namfact,c("Start","End"))
}
#########################################################################################
# prior information
#########################################################################################
if(nfixed==0)
{
prec <- matrix(0,nrow=1,ncol=1)
sb <- matrix(0,nrow=1,ncol=1)
}
else
{
b0 <- prior$beta0
prec <- solve(prior$Sbeta0)
sb <- prec%*%b0
if(length(b0)!=p)
{
stop("Error in the dimension of the mean of the normal prior for the fixed effects.\n")
}
if(dim(prec)[1]!=p || dim(prec)[2]!=p)
{
stop("Error in the dimension of the covariance of the normal prior for the fixed effects.\n")
}
}
nu0 <- prior$nu0
if(nu0<=0)
{
stop("The parameter of the IW prior distribution for the normal kernel must be positive")
}
tinv <- prior$tinv
if(dim(tinv)[1]!=q || dim(tinv)[2]!=q)
{
stop("Error in the dimension of the matrix of the IW prior for the covariance of the normal kernel.\n")
}
if(is.null(prior$a0))
{
a0b0 <- c(-10,-10)
alpha <- prior$alpha
alphapr <- 0
}
else
{
a0b0 <- c(prior$a0,prior$b0)
alpha <- rgamma(1,shape=prior$a0,scale=prior$b0)
alphapr <- 1
if(prior$a0<0 || prior$b0<0)
{
stop("The parameters of the Gamma prior for the precision parameter must be possitive.\n")
}
}
psiinv <- solve(prior$Sb)
smu <- psiinv%*%prior$mb
if(length(prior$mb) != q)
{
stop("Error in the dimension of the mean of the normal prior for the mean of the centering distribution.\n")
}
if(is.null(dim(psiinv)) && q==1)
{
stop("Error in the dimension of the covariance of the normal prior for the mean of the centering distribution.\n")
}
if(!is.null(dim(psiinv)) && ( dim(psiinv)[1]!=q || dim(psiinv)[2]!=q ))
{
stop("Error in the dimension of the covariance of the normal prior for the mean of the centering distribution.\n")
}
nub<-prior$nub
if(nub<=0)
{
stop("The parameter of the IW prior for the covariance of the centering distribution must be positive")
}
tbinv <- prior$tbinv
if(dim(tbinv)[1]!=q || dim(tbinv)[2]!=q)
{
stop("Error in the dimension of the matrix of the IW prior for the covariance of the centering distribution.\n")
}
nu <- c(prior$nu0,prior$nub)
#########################################################################################
# mcmc specification
#########################################################################################
if(missing(mcmc))
{
nburn <- 1000
nsave <- 1000
nskip <- 0
ndisplay <- 100
mcmcvec<-c(nburn,nskip,ndisplay)
}
else
{
mcmcvec<-c(mcmc$nburn,mcmc$nskip,mcmc$ndisplay)
nsave<-mcmc$nsave
}
#########################################################################################
# output
#########################################################################################
nuniq<-q*(q+1)
mc<-rep(0,5)
musave<-matrix(0,nrow=nsave,ncol=q*nsubject)
clustsave<-matrix(0,nrow=nsave,ncol=nsubject)
randsave<-matrix(0,nrow=nsave,ncol=q*(nsubject+1))
thetasave<-matrix(0,nrow=nsave,ncol=q+nfixed+q+nuniq+2+ncateg-2)
cpo<-matrix(0,nrow=nrec,ncol=2)
#########################################################################################
# MLE estimation
#########################################################################################
MLEordprobit<-function(x,y,p,ncateg,nrec)
{
fn<-function(theta)
{
eta<-x%*%theta[1:p]
cutoff<-c(0,theta[(p+1):(p+ncateg-2)])
cc<-cumsum(c(cutoff[1], exp(cutoff[-1])))
cutoff<-c(-100,cc,100)
like <- pnorm(cutoff[y+1] - eta) - pnorm(cutoff[y] - eta)
if (all(like > 0))
eval<- -sum(log(like))
else eval<-Inf
return(eval)
}
z<-rep(0,nrec)
for(i in 1:nrec)
{
if(y[i]==1)
{
z[i]<-0
}
else
{
z[i]<-1
}
}
start<-coefficients(glm.fit(x, z, family= binomial(probit)))
start<-c(start,seq(ncateg-2)/(ncateg-2))
foo<-optim(start,fn=fn,method="BFGS",hessian=TRUE)
out<-NULL
out$beta<-foo$par
out$stderr<-sqrt(diag(-solve(-foo$hessian)))
out$covb<-(-solve(-foo$hessian))
return(out)
}
#########################################################################################
# parameters depending on status
#########################################################################################
if(status==TRUE)
{
wsigma <- prior$tinv/(prior$nu0-q-1)
wsigma2 <- prior$tbinv/(prior$nub-q-1)
bzs<-NULL
bzsb<-NULL
for(i in 1:q)
{
work<-rnorm(nsubject,mean=0,sd=sqrt(wsigma[i,i]))
bzs<-cbind(bzs,work)
work<-rnorm(nsubject,mean=0,sd=sqrt(wsigma2[i,i]))
bzsb<-cbind(bzsb,work)
}
if(nfixed==0)
{
beta<-matrix(0,nrow=1,ncol=1)
fit0<- MLEordprobit(z,yr,q,ncateg,nrec)
b<-matrix(0,nrow=nsubject,ncol=q)
mu<-bzsb
for(i in 1:nsubject){
b[i,]<-fit0$beta[1:q]+bzs[i,]
}
sigma <- prior$tinv/(prior$nu0-q-1)
sigmainv <- solve(sigma)
sigmab <- prior$tbinv/(prior$nub-q-1)
sigmabinv <- solve(sigmab)
cutoff<-c(0,fit0$beta[(q+1):(q+ncateg-2)])
cutoff<-cumsum(c(cutoff[1], exp(cutoff[-1])))
}
if(nfixed>0)
{
fit0<- MLEordprobit(cbind(x,z),yr,(p+q),ncateg,nrec)
b<-matrix(0,nrow=nsubject,ncol=q)
beta<-fit0$beta[1:p]
mu<-bzsb
for(i in 1:nsubject){
b[i,]<-fit0$beta[(p+1):(p+q)]+bzs[i,]
}
sigma <- prior$tinv/(prior$nu0-q-1)
sigmainv <- solve(sigma)
sigmab <- prior$tbinv/(prior$nub-q-1)
sigmabinv <- solve(sigmab)
cutoff<-c(0,fit0$beta[(p+q+1):(p+q+ncateg-2)])
cutoff<-cumsum(c(cutoff[1], exp(cutoff[-1])))
}
betar<-rep(0,q)
mub<-rep(0,q)
ncluster<-nsubject
ss<-seq(1,nsubject)
}
if(status==FALSE)
{
alpha<-state$alpha
b<-state$b
if(nfixed>0)
{
beta<-state$beta
}
else
{
beta<-rep(0,p)
}
cutoff<-state$cutoff
mu<-state$mu
mub<-state$mub
ncluster<-state$ncluster
sigma<-state$sigma
sigmab<-state$sigmab
sigmainv<-solve(sigma)
sigmabinv<-solve(sigmab)
ss<-state$ss
betar<-rep(0,q)
}
#########################################################################################
# working space
#########################################################################################
iflagp<-rep(0,p)
iflagr<-rep(0,q)
prob<-rep(0,nsubject+1)
quadf<-matrix(0,nrow=q,ncol=q)
seed1<-sample(1:29000,1)
seed2<-sample(1:29000,1)
seed<-c(seed1,seed2)
theta<-rep(0,q)
workmhp<-rep(0,p*(p+1)/2)
workmp<-matrix(0,nrow=p,ncol=p)
workvp<-rep(0,p)
xty<-rep(0,p)
workmhr<-rep(0,q*(q+1)/2)
workmhr2<-rep(0,q*(q+1)/2)
workmr<-matrix(0,nrow=q,ncol=q)
workvr<-rep(0,q)
zty<-rep(0,q)
ztz<-matrix(0,nrow=q,ncol=q)
cstrt<-matrix(0,nrow=nsubject,ncol=nsubject)
ccluster<-rep(0,nsubject)
y<-rep(0,nrec)
betasave<-rep(0,(p+ncateg-1))
bsave<-matrix(0,nrow=nsubject,ncol=q)
#########################################################################################
# calling the fortran code
#########################################################################################
foo <- .Fortran("dpmolmmp",
maxni =as.integer(maxni),
nrec =as.integer(nrec),
ncateg =as.integer(ncateg),
nsubject =as.integer(nsubject),
nfixed =as.integer(nfixed),
p =as.integer(p),
q =as.integer(q),
subject =as.integer(newid),
datastr =as.integer(datastr),
yr =as.integer(yr),
x =as.double(x),
z =as.double(z),
xtx =as.double(xtx),
a0b0 =as.double(a0b0),
prec =as.double(prec),
sb =as.double(sb),
nu =as.integer(nu),
tinv1 =as.double(tinv),
smu =as.double(smu),
psiinv =as.double(psiinv),
tinv2 =as.double(tbinv),
mcmc =as.integer(mcmcvec),
nsave =as.integer(nsave),
cutoff =as.double(cutoff),
ncluster =as.integer(ncluster),
ss =as.integer(ss),
alpha =as.double(alpha),
beta =as.double(beta),
b =as.double(b),
betar =as.double(betar),
mu =as.double(mu),
sigma =as.double(sigma),
sigmainv =as.double(sigmainv),
mub =as.double(mub),
sigmab =as.double(sigmab),
sigmabinv =as.double(sigmabinv),
y =as.double(y),
mc =as.double(mc),
cpo =as.double(cpo),
randsave =as.double(randsave),
thetasave =as.double(thetasave),
musave =as.double(musave),
clustsave =as.integer(clustsave),
iflagp =as.integer(iflagp),
workmhp =as.double(workmhp),
workmp =as.double(workmp),
workvp =as.double(workvp),
xty =as.double(xty),
iflagr =as.integer(iflagr),
theta =as.double(theta),
workmhr =as.double(workmhr),
workmhr2 =as.double(workmhr2),
workmr =as.double(workmr),
workvr =as.double(workvr),
ztz =as.double(ztz),
zty =as.double(zty),
cstrt =as.integer(cstrt),
ccluster =as.integer(ccluster),
prob =as.double(prob),
quadf =as.double(quadf),
seed =as.integer(seed),
betasave =as.double(betasave),
bsave =as.double(bsave),
PACKAGE ="DPpackage")
#########################################################################################
# save state
#########################################################################################
dimen<-q+nfixed+q+nuniq+2+ncateg-2
mc<-foo$mc
names(mc)<-c("Dbar", "Dhat", "pD", "DIC","LPML")
thetasave<-matrix(foo$thetasave,nrow=nsave, ncol=dimen)
randsave<-matrix(foo$randsave,nrow=nsave, ncol=q*(nsubject+1))
musave<-matrix(foo$musave,nrow=nsave,ncol=q*nsubject)
clustsave<-matrix(foo$clustsave,nrow=nsave,ncol=nsubject)
cpom<-matrix(foo$cpo,nrow=nrec,ncol=2)
cpo<-cpom[,1]
fso<-cpom[,2]
if(nfixed==0)
{
pnames1 <- colnames(z)
}
if(nfixed==1)
{
pnames1 <- c(colnames(z),cfixed)
}
if(nfixed>1)
{
pnames1 <- c(colnames(z),colnames(x))
}
pnames2 <- NULL
for(i in 1:q)
{
for(j in i:q)
{
if(i==j) aa <-paste("sigma",colnames(z)[i],sep="-")
if(i!=j) aa <-paste("sigma",colnames(z)[i],colnames(z)[j],sep="-")
pnames2<-c(pnames2,aa)
}
}
pnames3 <- paste("mub",colnames(z),sep="-")
pnames4<-NULL
for(i in 1:q)
{
for(j in i:q)
{
if(i==j) aa <-paste("sigmab",colnames(z)[i],sep="-")
if(i!=j) aa <-paste("sigmab",colnames(z)[i],colnames(z)[j],sep="-")
pnames4<-c(pnames4,aa)
}
}
pnames5<-paste("cutoff",2:(ncateg-1))
pnames6<- c("ncluster","alpha")
colnames(thetasave)<-c(pnames1,pnames2,pnames3,pnames4,pnames5,pnames6)
qnames <- NULL
for(i in 1:nsubject)
{
for(j in 1:q)
{
idname <- paste("(Subject",namesre[i],sep="=")
idname <- paste(idname,")")
qnamestemp <- paste(colnames(z)[j],idname,sep=" ")
qnames <- c(qnames,qnamestemp)
}
}
for(j in 1:q)
{
qnamestemp <- paste("pred",colnames(z)[j],sep="-")
qnames <- c(qnames,qnamestemp)
}
colnames(randsave) <- qnames
model.name<-"Bayesian semiparametric ordinal linear mixed effect model"
coeff<-apply(thetasave, 2, mean)
state <- list(alpha=foo$alpha,
b=matrix(foo$b,nrow=nsubject,ncol=q),
beta=foo$beta,
cutoff=foo$cutoff,
mu=matrix(foo$mu,nrow=nsubject,ncol=q),
mub=foo$mub,
ncluster=foo$ncluster,
sigma=matrix(foo$sigma,nrow=q,ncol=q),
sigmab=matrix(foo$sigmab,nrow=q,ncol=q),
ss=foo$ss)
save.state <- list(thetasave=thetasave,
randsave=randsave,
musave=musave,
clustsave=clustsave)
z<-list(modelname=model.name,
coefficients=coeff,call=cl,
prior=prior,
mcmc=mcmc,
state=state,
save.state=save.state,
nrec=foo$nrec,
nsubject=foo$nsubject,
nfixed=foo$nfixed,
nrandom=foo$q,
cpo=cpo,
fso=fso,
alphapr=alphapr,
namesre1=namesre,
namesre2=colnames(z),
z=z,
x=x,
mf=mf,
dimen=dimen,
ncateg=ncateg,
nsave=nsave,
y=resp,
possiP=possiP,
fixed=fixed,
mc=mc)
cat("\n\n")
class(z)<-c("DPMolmm")
return(z)
}
###
### Tools for DPMolmm: anova, print, summary, plot
###
### Copyright: Alejandro Jara, 2006-2007
### Last modification: 19-04-2007.
"anova.DPMolmm"<-function(object, ...)
{
######################################################################################
cregion<-function(x,probs=c(0.90,0.975))
######################################################################################
# Function to compute a simultaneous credible region for a vector
# parameter from the MCMC sample
#
# Reference: Besag, J., Green, P., Higdon, D. and Mengersen, K. (1995)
# Bayesian computation and stochastic systems (with Discussion)
# Statistical Science, vol. 10, 3 - 66, page 30
# and Held, L. (2004) Simultaneous inference in risk assessment; a Bayesian
# perspective In: COMPSTAT 2004, Proceedings in Computational
# Statistics (J. Antoch, Ed.) 213 - 222, page 214
#
# Arguments
# sample : a data frame or matrix with sampled values (one column = one parameter).
# probs : probabilities for which the credible regions are computed.
######################################################################################
{
#Basic information
nmonte<-dim(x)[1]
p<-dim(x)[2]
#Ranks for each component
ranks <- apply(x, 2, rank, ties.method="first")
#Compute the set S={max(nmonte+1-min r_i(t) , max r_i(t)): t=1,..,nmonte}
left <- nmonte + 1 - apply(ranks, 1, min)
right <- apply(ranks, 1, max)
S <- apply(cbind(left, right), 1, max)
S <- S[order(S)]
#Compute the credible region
k <- floor(nmonte*probs)
tstar <- S[k]
out<-list()
for(i in 1:length(tstar))
{
upelim <- x[ranks == tstar[i]]
lowlim <- x[ranks == nmonte + 1 - tstar[i]]
out[[i]] <- rbind(lowlim, upelim)
rownames(out[[i]]) <- c("Lower", "Upper")
colnames(out[[i]]) <- colnames(x)
}
names(out) <- paste(probs)
return(out)
}
######################################################################################
cint<-function(x,probs=c(0.90,0.975))
######################################################################################
# Function to compute a credible interval from the MCMC sample
#
# Arguments
# sample : a data frame or matrix with sampled values (one column = one parameter).
# probs : probabilities for which the credible regions are to be computed.
######################################################################################
{
#Compute the credible interval
delta<-(1-probs)/2
lprobs<-cbind(delta,probs+delta)
out<-matrix(quantile(x,probs=lprobs),ncol=2)
colnames(out) <- c("Lower","Upper")
rownames(out) <- paste(probs)
return(out)
}
######################################################################################
hnulleval<-function(mat,hnull)
######################################################################################
# Evaluate H0
# AJV, 2006
######################################################################################
{
npar<-dim(mat)[2]
lower<-rep(0,npar)
upper<-rep(0,npar)
for(i in 1:npar)
{
lower[i]<-mat[1,i]< hnull[i]
upper[i]<-mat[2,i]> hnull[i]
}
total<-lower+upper
out<-(sum(total==2) == npar)
return(out)
}
######################################################################################
hnulleval2<-function(vec,hnull)
######################################################################################
# Evaluate H0
# AJV, 2006
######################################################################################
{
lower<-vec[1]< hnull
upper<-vec[2]> hnull
total<-lower+upper
out<-(total==2)
return(out)
}
######################################################################################
pcp<-function(x,hnull=NULL,precision=0.001,prob=0.95,digits=digits)
######################################################################################
# Function to compute Pseudo Countour Probabilities (Region)
# AJV, 2006
######################################################################################
{
if(is.null(hnull))hnull<-rep(0,dim(x)[2])
if (dim(x)[2]!=length(hnull)) stop("Dimension of x and hnull must be equal!!")
probs <- seq(precision, 1-precision, by=precision)
neval <- length(probs)
probsf <- c(prob,probs)
cr <- cregion(x,probs=probsf)
is.hnull <- hnulleval(cr[[2]],hnull)
if(is.hnull)
{
pval <- 1-precision
}
else
{
is.hnull <- hnulleval(cr[[length(cr)]],hnull)
if (!is.hnull)
{
pval <- precision
}
else
{
is.hnull<-rep(0,neval+1)
for(i in 1:(neval+1))
{
is.hnull[i] <- hnulleval(cr[[i]],hnull)
}
is.hnull <- is.hnull[-1]
first <- neval - sum(is.hnull) + 1
pval <- 1 - probs[first]
}
}
output <- list(cr=cr[[1]], prob=prob, pval=pval,hnull=hnull)
return(output)
}
######################################################################################
pcp2<-function(x,hnull=NULL,precision=0.001,prob=0.95)
######################################################################################
# Function to compute Pseudo Countour Probabilities (Interval)
# AJV, 2006
######################################################################################
{
if(is.null(hnull))hnull<-0
probs <- seq(precision, 1-precision, by=precision)
neval <- length(probs)
probsf <- c(prob,probs)
cr <- cint(x,probs=probsf)
is.hnull <- hnulleval2(cr[2,],hnull)
if(is.hnull)
{
pval <- 1-precision
}
else
{
is.hnull <- hnulleval2(cr[(neval+1),],hnull)
if (!is.hnull)
{
pval <- precision
}
else
{
is.hnull<-rep(0,neval+1)
for(i in 1:(neval+1))
{
is.hnull[i] <- hnulleval2(cr[i,],hnull)
}
is.hnull <- is.hnull[-1]
first <- neval - sum(is.hnull) + 1
pval <- 1-probs[first]
}
}
output <- list(cr=cr[1,], prob=prob, pval=pval,hnull=hnull)
return(output)
}
######################################################################################
######################################################################################
######################################################################################
if(object$nfixed>0)
{
possiP<-object$possiP
nfact<-dim(possiP)[1]
P<-rep(0,nfact)
df<-rep(0,nfact)
for(i in 1:nfact)
{
df[i]<-1
if((possiP[i,2]-possiP[i,1])>0)
{
x<-matrix(object$save.state$thetasave[,possiP[i,1]:possiP[i,2]])
foo<-pcp(x=x)
P[i]<-foo$pval
df[i]<-(possiP[i,2]-possiP[i,1])+1
}
else
{
x<-object$save.state$thetasave[,possiP[i,1]:possiP[i,2]]
foo<-pcp2(x=x)
P[i]<-foo$pval
}
}
table <- data.frame(df,P)
dimnames(table) <- list(rownames(possiP), c("Df","PsCP"))
structure(table, heading = c("Table of Pseudo Contour Probabilities\n",
paste("Response:", deparse(formula(object$fixed)[[2]]))), class = c("anovaPsCP",
"data.frame"))
}
}
"print.DPMolmm"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
if (length(x$coefficients)) {
cat("Posterior Inference of Parameters:\n")
if(x$alphapr==1){
print.default(format(x$coefficients, digits = digits), print.gap = 2,
quote = FALSE)}
if(x$alphapr==0){
print.default(format(x$coefficients[1:(length(x$coefficients)-1)], digits = digits), print.gap = 2,
quote = FALSE)}
}
else cat("No coefficients\n")
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Groups:",x$nsubject,"\n")
cat("\n\n")
invisible(x)
}
"summary.DPMolmm"<-function(object, hpd=TRUE, ...)
{
stde<-function(x)
{
n<-length(x)
return(sd(x)/sqrt(n))
}
hpdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[1],a$aupp[1]))
}
pdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[2],a$aupp[2]))
}
#nsave<-object$nsave
#dimen<-length(object$coefficients)
#thetasave<-matrix(object$save.state$thetasave,nrow=nsave, ncol=dimen)
thetasave<-object$save.state$thetasave
### Fixed part of the model
dimen1<-object$nrandom+object$nfixed
if(dimen1==1)
{
mat<-matrix(thetasave[,1:dimen1],ncol=1)
}
else
{
mat<-thetasave[,1:dimen1]
}
coef.p<-object$coefficients[1:dimen1]
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans <- c(object[c("call", "modelname")])
ans$coefficients<-coef.table
### Kernel variance
dimen2<-object$nrandom*(object$nrandom+1)/2
if(dimen2==1)
{
mat<-matrix(thetasave[,(dimen1+1):(dimen1+dimen2)],ncol=1)
}
else
{
mat<-thetasave[,(dimen1+1):(dimen1+dimen2)]
}
coef.p<-object$coefficients[(dimen1+1):(dimen1+dimen2)]
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd)
{
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$kernel<-coef.table
### CPO
ans$cpo<-object$cpo
### Baseline Information
dimen3<-object$nrandom+object$nrandom*(object$nrandom+1)/2
if(dimen3==1)
{
mat<-matrix(thetasave[,(dimen1+dimen2+1):(dimen1+dimen2+dimen3)],ncol=1)
}
else
{
mat<-thetasave[,(dimen1+dimen2+1):(dimen1+dimen2+dimen3)]
}
coef.p<-object$coefficients[(dimen1+dimen2+1):(dimen1+dimen2+dimen3)]
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$base<-coef.table
### Cutoff Points
dimen4<-object$ncateg-2
if(dimen4==1)
{
mat<-matrix(thetasave[,(dimen1+dimen2+dimen3+1):(dimen1+dimen2+dimen3+dimen4)],ncol=1)
}
else
{
mat<-thetasave[,(dimen1+dimen2+dimen3+1):(dimen1+dimen2+dimen3+dimen4)]
}
coef.p<-object$coefficients[(dimen1+dimen2+dimen3+1):(dimen1+dimen2+dimen3+dimen4)]
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$cutoff<-coef.table
### Precision parameter
if(is.null(object$prior$a0))
{
dimen5<-1
coef.p<-object$coefficients[(dimen1+dimen2+dimen3+dimen4+1)]
mat<-matrix(thetasave[,(dimen1+dimen2+dimen3+dimen4+1):(dimen1+dimen2+dimen3+dimen4+1)],ncol=1)
}
else
{
dimen5<-2
coef.p<-object$coefficients[(dimen1+dimen2+dimen3+dimen4+1):length(object$coefficients)]
mat<-thetasave[,(dimen1+dimen2+dimen3+dimen4+1):(dimen1+dimen2+dimen3+dimen4+dimen5)]
}
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$prec<-coef.table
coef.table<-matrix(object$mc,nrow=1,ncol=5)
dimnames(coef.table) <- list(" ", c("Dbar", "Dhat", "pD", "DIC","LPML"))
ans$mc<-coef.table
ans$nrec<-object$nrec
ans$nsubject<-object$nsubject
class(ans) <- "summaryDPMolmm"
return(ans)
}
"print.summaryDPMolmm"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(x$cpo)), digits = digits), print.gap = 2,
quote = FALSE)
cat("\nModel's performance:\n")
print.default(format(x$mc, digits = digits), print.gap = 2,
quote = FALSE)
if (length(x$coefficients)) {
cat("\nRegression coefficients:\n")
print.default(format(x$coefficients, digits = digits), print.gap = 2,
quote = FALSE)
}
else cat("No coefficients\n")
cat("\nThreshold:\n")
print.default(format(x$cutoff, digits = digits), print.gap = 2,
quote = FALSE)
cat("\nKernel variance:\n")
print.default(format(x$kernel, digits = digits), print.gap = 2,
quote = FALSE)
if (length(x$base)) {
cat("\nBaseline distribution:\n")
print.default(format(x$base, digits = digits), print.gap = 2,
quote = FALSE)
}
else cat("No baseline parameters\n")
if (length(x$prec)) {
cat("\nPrecision parameter:\n")
print.default(format(x$prec, digits = digits), print.gap = 2,
quote = FALSE)
}
else cat("No precision parameter\n")
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Groups:",x$nsubject,"\n")
cat("\n\n")
invisible(x)
}
"plot.DPMolmm"<-function(x, hpd=TRUE, ask=TRUE, nfigr=2, nfigc=2, param=NULL, col="#bdfcc9", ...)
{
fancydensplot1<-function(x, hpd=TRUE, npts=200, xlab="", ylab="", main="",col="#bdfcc9", ...)
# Author: AJV, 2006
#
{
dens <- density(x,n=npts)
densx <- dens$x
densy <- dens$y
meanvar <- mean(x)
densx1 <- max(densx[densx<=meanvar])
densx2 <- min(densx[densx>=meanvar])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ymean <- densy1 + ((densy2-densy1)/(densx2-densx1))*(meanvar-densx1)
if(hpd==TRUE)
{
alpha<-0.05
alow<-rep(0,2)
aupp<-rep(0,2)
n<-length(x)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(x),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
xlinf<-a$alow[1]
xlsup<-a$aupp[1]
}
else
{
xlinf <- quantile(x,0.025)
xlsup <- quantile(x,0.975)
}
densx1 <- max(densx[densx<=xlinf])
densx2 <- min(densx[densx>=xlinf])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylinf <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlinf-densx1)
densx1 <- max(densx[densx<=xlsup])
densx2 <- min(densx[densx>=xlsup])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylsup <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlsup-densx1)
plot(0.,0.,xlim = c(min(densx), max(densx)), ylim = c(min(densy), max(densy)),
axes = F,type = "n" , xlab=xlab, ylab=ylab, main=main, cex=1.2)
xpol<-c(xlinf,xlinf,densx[densx>=xlinf & densx <=xlsup],xlsup,xlsup)
ypol<-c(0,ylinf,densy[densx>=xlinf & densx <=xlsup] ,ylsup,0)
polygon(xpol, ypol, border = FALSE,col=col)
lines(c(min(densx), max(densx)),c(0,0),lwd=1.2)
segments(min(densx),0, min(densx),max(densy),lwd=1.2)
lines(densx,densy,lwd=1.2)
segments(meanvar, 0, meanvar, ymean,lwd=1.2)
segments(xlinf, 0, xlinf, ylinf,lwd=1.2)
segments(xlsup, 0, xlsup, ylsup,lwd=1.2)
axis(1., at = round(c(xlinf, meanvar,xlsup), 2.), labels = T,pos = 0.)
axis(1., at = round(seq(min(densx),max(densx),length=15), 2.), labels = F,pos = 0.)
axis(2., at = round(seq(0,max(densy),length=5), 2.), labels = T,pos =min(densx))
}
if(is(x, "DPMolmm"))
{
if(is.null(param))
{
coef.p<-x$coefficients
n<-length(coef.p)
pnames<-names(coef.p)
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr , ncol=nfigc ,byrow=TRUE))
for(i in 1:(n-1))
{
title1<-paste("Trace of",pnames[i],sep=" ")
title2<-paste("Density of",pnames[i],sep=" ")
plot(ts(x$save.state$thetasave[,i]),main=title1,xlab="MCMC scan",ylab=" ")
if(pnames[i]=="ncluster")
{
hist(x$save.state$thetasave[,i],main=title2,xlab="values", ylab="probability",probability=TRUE)
}
else
{
fancydensplot1(x$save.state$thetasave[,i],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
if(is.null(x$prior$a0))
{
cat("")
}
else
{
title1<-paste("Trace of",pnames[n],sep=" ")
title2<-paste("Density of",pnames[n],sep=" ")
plot(ts(x$save.state$thetasave[,n]),main=title1,xlab="MCMC scan",ylab=" ")
fancydensplot1(x$save.state$thetasave[,n],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
else
{
coef.p<-x$coefficients
n<-length(coef.p)
pnames<-names(coef.p)
poss<-0
for(i in 1:n)
{
if(pnames[i]==param)poss=i
}
if (poss==0)
{
stop("This parameter is not present in the original model.\n")
}
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr, ncol=nfigc, byrow = TRUE))
title1<-paste("Trace of",pnames[poss],sep=" ")
title2<-paste("Density of",pnames[poss],sep=" ")
plot(ts(x$save.state$thetasave[,poss]),main=title1,xlab="MCMC scan",ylab=" ")
if(param=="ncluster")
{
hist(x$save.state$thetasave[,poss],main=title2,xlab="values", ylab="probability",probability=TRUE)
}
else
{
fancydensplot1(x$save.state$thetasave[,poss],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
}
}
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### DPMolmm.R
### Fit a ordinal linear mixed model with a Dirichlet Process mixture of
### normals prior for the random effect distribution.
###
### Copyright: Alejandro Jara, 2006-2012.
###
### Last modification: 17-08-2009.
###
### This program is free software; you can redistribute it and/or modify
### it under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2 of the License, or (at
### your option) any later version.
###
### This program is distributed in the hope that it will be useful, but
### WITHOUT ANY WARRANTY; without even the implied warranty of
### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
### General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with this program; if not, write to the Free Software
### Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
###
### The author's contact information:
###
### Alejandro Jara
### Department of Statistics
### Facultad de Matematicas
### Pontificia Universidad Catolica de Chile
### Casilla 306, Correo 22
### Santiago
### Chile
### Voice: +56-2-3544506 URL : http://www.mat.puc.cl/~ajara
### Fax : +56-2-3547729 Email: atjara@uc.cl
###
"DPMolmm"<-
function(fixed,random,prior,mcmc,state,status,data=sys.frame(sys.parent()),na.action=na.fail)
UseMethod("DPMolmm")
"DPMolmm.default"<-
function(fixed,
random,
prior,
mcmc,
state,
status,
data=sys.frame(sys.parent()),
na.action=na.fail)
{
#########################################################################################
# call parameters
#########################################################################################
m <- mcall <- cl <- match.call()
nm <- names(m)[-1]
keep <- is.element(nm, c("data", "na.action"))
for (i in nm[!keep]) m[[i]] <- NULL
allvars <- c(all.vars(fixed), all.vars(random))
Terms <- if (missing(data))
terms(fixed)
else terms(fixed, data = data)
cl$fixed <- eval(fixed)
cl$random <- eval(random)
m$formula <- as.formula(paste("~", paste(allvars, collapse = "+")))
environment(m$formula) <- environment(fixed)
m$drop.unused.levels <- TRUE
m[[1]] <- as.name("model.frame")
mf <- eval.parent(m)
#########################################################################################
# data structure
#########################################################################################
nrec <- dim(mf)[1]
resp <- mf[,1]
if(!is.factor(resp)) stop("the response must be a factor")
categ<-levels(resp)
ncateg<-length(categ)
if(ncateg <= 2) stop("the response must have 3 or more levels")
yr <- unclass(resp)
if(min(yr)==0)yr<-yr+1
if(min(yr)>1)yr<-yr+min(yr)+1
categn<-seq(1,ncateg)
crandom <- all.vars(random)
namesre <- (names(mf)==crandom[length(crandom)])
oldid <- mf[,namesre]
freqsub<-table(oldid)
namesre <- names(freqsub)
nsubject <- length(namesre)
newid <- seq(1,nrec)
for(i in 1:nsubject)
{
newid[oldid==namesre[i]] <- i
}
maxni <- max(freqsub)
idrec <- seq(1,nrec)
datastr <- matrix(0,nrow=nsubject,ncol=maxni+1)
datastr[,1] <- freqsub
for(i in 1:nsubject)
{
for(j in 1:freqsub[i])
{
datastr[i,(j+1)] <- idrec[newid==i][j]
}
}
#########################################################################################
# model structure
#########################################################################################
q <- length(crandom)
z <- matrix(1,nrow=nrec,ncol=1)
colnames(z) <- "(Intercept)"
nvarrand <- "(Intercept)"
if(q>1)
{
for(i in 1:(q-1))
{
zwork <- (names(mf)==crandom[i])
zwork <- matrix(mf[,zwork],nrow=nrec,ncol=1)
colnames(zwork) <- crandom[i]
nvarrand <- c(nvarrand,crandom[i])
z <- cbind(z,zwork)
}
}
cfixed <- all.vars(fixed)
cfixed <- cfixed[-1]
for(i in 1:q)
{
if(sum(nvarrand[i]==cfixed) != 0)
{
stop("Covariates cannot be included in the random and fixed part of the model")
}
}
x <- model.matrix(fixed,data=mf)
p <- dim(x)[2]
x <- x[,-1]
p <- p-1
nfixed <- p
if(p==0)
{
nfixed <- 0
p <- 1
x <- matrix(0,nrow=nrec,ncol=1)
}
xtx <- t(x)%*%x
#########################################################################################
# elements for Pseudo Countour Probabilities' computation
#########################################################################################
possiP <- NULL
if(nfixed>0)
{
mat <- attr(Terms,"factors")
namfact <- colnames(mat)
nvar <- dim(mat)[1]
nfact <- dim(mat)[2]
possiP <- matrix(0,ncol=2,nrow=nfact)
if (missing(data)) dataF <- model.frame(formula=fixed,xlev=NULL)
dataF <- model.frame(formula=fixed,data,xlev=NULL)
namD <- names(dataF)
isF <- sapply(dataF, function(x) is.factor(x) || is.logical(x))
nlevel <- rep(0,nvar)
for(i in 1:nvar)
{
if(isF[i])
{
nlevel[i]<-length(table(dataF[[i]]))
}
else
{
nlevel[i]<-1
}
}
startp<-1+q
for(i in 1:nfact)
{
tmp1<-1
for(j in 1:nvar)
{
if(mat[j,i]==1 && isF[j])
{
tmp1<-tmp1*(nlevel[j]-1)
}
}
endp<-startp+tmp1-1
possiP[i,1]<-startp
possiP[i,2]<-endp
startp<-endp+1
}
dimnames(possiP)<-list(namfact,c("Start","End"))
}
#########################################################################################
# prior information
#########################################################################################
if(nfixed==0)
{
prec <- matrix(0,nrow=1,ncol=1)
sb <- matrix(0,nrow=1,ncol=1)
}
else
{
b0 <- prior$beta0
prec <- solve(prior$Sbeta0)
sb <- prec%*%b0
if(length(b0)!=p)
{
stop("Error in the dimension of the mean of the normal prior for the fixed effects.\n")
}
if(dim(prec)[1]!=p || dim(prec)[2]!=p)
{
stop("Error in the dimension of the covariance of the normal prior for the fixed effects.\n")
}
}
nu0 <- prior$nu0
if(nu0<=0)
{
stop("The parameter of the IW prior distribution for the normal kernel must be positive")
}
tinv <- prior$tinv
if(dim(tinv)[1]!=q || dim(tinv)[2]!=q)
{
stop("Error in the dimension of the matrix of the IW prior for the covariance of the normal kernel.\n")
}
if(is.null(prior$a0))
{
a0b0 <- c(-10,-10)
alpha <- prior$alpha
alphapr <- 0
}
else
{
a0b0 <- c(prior$a0,prior$b0)
alpha <- rgamma(1,shape=prior$a0,scale=prior$b0)
alphapr <- 1
if(prior$a0<0 || prior$b0<0)
{
stop("The parameters of the Gamma prior for the precision parameter must be possitive.\n")
}
}
psiinv <- solve(prior$Sb)
smu <- psiinv%*%prior$mb
if(length(prior$mb) != q)
{
stop("Error in the dimension of the mean of the normal prior for the mean of the centering distribution.\n")
}
if(is.null(dim(psiinv)) && q==1)
{
stop("Error in the dimension of the covariance of the normal prior for the mean of the centering distribution.\n")
}
if(!is.null(dim(psiinv)) && ( dim(psiinv)[1]!=q || dim(psiinv)[2]!=q ))
{
stop("Error in the dimension of the covariance of the normal prior for the mean of the centering distribution.\n")
}
nub<-prior$nub
if(nub<=0)
{
stop("The parameter of the IW prior for the covariance of the centering distribution must be positive")
}
tbinv <- prior$tbinv
if(dim(tbinv)[1]!=q || dim(tbinv)[2]!=q)
{
stop("Error in the dimension of the matrix of the IW prior for the covariance of the centering distribution.\n")
}
nu <- c(prior$nu0,prior$nub)
#########################################################################################
# mcmc specification
#########################################################################################
if(missing(mcmc))
{
nburn <- 1000
nsave <- 1000
nskip <- 0
ndisplay <- 100
mcmcvec<-c(nburn,nskip,ndisplay)
}
else
{
mcmcvec<-c(mcmc$nburn,mcmc$nskip,mcmc$ndisplay)
nsave<-mcmc$nsave
}
#########################################################################################
# output
#########################################################################################
nuniq<-q*(q+1)
mc<-rep(0,5)
musave<-matrix(0,nrow=nsave,ncol=q*nsubject)
clustsave<-matrix(0,nrow=nsave,ncol=nsubject)
randsave<-matrix(0,nrow=nsave,ncol=q*(nsubject+1))
thetasave<-matrix(0,nrow=nsave,ncol=q+nfixed+q+nuniq+2+ncateg-2)
cpo<-matrix(0,nrow=nrec,ncol=2)
#########################################################################################
# MLE estimation
#########################################################################################
MLEordprobit<-function(x,y,p,ncateg,nrec)
{
fn<-function(theta)
{
eta<-x%*%theta[1:p]
cutoff<-c(0,theta[(p+1):(p+ncateg-2)])
cc<-cumsum(c(cutoff[1], exp(cutoff[-1])))
cutoff<-c(-100,cc,100)
like <- pnorm(cutoff[y+1] - eta) - pnorm(cutoff[y] - eta)
if (all(like > 0))
eval<- -sum(log(like))
else eval<-Inf
return(eval)
}
z<-rep(0,nrec)
for(i in 1:nrec)
{
if(y[i]==1)
{
z[i]<-0
}
else
{
z[i]<-1
}
}
start<-coefficients(glm.fit(x, z, family= binomial(probit)))
start<-c(start,seq(ncateg-2)/(ncateg-2))
foo<-optim(start,fn=fn,method="BFGS",hessian=TRUE)
out<-NULL
out$beta<-foo$par
out$stderr<-sqrt(diag(-solve(-foo$hessian)))
out$covb<-(-solve(-foo$hessian))
return(out)
}
#########################################################################################
# parameters depending on status
#########################################################################################
if(status==TRUE)
{
wsigma <- prior$tinv/(prior$nu0-q-1)
wsigma2 <- prior$tbinv/(prior$nub-q-1)
bzs<-NULL
bzsb<-NULL
for(i in 1:q)
{
work<-rnorm(nsubject,mean=0,sd=sqrt(wsigma[i,i]))
bzs<-cbind(bzs,work)
work<-rnorm(nsubject,mean=0,sd=sqrt(wsigma2[i,i]))
bzsb<-cbind(bzsb,work)
}
if(nfixed==0)
{
beta<-matrix(0,nrow=1,ncol=1)
fit0<- MLEordprobit(z,yr,q,ncateg,nrec)
b<-matrix(0,nrow=nsubject,ncol=q)
mu<-bzsb
for(i in 1:nsubject){
b[i,]<-fit0$beta[1:q]+bzs[i,]
}
sigma <- prior$tinv/(prior$nu0-q-1)
sigmainv <- solve(sigma)
sigmab <- prior$tbinv/(prior$nub-q-1)
sigmabinv <- solve(sigmab)
cutoff<-c(0,fit0$beta[(q+1):(q+ncateg-2)])
cutoff<-cumsum(c(cutoff[1], exp(cutoff[-1])))
}
if(nfixed>0)
{
fit0<- MLEordprobit(cbind(x,z),yr,(p+q),ncateg,nrec)
b<-matrix(0,nrow=nsubject,ncol=q)
beta<-fit0$beta[1:p]
mu<-bzsb
for(i in 1:nsubject){
b[i,]<-fit0$beta[(p+1):(p+q)]+bzs[i,]
}
sigma <- prior$tinv/(prior$nu0-q-1)
sigmainv <- solve(sigma)
sigmab <- prior$tbinv/(prior$nub-q-1)
sigmabinv <- solve(sigmab)
cutoff<-c(0,fit0$beta[(p+q+1):(p+q+ncateg-2)])
cutoff<-cumsum(c(cutoff[1], exp(cutoff[-1])))
}
betar<-rep(0,q)
mub<-rep(0,q)
ncluster<-nsubject
ss<-seq(1,nsubject)
}
if(status==FALSE)
{
alpha<-state$alpha
b<-state$b
if(nfixed>0)
{
beta<-state$beta
}
else
{
beta<-rep(0,p)
}
cutoff<-state$cutoff
mu<-state$mu
mub<-state$mub
ncluster<-state$ncluster
sigma<-state$sigma
sigmab<-state$sigmab
sigmainv<-solve(sigma)
sigmabinv<-solve(sigmab)
ss<-state$ss
betar<-rep(0,q)
}
#########################################################################################
# working space
#########################################################################################
iflagp<-rep(0,p)
iflagr<-rep(0,q)
prob<-rep(0,nsubject+1)
quadf<-matrix(0,nrow=q,ncol=q)
seed1<-sample(1:29000,1)
seed2<-sample(1:29000,1)
seed<-c(seed1,seed2)
theta<-rep(0,q)
workmhp<-rep(0,p*(p+1)/2)
workmp<-matrix(0,nrow=p,ncol=p)
workvp<-rep(0,p)
xty<-rep(0,p)
workmhr<-rep(0,q*(q+1)/2)
workmhr2<-rep(0,q*(q+1)/2)
workmr<-matrix(0,nrow=q,ncol=q)
workvr<-rep(0,q)
zty<-rep(0,q)
ztz<-matrix(0,nrow=q,ncol=q)
cstrt<-matrix(0,nrow=nsubject,ncol=nsubject)
ccluster<-rep(0,nsubject)
y<-rep(0,nrec)
betasave<-rep(0,(p+ncateg-1))
bsave<-matrix(0,nrow=nsubject,ncol=q)
#########################################################################################
# calling the fortran code
#########################################################################################
foo <- .Fortran("dpmolmmp",
maxni =as.integer(maxni),
nrec =as.integer(nrec),
ncateg =as.integer(ncateg),
nsubject =as.integer(nsubject),
nfixed =as.integer(nfixed),
p =as.integer(p),
q =as.integer(q),
subject =as.integer(newid),
datastr =as.integer(datastr),
yr =as.integer(yr),
x =as.double(x),
z =as.double(z),
xtx =as.double(xtx),
a0b0 =as.double(a0b0),
prec =as.double(prec),
sb =as.double(sb),
nu =as.integer(nu),
tinv1 =as.double(tinv),
smu =as.double(smu),
psiinv =as.double(psiinv),
tinv2 =as.double(tbinv),
mcmc =as.integer(mcmcvec),
nsave =as.integer(nsave),
cutoff =as.double(cutoff),
ncluster =as.integer(ncluster),
ss =as.integer(ss),
alpha =as.double(alpha),
beta =as.double(beta),
b =as.double(b),
betar =as.double(betar),
mu =as.double(mu),
sigma =as.double(sigma),
sigmainv =as.double(sigmainv),
mub =as.double(mub),
sigmab =as.double(sigmab),
sigmabinv =as.double(sigmabinv),
y =as.double(y),
mc =as.double(mc),
cpo =as.double(cpo),
randsave =as.double(randsave),
thetasave =as.double(thetasave),
musave =as.double(musave),
clustsave =as.integer(clustsave),
iflagp =as.integer(iflagp),
workmhp =as.double(workmhp),
workmp =as.double(workmp),
workvp =as.double(workvp),
xty =as.double(xty),
iflagr =as.integer(iflagr),
theta =as.double(theta),
workmhr =as.double(workmhr),
workmhr2 =as.double(workmhr2),
workmr =as.double(workmr),
workvr =as.double(workvr),
ztz =as.double(ztz),
zty =as.double(zty),
cstrt =as.integer(cstrt),
ccluster =as.integer(ccluster),
prob =as.double(prob),
quadf =as.double(quadf),
seed =as.integer(seed),
betasave =as.double(betasave),
bsave =as.double(bsave),
PACKAGE ="DPpackage")
#########################################################################################
# save state
#########################################################################################
dimen<-q+nfixed+q+nuniq+2+ncateg-2
mc<-foo$mc
names(mc)<-c("Dbar", "Dhat", "pD", "DIC","LPML")
thetasave<-matrix(foo$thetasave,nrow=nsave, ncol=dimen)
randsave<-matrix(foo$randsave,nrow=nsave, ncol=q*(nsubject+1))
musave<-matrix(foo$musave,nrow=nsave,ncol=q*nsubject)
clustsave<-matrix(foo$clustsave,nrow=nsave,ncol=nsubject)
cpom<-matrix(foo$cpo,nrow=nrec,ncol=2)
cpo<-cpom[,1]
fso<-cpom[,2]
if(nfixed==0)
{
pnames1 <- colnames(z)
}
if(nfixed==1)
{
pnames1 <- c(colnames(z),cfixed)
}
if(nfixed>1)
{
pnames1 <- c(colnames(z),colnames(x))
}
pnames2 <- NULL
for(i in 1:q)
{
for(j in i:q)
{
if(i==j) aa <-paste("sigma",colnames(z)[i],sep="-")
if(i!=j) aa <-paste("sigma",colnames(z)[i],colnames(z)[j],sep="-")
pnames2<-c(pnames2,aa)
}
}
pnames3 <- paste("mub",colnames(z),sep="-")
pnames4<-NULL
for(i in 1:q)
{
for(j in i:q)
{
if(i==j) aa <-paste("sigmab",colnames(z)[i],sep="-")
if(i!=j) aa <-paste("sigmab",colnames(z)[i],colnames(z)[j],sep="-")
pnames4<-c(pnames4,aa)
}
}
pnames5<-paste("cutoff",2:(ncateg-1))
pnames6<- c("ncluster","alpha")
colnames(thetasave)<-c(pnames1,pnames2,pnames3,pnames4,pnames5,pnames6)
qnames <- NULL
for(i in 1:nsubject)
{
for(j in 1:q)
{
idname <- paste("(Subject",namesre[i],sep="=")
idname <- paste(idname,")")
qnamestemp <- paste(colnames(z)[j],idname,sep=" ")
qnames <- c(qnames,qnamestemp)
}
}
for(j in 1:q)
{
qnamestemp <- paste("pred",colnames(z)[j],sep="-")
qnames <- c(qnames,qnamestemp)
}
colnames(randsave) <- qnames
model.name<-"Bayesian semiparametric ordinal linear mixed effect model"
coeff<-apply(thetasave, 2, mean)
state <- list(alpha=foo$alpha,
b=matrix(foo$b,nrow=nsubject,ncol=q),
beta=foo$beta,
cutoff=foo$cutoff,
mu=matrix(foo$mu,nrow=nsubject,ncol=q),
mub=foo$mub,
ncluster=foo$ncluster,
sigma=matrix(foo$sigma,nrow=q,ncol=q),
sigmab=matrix(foo$sigmab,nrow=q,ncol=q),
ss=foo$ss)
save.state <- list(thetasave=thetasave,
randsave=randsave,
musave=musave,
clustsave=clustsave)
z<-list(modelname=model.name,
coefficients=coeff,call=cl,
prior=prior,
mcmc=mcmc,
state=state,
save.state=save.state,
nrec=foo$nrec,
nsubject=foo$nsubject,
nfixed=foo$nfixed,
nrandom=foo$q,
cpo=cpo,
fso=fso,
alphapr=alphapr,
namesre1=namesre,
namesre2=colnames(z),
z=z,
x=x,
mf=mf,
dimen=dimen,
ncateg=ncateg,
nsave=nsave,
y=resp,
possiP=possiP,
fixed=fixed,
mc=mc)
cat("\n\n")
class(z)<-c("DPMolmm")
return(z)
}
###
### Tools for DPMolmm: anova, print, summary, plot
###
### Copyright: Alejandro Jara, 2006-2007
### Last modification: 19-04-2007.
"anova.DPMolmm"<-function(object, ...)
{
######################################################################################
cregion<-function(x,probs=c(0.90,0.975))
######################################################################################
# Function to compute a simultaneous credible region for a vector
# parameter from the MCMC sample
#
# Reference: Besag, J., Green, P., Higdon, D. and Mengersen, K. (1995)
# Bayesian computation and stochastic systems (with Discussion)
# Statistical Science, vol. 10, 3 - 66, page 30
# and Held, L. (2004) Simultaneous inference in risk assessment; a Bayesian
# perspective In: COMPSTAT 2004, Proceedings in Computational
# Statistics (J. Antoch, Ed.) 213 - 222, page 214
#
# Arguments
# sample : a data frame or matrix with sampled values (one column = one parameter).
# probs : probabilities for which the credible regions are computed.
######################################################################################
{
#Basic information
nmonte<-dim(x)[1]
p<-dim(x)[2]
#Ranks for each component
ranks <- apply(x, 2, rank, ties.method="first")
#Compute the set S={max(nmonte+1-min r_i(t) , max r_i(t)): t=1,..,nmonte}
left <- nmonte + 1 - apply(ranks, 1, min)
right <- apply(ranks, 1, max)
S <- apply(cbind(left, right), 1, max)
S <- S[order(S)]
#Compute the credible region
k <- floor(nmonte*probs)
tstar <- S[k]
out<-list()
for(i in 1:length(tstar))
{
upelim <- x[ranks == tstar[i]]
lowlim <- x[ranks == nmonte + 1 - tstar[i]]
out[[i]] <- rbind(lowlim, upelim)
rownames(out[[i]]) <- c("Lower", "Upper")
colnames(out[[i]]) <- colnames(x)
}
names(out) <- paste(probs)
return(out)
}
######################################################################################
cint<-function(x,probs=c(0.90,0.975))
######################################################################################
# Function to compute a credible interval from the MCMC sample
#
# Arguments
# sample : a data frame or matrix with sampled values (one column = one parameter).
# probs : probabilities for which the credible regions are to be computed.
######################################################################################
{
#Compute the credible interval
delta<-(1-probs)/2
lprobs<-cbind(delta,probs+delta)
out<-matrix(quantile(x,probs=lprobs),ncol=2)
colnames(out) <- c("Lower","Upper")
rownames(out) <- paste(probs)
return(out)
}
######################################################################################
hnulleval<-function(mat,hnull)
######################################################################################
# Evaluate H0
# AJV, 2006
######################################################################################
{
npar<-dim(mat)[2]
lower<-rep(0,npar)
upper<-rep(0,npar)
for(i in 1:npar)
{
lower[i]<-mat[1,i]< hnull[i]
upper[i]<-mat[2,i]> hnull[i]
}
total<-lower+upper
out<-(sum(total==2) == npar)
return(out)
}
######################################################################################
hnulleval2<-function(vec,hnull)
######################################################################################
# Evaluate H0
# AJV, 2006
######################################################################################
{
lower<-vec[1]< hnull
upper<-vec[2]> hnull
total<-lower+upper
out<-(total==2)
return(out)
}
######################################################################################
pcp<-function(x,hnull=NULL,precision=0.001,prob=0.95,digits=digits)
######################################################################################
# Function to compute Pseudo Countour Probabilities (Region)
# AJV, 2006
######################################################################################
{
if(is.null(hnull))hnull<-rep(0,dim(x)[2])
if (dim(x)[2]!=length(hnull)) stop("Dimension of x and hnull must be equal!!")
probs <- seq(precision, 1-precision, by=precision)
neval <- length(probs)
probsf <- c(prob,probs)
cr <- cregion(x,probs=probsf)
is.hnull <- hnulleval(cr[[2]],hnull)
if(is.hnull)
{
pval <- 1-precision
}
else
{
is.hnull <- hnulleval(cr[[length(cr)]],hnull)
if (!is.hnull)
{
pval <- precision
}
else
{
is.hnull<-rep(0,neval+1)
for(i in 1:(neval+1))
{
is.hnull[i] <- hnulleval(cr[[i]],hnull)
}
is.hnull <- is.hnull[-1]
first <- neval - sum(is.hnull) + 1
pval <- 1 - probs[first]
}
}
output <- list(cr=cr[[1]], prob=prob, pval=pval,hnull=hnull)
return(output)
}
######################################################################################
pcp2<-function(x,hnull=NULL,precision=0.001,prob=0.95)
######################################################################################
# Function to compute Pseudo Countour Probabilities (Interval)
# AJV, 2006
######################################################################################
{
if(is.null(hnull))hnull<-0
probs <- seq(precision, 1-precision, by=precision)
neval <- length(probs)
probsf <- c(prob,probs)
cr <- cint(x,probs=probsf)
is.hnull <- hnulleval2(cr[2,],hnull)
if(is.hnull)
{
pval <- 1-precision
}
else
{
is.hnull <- hnulleval2(cr[(neval+1),],hnull)
if (!is.hnull)
{
pval <- precision
}
else
{
is.hnull<-rep(0,neval+1)
for(i in 1:(neval+1))
{
is.hnull[i] <- hnulleval2(cr[i,],hnull)
}
is.hnull <- is.hnull[-1]
first <- neval - sum(is.hnull) + 1
pval <- 1-probs[first]
}
}
output <- list(cr=cr[1,], prob=prob, pval=pval,hnull=hnull)
return(output)
}
######################################################################################
######################################################################################
######################################################################################
if(object$nfixed>0)
{
possiP<-object$possiP
nfact<-dim(possiP)[1]
P<-rep(0,nfact)
df<-rep(0,nfact)
for(i in 1:nfact)
{
df[i]<-1
if((possiP[i,2]-possiP[i,1])>0)
{
x<-matrix(object$save.state$thetasave[,possiP[i,1]:possiP[i,2]])
foo<-pcp(x=x)
P[i]<-foo$pval
df[i]<-(possiP[i,2]-possiP[i,1])+1
}
else
{
x<-object$save.state$thetasave[,possiP[i,1]:possiP[i,2]]
foo<-pcp2(x=x)
P[i]<-foo$pval
}
}
table <- data.frame(df,P)
dimnames(table) <- list(rownames(possiP), c("Df","PsCP"))
structure(table, heading = c("Table of Pseudo Contour Probabilities\n",
paste("Response:", deparse(formula(object$fixed)[[2]]))), class = c("anovaPsCP",
"data.frame"))
}
}
"print.DPMolmm"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
if (length(x$coefficients)) {
cat("Posterior Inference of Parameters:\n")
if(x$alphapr==1){
print.default(format(x$coefficients, digits = digits), print.gap = 2,
quote = FALSE)}
if(x$alphapr==0){
print.default(format(x$coefficients[1:(length(x$coefficients)-1)], digits = digits), print.gap = 2,
quote = FALSE)}
}
else cat("No coefficients\n")
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Groups:",x$nsubject,"\n")
cat("\n\n")
invisible(x)
}
"summary.DPMolmm"<-function(object, hpd=TRUE, ...)
{
stde<-function(x)
{
n<-length(x)
return(sd(x)/sqrt(n))
}
hpdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[1],a$aupp[1]))
}
pdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[2],a$aupp[2]))
}
#nsave<-object$nsave
#dimen<-length(object$coefficients)
#thetasave<-matrix(object$save.state$thetasave,nrow=nsave, ncol=dimen)
thetasave<-object$save.state$thetasave
### Fixed part of the model
dimen1<-object$nrandom+object$nfixed
if(dimen1==1)
{
mat<-matrix(thetasave[,1:dimen1],ncol=1)
}
else
{
mat<-thetasave[,1:dimen1]
}
coef.p<-object$coefficients[1:dimen1]
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans <- c(object[c("call", "modelname")])
ans$coefficients<-coef.table
### Kernel variance
dimen2<-object$nrandom*(object$nrandom+1)/2
if(dimen2==1)
{
mat<-matrix(thetasave[,(dimen1+1):(dimen1+dimen2)],ncol=1)
}
else
{
mat<-thetasave[,(dimen1+1):(dimen1+dimen2)]
}
coef.p<-object$coefficients[(dimen1+1):(dimen1+dimen2)]
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd)
{
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$kernel<-coef.table
### CPO
ans$cpo<-object$cpo
### Baseline Information
dimen3<-object$nrandom+object$nrandom*(object$nrandom+1)/2
if(dimen3==1)
{
mat<-matrix(thetasave[,(dimen1+dimen2+1):(dimen1+dimen2+dimen3)],ncol=1)
}
else
{
mat<-thetasave[,(dimen1+dimen2+1):(dimen1+dimen2+dimen3)]
}
coef.p<-object$coefficients[(dimen1+dimen2+1):(dimen1+dimen2+dimen3)]
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$base<-coef.table
### Cutoff Points
dimen4<-object$ncateg-2
if(dimen4==1)
{
mat<-matrix(thetasave[,(dimen1+dimen2+dimen3+1):(dimen1+dimen2+dimen3+dimen4)],ncol=1)
}
else
{
mat<-thetasave[,(dimen1+dimen2+dimen3+1):(dimen1+dimen2+dimen3+dimen4)]
}
coef.p<-object$coefficients[(dimen1+dimen2+dimen3+1):(dimen1+dimen2+dimen3+dimen4)]
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$cutoff<-coef.table
### Precision parameter
if(is.null(object$prior$a0))
{
dimen5<-1
coef.p<-object$coefficients[(dimen1+dimen2+dimen3+dimen4+1)]
mat<-matrix(thetasave[,(dimen1+dimen2+dimen3+dimen4+1):(dimen1+dimen2+dimen3+dimen4+1)],ncol=1)
}
else
{
dimen5<-2
coef.p<-object$coefficients[(dimen1+dimen2+dimen3+dimen4+1):length(object$coefficients)]
mat<-thetasave[,(dimen1+dimen2+dimen3+dimen4+1):(dimen1+dimen2+dimen3+dimen4+dimen5)]
}
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$prec<-coef.table
coef.table<-matrix(object$mc,nrow=1,ncol=5)
dimnames(coef.table) <- list(" ", c("Dbar", "Dhat", "pD", "DIC","LPML"))
ans$mc<-coef.table
ans$nrec<-object$nrec
ans$nsubject<-object$nsubject
class(ans) <- "summaryDPMolmm"
return(ans)
}
"print.summaryDPMolmm"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(x$cpo)), digits = digits), print.gap = 2,
quote = FALSE)
cat("\nModel's performance:\n")
print.default(format(x$mc, digits = digits), print.gap = 2,
quote = FALSE)
if (length(x$coefficients)) {
cat("\nRegression coefficients:\n")
print.default(format(x$coefficients, digits = digits), print.gap = 2,
quote = FALSE)
}
else cat("No coefficients\n")
cat("\nThreshold:\n")
print.default(format(x$cutoff, digits = digits), print.gap = 2,
quote = FALSE)
cat("\nKernel variance:\n")
print.default(format(x$kernel, digits = digits), print.gap = 2,
quote = FALSE)
if (length(x$base)) {
cat("\nBaseline distribution:\n")
print.default(format(x$base, digits = digits), print.gap = 2,
quote = FALSE)
}
else cat("No baseline parameters\n")
if (length(x$prec)) {
cat("\nPrecision parameter:\n")
print.default(format(x$prec, digits = digits), print.gap = 2,
quote = FALSE)
}
else cat("No precision parameter\n")
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Groups:",x$nsubject,"\n")
cat("\n\n")
invisible(x)
}
"plot.DPMolmm"<-function(x, hpd=TRUE, ask=TRUE, nfigr=2, nfigc=2, param=NULL, col="#bdfcc9", ...)
{
fancydensplot1<-function(x, hpd=TRUE, npts=200, xlab="", ylab="", main="",col="#bdfcc9", ...)
# Author: AJV, 2006
#
{
dens <- density(x,n=npts)
densx <- dens$x
densy <- dens$y
meanvar <- mean(x)
densx1 <- max(densx[densx<=meanvar])
densx2 <- min(densx[densx>=meanvar])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ymean <- densy1 + ((densy2-densy1)/(densx2-densx1))*(meanvar-densx1)
if(hpd==TRUE)
{
alpha<-0.05
alow<-rep(0,2)
aupp<-rep(0,2)
n<-length(x)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(x),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
xlinf<-a$alow[1]
xlsup<-a$aupp[1]
}
else
{
xlinf <- quantile(x,0.025)
xlsup <- quantile(x,0.975)
}
densx1 <- max(densx[densx<=xlinf])
densx2 <- min(densx[densx>=xlinf])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylinf <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlinf-densx1)
densx1 <- max(densx[densx<=xlsup])
densx2 <- min(densx[densx>=xlsup])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylsup <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlsup-densx1)
plot(0.,0.,xlim = c(min(densx), max(densx)), ylim = c(min(densy), max(densy)),
axes = F,type = "n" , xlab=xlab, ylab=ylab, main=main, cex=1.2)
xpol<-c(xlinf,xlinf,densx[densx>=xlinf & densx <=xlsup],xlsup,xlsup)
ypol<-c(0,ylinf,densy[densx>=xlinf & densx <=xlsup] ,ylsup,0)
polygon(xpol, ypol, border = FALSE,col=col)
lines(c(min(densx), max(densx)),c(0,0),lwd=1.2)
segments(min(densx),0, min(densx),max(densy),lwd=1.2)
lines(densx,densy,lwd=1.2)
segments(meanvar, 0, meanvar, ymean,lwd=1.2)
segments(xlinf, 0, xlinf, ylinf,lwd=1.2)
segments(xlsup, 0, xlsup, ylsup,lwd=1.2)
axis(1., at = round(c(xlinf, meanvar,xlsup), 2.), labels = T,pos = 0.)
axis(1., at = round(seq(min(densx),max(densx),length=15), 2.), labels = F,pos = 0.)
axis(2., at = round(seq(0,max(densy),length=5), 2.), labels = T,pos =min(densx))
}
if(is(x, "DPMolmm"))
{
if(is.null(param))
{
coef.p<-x$coefficients
n<-length(coef.p)
pnames<-names(coef.p)
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr , ncol=nfigc ,byrow=TRUE))
for(i in 1:(n-1))
{
title1<-paste("Trace of",pnames[i],sep=" ")
title2<-paste("Density of",pnames[i],sep=" ")
plot(ts(x$save.state$thetasave[,i]),main=title1,xlab="MCMC scan",ylab=" ")
if(pnames[i]=="ncluster")
{
hist(x$save.state$thetasave[,i],main=title2,xlab="values", ylab="probability",probability=TRUE)
}
else
{
fancydensplot1(x$save.state$thetasave[,i],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
if(is.null(x$prior$a0))
{
cat("")
}
else
{
title1<-paste("Trace of",pnames[n],sep=" ")
title2<-paste("Density of",pnames[n],sep=" ")
plot(ts(x$save.state$thetasave[,n]),main=title1,xlab="MCMC scan",ylab=" ")
fancydensplot1(x$save.state$thetasave[,n],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
else
{
coef.p<-x$coefficients
n<-length(coef.p)
pnames<-names(coef.p)
poss<-0
for(i in 1:n)
{
if(pnames[i]==param)poss=i
}
if (poss==0)
{
stop("This parameter is not present in the original model.\n")
}
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr, ncol=nfigc, byrow = TRUE))
title1<-paste("Trace of",pnames[poss],sep=" ")
title2<-paste("Density of",pnames[poss],sep=" ")
plot(ts(x$save.state$thetasave[,poss]),main=title1,xlab="MCMC scan",ylab=" ")
if(param=="ncluster")
{
hist(x$save.state$thetasave[,poss],main=title2,xlab="values", ylab="probability",probability=TRUE)
}
else
{
fancydensplot1(x$save.state$thetasave[,poss],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
}
}
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