Nothing
R/DPMmeta.R
In DPpackage: Bayesian Nonparametric Modeling in R
### DPMmeta.R
### Fit a semiparametric linear mixed effects meta-analysis using a
### Dirichlet Process mixture of normals prior for the distribution of
### the random effects.
###
### Copyright: Alejandro Jara, 2006-2012.
###
### Last modification: 30-04-2007.
###
### 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
###
"DPMmeta"<-
function(formula,prior,mcmc,state,status,data=sys.frame(sys.parent()),na.action=na.fail)
UseMethod("DPMmeta")
"DPMmeta.default"<-
function(formula,
prior,
mcmc,
state,
status,
data=sys.frame(sys.parent()),
na.action=na.fail)
{
#########################################################################################
# call parameters
#########################################################################################
cl <- match.call()
mf <- match.call(expand.dots = FALSE)
m <- match(c("formula", "data","na.action"), names(mf), 0)
mf <- mf[c(1, m)]
mf$drop.unused.levels <- TRUE
mf[[1]] <- as.name("model.frame")
mf <- eval(mf, parent.frame())
#########################################################################################
# data structure
#########################################################################################
yy<- model.response(mf,"numeric")
namesre<-rownames(yy)
nameresp<-colnames(yy)[1]
if(dim(yy)[2] != 2)
{
stop("Both effect and variance must be included in the LHS of the formula object")
}
y<-yy[,1]
sigma2e<-yy[,2]
nrec<-length(y)
#########################################################################################
# model structure
#########################################################################################
x<-model.matrix(formula)
namesxm<-colnames(x)
p<-dim(x)[2]
p<-p-1
x<-x[,-1]
if(p==0)
{
nfixed <- 0
p <- 1
x <- matrix(0,nrow=nrec,ncol=1)
}
#########################################################################################
# elements for Pseudo Countour Probabilities' computation
#########################################################################################
Terms <- if (missing(data))
terms(formula)
else terms(formula, data = data)
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=formula,xlev=NULL)
dataF <- model.frame(formula=formula,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$Sbeta0)
sb<-prec%*%b0
if(length(b0)!=p)
{
stop("Error in the dimension of the mean of the normal prior for the fixed effects.\n")
}
if(dim(prec)[1]!=p || dim(prec)[2]!=p)
{
stop("Error in the dimension of the covariance of the normal prior for the fixed effects.\n")
}
}
tau01<-prior$tau01
tau02<-prior$tau02
tau<-c(tau01,tau02)
if(tau01<0 || tau02<0)
{
stop("The parameters of the Gamma prior for the normal kernel variance must be possitive.\n")
}
if(is.null(prior$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$b0<0)
{
stop("The parameters of the Gamma prior for the precision parameter must be possitive.\n")
}
}
if(is.null(prior$mb))
{
murand<-0
if(is.null(prior$mub))
{
stop("*mub* must be specified in the prior object when it is not considered as random.\n")
}
if(length(prior$mub) != 1)
{
stop("Error in the dimension of the mean the centering distribution.\n")
}
psiinv<-1
smu<-0
}
else
{
murand<-1
psiinv<-1/prior$Sb
smu<-psiinv*prior$mb
if(length(prior$mb) != 1)
{
stop("Error in the dimension of the mean of the normal prior for the mean of the centering distribution.\n")
}
if(!is.null(dim(psiinv)) && ( dim(psiinv)[1]!=1 || dim(psiinv)[2]!=1 ))
{
stop("Error in the dimension of the variance of the normal prior for the mean of the centering distribution.\n")
}
}
if(is.null(prior$tau11))
{
sigmarand<-0
if(is.null(prior$sigmab))
{
stop("*sigmab* must be specified in the prior object when it is not considered as random.\n")
}
tau1 <- -1
tau2 <- -1
}
else
{
sigmarand<-1
tau11<-prior$tau11
tau12<-prior$tau12
tau<-c(tau,tau11,tau12)
if(tau11<0 || tau12<0)
{
stop("The parameters of the Gamma prior for the variance of the centering distribution must be possitive.\n")
}
}
#########################################################################################
# mcmc specification
#########################################################################################
if(missing(mcmc))
{
nburn <- 1000
nsave <- 1000
nskip <- 0
ndisplay <- 100
mcmcvec<-c(nburn,nskip,ndisplay)
}
else
{
mcmcvec<-c(mcmc$nburn,mcmc$nskip,mcmc$ndisplay,murand,sigmarand)
nsave<-mcmc$nsave
}
#########################################################################################
# output
#########################################################################################
mc<-rep(0,5)
musave<-matrix(0,nrow=nsave,ncol=nrec)
clustsave<-matrix(0,nrow=nsave,ncol=nrec)
randsave<-matrix(0,nrow=nsave,ncol=(nrec+1))
thetasave<-matrix(0,nrow=nsave,ncol=nfixed+6)
cpo<-matrix(0,nrow=nrec,ncol=2)
#########################################################################################
# parameters depending on status
#########################################################################################
if(status==TRUE)
{
if(sigmarand==1)
{
wsigma <- 1/rgamma(1,shape=tau11/2,scale=tau12/2)
}
else
{
wsigma <- prior$sigmab
}
wsigma2 <- 1/rgamma(1,shape=tau01/2,scale=tau02/2)
bzs<-rnorm(nrec,mean=0,sd=sqrt(wsigma))
bzsb<-rnorm(nrec,mean=0,sd=sqrt(wsigma2))
if(nfixed==0){
beta<-matrix(0,nrow=1,ncol=1)
b<-rep(0,nrec)
mu<-rep(0,nrec)
for(i in 1:nrec){
b[i]<-mean(y)+bzs[i]
mu[i]<-mean(y)+bzsb[i]
}
if(murand==1)
{
mub<-mean(y)
}
else
{
mub<-prior$mub
}
if(sigmarand==1)
{
sigmab<-var(y)
}
else
{
sigmab<-prior$sigmab
}
}
if(nfixed>0){
fit0<- glm.fit(cbind(x,rep(1,nrec)), y, family= gaussian(link = "identity"))
b<-rep(0,nrec)
mu<-rep(0,nrec)
beta<-coefficients(fit0)[1:p]
for(i in 1:nrec){
b[i]<-coefficients(fit0)[p+1]+bzs[i]
mu[i]<-coefficients(fit0)[p+1]+bzsb[i]
}
if(murand==1)
{
mub<-coefficients(fit0)[p+1]
}
else
{
mub<-prior$mub
}
if(sigmarand==1)
{
sigmab<-var(y)
}
else
{
sigmab<-prior$sigmab
}
}
betar<-0
sigma<-wsigma2
ncluster<-nrec
ss<-seq(1,nrec)
}
if(status==FALSE)
{
alpha<-state$alpha
b<-state$b
if(nfixed>0)
{
beta<-state$beta
}
else
{
beta<-rep(0,p)
}
mu<-state$mu
mub<-state$mub
ncluster<-state$ncluster
sigma<-state$sigma2
sigmab<-state$sigma2b
ss<-state$ss
betar<-0
}
#########################################################################################
# working space
#########################################################################################
iflagp<-rep(0,p)
prob<-rep(0,nrec+1)
seed1<-sample(1:29000,1)
seed2<-sample(1:29000,1)
seed<-c(seed1,seed2)
workmhp<-rep(0,p*(p+1)/2)
workmp<-matrix(0,nrow=p,ncol=p)
workvp<-rep(0,p)
xty<-rep(0,p)
cstrt<-matrix(0,nrow=nrec,ncol=nrec)
ccluster<-rep(0,nrec)
betasave<-rep(0,p)
bsave<-rep(0,nrec)
#########################################################################################
# calling the fortran code
#########################################################################################
foo <- .Fortran("dpmmeta",
nrec =as.integer(nrec),
nfixed =as.integer(nfixed),
p =as.integer(p),
y =as.double(y),
x =as.double(x),
sigma2e =as.double(sigma2e),
a0b0 =as.double(a0b0),
prec =as.double(prec),
sb =as.double(sb),
tau =as.double(tau),
smu =as.double(smu),
psiinv =as.double(psiinv),
mcmc =as.integer(mcmcvec),
nsave =as.integer(nsave),
ncluster =as.integer(ncluster),
ss =as.integer(ss),
alpha =as.double(alpha),
beta =as.double(beta),
b =as.double(b),
mu =as.double(mu),
sigma =as.double(sigma),
mub =as.double(mub),
sigmab =as.double(sigmab),
mc =as.double(mc),
cpo =as.double(cpo),
randsave =as.double(randsave),
thetasave =as.double(thetasave),
musave =as.double(musave),
clustsave =as.integer(clustsave),
iflagp =as.integer(iflagp),
workmhp =as.double(workmhp),
workmp =as.double(workmp),
workvp =as.double(workvp),
xty =as.double(xty),
cstrt =as.integer(cstrt),
ccluster =as.integer(ccluster),
prob =as.double(prob),
seed =as.integer(seed),
betasave =as.double(betasave),
bsave =as.double(bsave),
PACKAGE ="DPpackage")
#########################################################################################
# save state
#########################################################################################
mc<-foo$mc
names(mc)<-c("Dbar", "Dhat", "pD", "DIC","LPML")
thetasave<-matrix(foo$thetasave,nrow=nsave, ncol=(nfixed+6))
randsave<-matrix(foo$randsave,nrow=nsave, ncol=(nrec+1))
musave<-matrix(foo$musave,nrow=nsave,ncol=nrec)
clustsave<-matrix(foo$clustsave,nrow=nsave,ncol=nrec)
cpom<-matrix(foo$cpo,nrow=nrec,ncol=2)
cpo<-cpom[,1]
fso<-cpom[,2]
if(nfixed==0)
{
pnames1 <- nameresp
}
if(nfixed>=1)
{
pnames1 <- c(nameresp,namesxm[-1])
}
pnames2 <- "sigma2"
pnames3 <- "mub"
pnames4 <- "sigma2b"
pnames5 <- c("ncluster","alpha")
qnames <- NULL
for(i in 1:nrec)
{
qnames <- c(qnames,namesre[i])
}
qnames <- c(qnames,"Prediction")
colnames(randsave) <- qnames
model.name<-"Bayesian semiparametric linear mixed effects meta-analysis"
colnames(thetasave)<-c(pnames1,pnames2,pnames3,pnames4,pnames5)
coeff<-apply(thetasave,2,mean)
state <- list(alpha=foo$alpha,
b=foo$b,
beta=foo$beta,
mu=foo$mu,
mub=foo$mub,
ncluster=foo$ncluster,
sigma2=foo$sigma,
sigma2b=foo$sigmab,
ss=foo$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$nrec,
nsubject=foo$nrec,
nfixed=foo$nfixed,
nrandom=1,
cpo=cpo,
fso=fso,
alphapr=alphapr,
x=x,
mf=mf,
y=y,
possiP=possiP,
formula=formula,
mc=mc)
cat("\n\n")
class(z)<-c("DPMmeta")
return(z)
}
###
### Tools: anova, print, summary, plot
###
### Copyright: Alejandro Jara, 2007
### Last modification: 16-04-2007.
"anova.DPMmeta"<-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$pval
}
}
table <- data.frame(df,P)
dimnames(table) <- list(rownames(possiP), c("Df","PsCP"))
structure(table, heading = c("Table of Pseudo Contour Probabilities\n",
paste("Response:", deparse(formula(object$formula)[[2]]))), class = c("anovaPsCP",
"data.frame"))
}
}
"print.DPMmeta"<-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 Studies:",x$nrec)
cat("\n\n")
invisible(x)
}
"summary.DPMmeta"<-function(object, hpd=TRUE, ...)
{
stde<-function(x)
{
n<-length(x)
return(sd(x)/sqrt(n))
}
hpdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$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$aupp[2]))
}
thetasave<-object$save.state$thetasave
### Fixed part of the model
dimen1<-1+object$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<-1
mat<-matrix(thetasave[,(dimen1+1):(dimen1+dimen2)],ncol=1)
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<-2
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
### Precision parameter
if(is.null(object$prior$a0))
{
dimen4<-1
mat<-matrix(thetasave[,(dimen1+dimen2+dimen3+1):(dimen1+dimen2+dimen3+dimen4)],ncol=1)
}
else
{
dimen4<-2
mat<-thetasave[,(dimen1+dimen2+dimen3+1):(dimen1+dimen2+dimen3+dimen4)]
}
coef.p<-object$coefficients[(dimen1+dimen2+dimen3+1):(dimen1+dimen2+dimen3+dimen4)]
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd)
{
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$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
class(ans) <- "summaryDPMmeta"
return(ans)
}
"print.summaryDPMmeta"<-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("\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$prec, digits = digits), print.gap = 2,
quote = FALSE)
}
else cat("No precision parameter\n")
cat("\nNumber of Studies:",x$nrec)
cat("\n\n")
invisible(x)
}
"plot.DPMmeta"<-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))
}
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]))
}
if(is(x, "DPMmeta"))
{
if(is.null(param))
{
coef.p<-x$coefficients
n<-length(coef.p)
pnames<-names(coef.p)
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr , ncol=nfigc ,byrow=TRUE))
for(i in 1:(n-1))
{
title1<-paste("Trace of",pnames[i],sep=" ")
title2<-paste("Density of",pnames[i],sep=" ")
plot(x$save.state$thetasave[,i],type='l',main=title1,xlab="MCMC scan",ylab=" ")
if(pnames[i]=="ncluster")
{
hist(x$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$a0))
{
cat("")
}
else
{
title1<-paste("Trace of",pnames[n],sep=" ")
title2<-paste("Density of",pnames[n],sep=" ")
plot(x$save.state$thetasave[,n],type='l',main=title1,xlab="MCMC scan",ylab=" ")
fancydensplot1(x$save.state$thetasave[,n],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
DPcaterpillar(DPrandom(x))
abline(v=x$coefficients[1],col="red",lty=1,lwd=1)
mat<-matrix(x$save.state$thetasave[,1],ncol=1)
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
abline(v=coef.l,col="red",lty=2,lwd=1)
abline(v=coef.u,col="red",lty=2,lwd=1)
}
else
{
coef.p<-x$coefficients
n<-length(coef.p)
pnames<-names(coef.p)
poss<-0
for(i in 1:n)
{
if(pnames[i]==param)poss=i
}
if (poss==0)
{
stop("This parameter is not present in the original model.\n")
}
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr, ncol=nfigc, byrow = TRUE))
title1<-paste("Trace of",pnames[poss],sep=" ")
title2<-paste("Density of",pnames[poss],sep=" ")
plot(x$save.state$thetasave[,poss],type='l',main=title1,xlab="MCMC scan",ylab=" ")
if(param=="ncluster")
{
hist(x$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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### DPMmeta.R
### Fit a semiparametric linear mixed effects meta-analysis using a
### Dirichlet Process mixture of normals prior for the distribution of
### the random effects.
###
### Copyright: Alejandro Jara, 2006-2012.
###
### Last modification: 30-04-2007.
###
### 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
###
"DPMmeta"<-
function(formula,prior,mcmc,state,status,data=sys.frame(sys.parent()),na.action=na.fail)
UseMethod("DPMmeta")
"DPMmeta.default"<-
function(formula,
prior,
mcmc,
state,
status,
data=sys.frame(sys.parent()),
na.action=na.fail)
{
#########################################################################################
# call parameters
#########################################################################################
cl <- match.call()
mf <- match.call(expand.dots = FALSE)
m <- match(c("formula", "data","na.action"), names(mf), 0)
mf <- mf[c(1, m)]
mf$drop.unused.levels <- TRUE
mf[[1]] <- as.name("model.frame")
mf <- eval(mf, parent.frame())
#########################################################################################
# data structure
#########################################################################################
yy<- model.response(mf,"numeric")
namesre<-rownames(yy)
nameresp<-colnames(yy)[1]
if(dim(yy)[2] != 2)
{
stop("Both effect and variance must be included in the LHS of the formula object")
}
y<-yy[,1]
sigma2e<-yy[,2]
nrec<-length(y)
#########################################################################################
# model structure
#########################################################################################
x<-model.matrix(formula)
namesxm<-colnames(x)
p<-dim(x)[2]
p<-p-1
x<-x[,-1]
if(p==0)
{
nfixed <- 0
p <- 1
x <- matrix(0,nrow=nrec,ncol=1)
}
#########################################################################################
# elements for Pseudo Countour Probabilities' computation
#########################################################################################
Terms <- if (missing(data))
terms(formula)
else terms(formula, data = data)
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=formula,xlev=NULL)
dataF <- model.frame(formula=formula,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")
}
}
tau01<-prior$tau01
tau02<-prior$tau02
tau<-c(tau01,tau02)
if(tau01<0 || tau02<0)
{
stop("The parameters of the Gamma prior for the normal kernel variance must be possitive.\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")
}
}
if(is.null(prior$mb))
{
murand<-0
if(is.null(prior$mub))
{
stop("*mub* must be specified in the prior object when it is not considered as random.\n")
}
if(length(prior$mub) != 1)
{
stop("Error in the dimension of the mean the centering distribution.\n")
}
psiinv<-1
smu<-0
}
else
{
murand<-1
psiinv<-1/prior$Sb
smu<-psiinv*prior$mb
if(length(prior$mb) != 1)
{
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)) && ( dim(psiinv)[1]!=1 || dim(psiinv)[2]!=1 ))
{
stop("Error in the dimension of the variance of the normal prior for the mean of the centering distribution.\n")
}
}
if(is.null(prior$tau11))
{
sigmarand<-0
if(is.null(prior$sigmab))
{
stop("*sigmab* must be specified in the prior object when it is not considered as random.\n")
}
tau1 <- -1
tau2 <- -1
}
else
{
sigmarand<-1
tau11<-prior$tau11
tau12<-prior$tau12
tau<-c(tau,tau11,tau12)
if(tau11<0 || tau12<0)
{
stop("The parameters of the Gamma prior for the variance of the centering distribution must be possitive.\n")
}
}
#########################################################################################
# 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$ndisplay,murand,sigmarand)
nsave<-mcmc$nsave
}
#########################################################################################
# output
#########################################################################################
mc<-rep(0,5)
musave<-matrix(0,nrow=nsave,ncol=nrec)
clustsave<-matrix(0,nrow=nsave,ncol=nrec)
randsave<-matrix(0,nrow=nsave,ncol=(nrec+1))
thetasave<-matrix(0,nrow=nsave,ncol=nfixed+6)
cpo<-matrix(0,nrow=nrec,ncol=2)
#########################################################################################
# parameters depending on status
#########################################################################################
if(status==TRUE)
{
if(sigmarand==1)
{
wsigma <- 1/rgamma(1,shape=tau11/2,scale=tau12/2)
}
else
{
wsigma <- prior$sigmab
}
wsigma2 <- 1/rgamma(1,shape=tau01/2,scale=tau02/2)
bzs<-rnorm(nrec,mean=0,sd=sqrt(wsigma))
bzsb<-rnorm(nrec,mean=0,sd=sqrt(wsigma2))
if(nfixed==0){
beta<-matrix(0,nrow=1,ncol=1)
b<-rep(0,nrec)
mu<-rep(0,nrec)
for(i in 1:nrec){
b[i]<-mean(y)+bzs[i]
mu[i]<-mean(y)+bzsb[i]
}
if(murand==1)
{
mub<-mean(y)
}
else
{
mub<-prior$mub
}
if(sigmarand==1)
{
sigmab<-var(y)
}
else
{
sigmab<-prior$sigmab
}
}
if(nfixed>0){
fit0<- glm.fit(cbind(x,rep(1,nrec)), y, family= gaussian(link = "identity"))
b<-rep(0,nrec)
mu<-rep(0,nrec)
beta<-coefficients(fit0)[1:p]
for(i in 1:nrec){
b[i]<-coefficients(fit0)[p+1]+bzs[i]
mu[i]<-coefficients(fit0)[p+1]+bzsb[i]
}
if(murand==1)
{
mub<-coefficients(fit0)[p+1]
}
else
{
mub<-prior$mub
}
if(sigmarand==1)
{
sigmab<-var(y)
}
else
{
sigmab<-prior$sigmab
}
}
betar<-0
sigma<-wsigma2
ncluster<-nrec
ss<-seq(1,nrec)
}
if(status==FALSE)
{
alpha<-state$alpha
b<-state$b
if(nfixed>0)
{
beta<-state$beta
}
else
{
beta<-rep(0,p)
}
mu<-state$mu
mub<-state$mub
ncluster<-state$ncluster
sigma<-state$sigma2
sigmab<-state$sigma2b
ss<-state$ss
betar<-0
}
#########################################################################################
# working space
#########################################################################################
iflagp<-rep(0,p)
prob<-rep(0,nrec+1)
seed1<-sample(1:29000,1)
seed2<-sample(1:29000,1)
seed<-c(seed1,seed2)
workmhp<-rep(0,p*(p+1)/2)
workmp<-matrix(0,nrow=p,ncol=p)
workvp<-rep(0,p)
xty<-rep(0,p)
cstrt<-matrix(0,nrow=nrec,ncol=nrec)
ccluster<-rep(0,nrec)
betasave<-rep(0,p)
bsave<-rep(0,nrec)
#########################################################################################
# calling the fortran code
#########################################################################################
foo <- .Fortran("dpmmeta",
nrec =as.integer(nrec),
nfixed =as.integer(nfixed),
p =as.integer(p),
y =as.double(y),
x =as.double(x),
sigma2e =as.double(sigma2e),
a0b0 =as.double(a0b0),
prec =as.double(prec),
sb =as.double(sb),
tau =as.double(tau),
smu =as.double(smu),
psiinv =as.double(psiinv),
mcmc =as.integer(mcmcvec),
nsave =as.integer(nsave),
ncluster =as.integer(ncluster),
ss =as.integer(ss),
alpha =as.double(alpha),
beta =as.double(beta),
b =as.double(b),
mu =as.double(mu),
sigma =as.double(sigma),
mub =as.double(mub),
sigmab =as.double(sigmab),
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),
cstrt =as.integer(cstrt),
ccluster =as.integer(ccluster),
prob =as.double(prob),
seed =as.integer(seed),
betasave =as.double(betasave),
bsave =as.double(bsave),
PACKAGE ="DPpackage")
#########################################################################################
# save state
#########################################################################################
mc<-foo$mc
names(mc)<-c("Dbar", "Dhat", "pD", "DIC","LPML")
thetasave<-matrix(foo$thetasave,nrow=nsave, ncol=(nfixed+6))
randsave<-matrix(foo$randsave,nrow=nsave, ncol=(nrec+1))
musave<-matrix(foo$musave,nrow=nsave,ncol=nrec)
clustsave<-matrix(foo$clustsave,nrow=nsave,ncol=nrec)
cpom<-matrix(foo$cpo,nrow=nrec,ncol=2)
cpo<-cpom[,1]
fso<-cpom[,2]
if(nfixed==0)
{
pnames1 <- nameresp
}
if(nfixed>=1)
{
pnames1 <- c(nameresp,namesxm[-1])
}
pnames2 <- "sigma2"
pnames3 <- "mub"
pnames4 <- "sigma2b"
pnames5 <- c("ncluster","alpha")
qnames <- NULL
for(i in 1:nrec)
{
qnames <- c(qnames,namesre[i])
}
qnames <- c(qnames,"Prediction")
colnames(randsave) <- qnames
model.name<-"Bayesian semiparametric linear mixed effects meta-analysis"
colnames(thetasave)<-c(pnames1,pnames2,pnames3,pnames4,pnames5)
coeff<-apply(thetasave,2,mean)
state <- list(alpha=foo$alpha,
b=foo$b,
beta=foo$beta,
mu=foo$mu,
mub=foo$mub,
ncluster=foo$ncluster,
sigma2=foo$sigma,
sigma2b=foo$sigmab,
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$nrec,
nfixed=foo$nfixed,
nrandom=1,
cpo=cpo,
fso=fso,
alphapr=alphapr,
x=x,
mf=mf,
y=y,
possiP=possiP,
formula=formula,
mc=mc)
cat("\n\n")
class(z)<-c("DPMmeta")
return(z)
}
###
### Tools: anova, print, summary, plot
###
### Copyright: Alejandro Jara, 2007
### Last modification: 16-04-2007.
"anova.DPMmeta"<-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$formula)[[2]]))), class = c("anovaPsCP",
"data.frame"))
}
}
"print.DPMmeta"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$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$coefficients)-1)], digits = digits), print.gap = 2,
quote = FALSE)}
}
else cat("No coefficients\n")
cat("\nNumber of Studies:",x$nrec)
cat("\n\n")
invisible(x)
}
"summary.DPMmeta"<-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]))
}
thetasave<-object$save.state$thetasave
### Fixed part of the model
dimen1<-1+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$coefficients<-coef.table
### Kernel variance
dimen2<-1
mat<-matrix(thetasave[,(dimen1+1):(dimen1+dimen2)],ncol=1)
coef.p<-object$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$cpo
### Baseline Information
dimen3<-2
mat<-thetasave[,(dimen1+dimen2+1):(dimen1+dimen2+dimen3)]
coef.p<-object$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$base<-coef.table
### Precision parameter
if(is.null(object$prior$a0))
{
dimen4<-1
mat<-matrix(thetasave[,(dimen1+dimen2+dimen3+1):(dimen1+dimen2+dimen3+dimen4)],ncol=1)
}
else
{
dimen4<-2
mat<-thetasave[,(dimen1+dimen2+dimen3+1):(dimen1+dimen2+dimen3+dimen4)]
}
coef.p<-object$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$prec<-coef.table
coef.table<-matrix(object$mc,nrow=1,ncol=5)
dimnames(coef.table) <- list(" ", c("Dbar", "Dhat", "pD", "DIC","LPML"))
ans$mc<-coef.table
ans$nrec<-object$nrec
class(ans) <- "summaryDPMmeta"
return(ans)
}
"print.summaryDPMmeta"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$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$coefficients, digits = digits), print.gap = 2,
quote = FALSE)
}
else cat("No coefficients\n")
cat("\nKernel variance:\n")
print.default(format(x$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 Studies:",x$nrec)
cat("\n\n")
invisible(x)
}
"plot.DPMmeta"<-function(x, hpd=TRUE, ask=TRUE, nfigr=2, nfigc=2, param=NULL, col="#bdfcc9", ...)
{
fancydensplot1<-function(x, hpd=TRUE, npts=200, xlab="", ylab="", main="",col="#bdfcc9", ...)
# Author: AJV, 2006
#
{
dens <- density(x,n=npts)
densx <- dens$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$aupp[1]
}
else
{
xlinf <- quantile(x,0.025)
xlsup <- quantile(x,0.975)
}
densx1 <- max(densx[densx<=xlinf])
densx2 <- min(densx[densx>=xlinf])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylinf <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlinf-densx1)
densx1 <- max(densx[densx<=xlsup])
densx2 <- min(densx[densx>=xlsup])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylsup <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlsup-densx1)
plot(0.,0.,xlim = c(min(densx), max(densx)), ylim = c(min(densy), max(densy)),
axes = F,type = "n" , xlab=xlab, ylab=ylab, main=main, cex=1.2)
xpol<-c(xlinf,xlinf,densx[densx>=xlinf & densx <=xlsup],xlsup,xlsup)
ypol<-c(0,ylinf,densy[densx>=xlinf & densx <=xlsup] ,ylsup,0)
polygon(xpol, ypol, border = FALSE,col=col)
lines(c(min(densx), max(densx)),c(0,0),lwd=1.2)
segments(min(densx),0, min(densx),max(densy),lwd=1.2)
lines(densx,densy,lwd=1.2)
segments(meanvar, 0, meanvar, ymean,lwd=1.2)
segments(xlinf, 0, xlinf, ylinf,lwd=1.2)
segments(xlsup, 0, xlsup, ylsup,lwd=1.2)
axis(1., at = round(c(xlinf, meanvar,xlsup), 2.), labels = T,pos = 0.)
axis(1., at = round(seq(min(densx),max(densx),length=15), 2.), labels = F,pos = 0.)
axis(2., at = round(seq(0,max(densy),length=5), 2.), labels = T,pos =min(densx))
}
hpdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[1],a$aupp[1]))
}
if(is(x, "DPMmeta"))
{
if(is.null(param))
{
coef.p<-x$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(x$save.state$thetasave[,i],type='l',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(x$save.state$thetasave[,n],type='l',main=title1,xlab="MCMC scan",ylab=" ")
fancydensplot1(x$save.state$thetasave[,n],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
DPcaterpillar(DPrandom(x))
abline(v=x$coefficients[1],col="red",lty=1,lwd=1)
mat<-matrix(x$save.state$thetasave[,1],ncol=1)
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
abline(v=coef.l,col="red",lty=2,lwd=1)
abline(v=coef.u,col="red",lty=2,lwd=1)
}
else
{
coef.p<-x$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(x$save.state$thetasave[,poss],type='l',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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