R/FPTrasch.R

In DPpackage: Bayesian Nonparametric Modeling in R

### FPTrasch.R                   
### Fit a Rasch model with a mixture of Polya Tree prior
### for the random effect distribution
###
### Copyright: Alejandro Jara, 2006-2012.
###
### Last modification: 04-09-2009.
###
### 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
###


FPTrasch <- function(y,prior,mcmc,offset,state,status,
                     grid=seq(-10,10,length=1000),data=sys.frame(sys.parent()),compute.band=FALSE)
UseMethod("FPTrasch")

FPTrasch.default<-
function(y,
         prior,
         mcmc,
         offset=NULL,         
         state,
         status,
         grid=seq(-10,10,length=1000),
         data=sys.frame(sys.parent()),
		 compute.band=FALSE)
{
         #########################################################################################
         # call parameters
         #########################################################################################
		   cl <- match.call()
	       y <- as.matrix(y)
	  
         #########################################################################################
         # data structure
         #########################################################################################
     	   nsubject <- nrow(y)
	       p <- ncol(y)

           ywork <- y
          
           datastrm <- NULL
           nmissing <- 0
           total <- 0
          
           for(i in 1:nsubject)
           {
              for(j in 1:p)
              {
                  if(is.na(y[i,j]))
                  {
                     nmissing <- nmissing+1
                     datastrm <- rbind(datastrm,c(i,j))   
                  }
                  else
                  {
                     total <- total+y[i,j]            
                  }
                  
              }
		   }
          
           nrec <- nsubject*p-nmissing
          
           if(nmissing>0)
           {
              imiss <- 1 
              for(i in 1:nmissing)
              {
                   ywork[datastrm[i,1],datastrm[i,2]] <- rbinom(1,1,total/nrec)               
              }
           }
           else
           {
              imiss <- 0
              nmissing <- 1
              datastrm <- matrix(0,nrow=1,ncol=2)
           }


         #########################################################################################
         # prior information
         #########################################################################################

       	   if(is.null(prior$a0))
  	       {
  	          a0 <- -1
  	          b0 <- -1 
	 		  alpha <- prior$alpha
  	          alpharand <- 0
  	       }
           else
           {
              a0 <- prior$a0
			  b0 <- prior$b0
  	          alpha <- 1
  	          alpharand <- 1
  	       }
  	       a0b0 <- c(a0,b0)
  	 

		   if(is.null(prior$tau1))
		   {
              tau1 <- -1
              tau2 <- -1
              sigma2 <- prior$sigma2
              sigmarand <- 0
		   }
		   else
		   {
              tau1 <- prior$tau1
              tau2 <- prior$tau2
              sigma2 <- 1
  	          sigmarand <- 1
		   }

		   if(is.null(prior$mub))
		   {
              m <- 0 
			  s <- 0
			  mu <- prior$mu
			  murand <- 0
		   }
		   else
		   {
			  m <- prior$mub
			  s <- prior$Sb
			  mu <- rnorm(1,prior$mub,sqrt(prior$Sb))
              murand <- 1
           }     

 		   maxm <- prior$M         
           ntsets <- 2**maxm
           ntprob <- 0
           for(i in 1:maxm)
           {
               ntprob <- ntprob+2**i 
           }

           b0 <- prior$beta0
           prec <- solve(prior$Sbeta0)
           sb <- prec%*%prior$beta0

           if(dim(prec)[1] != (p-1)) stop("the dimension of beta0 and Sbeta0 must be p-1")


         #########################################################################################
         # mcmc specification
         #########################################################################################
           if(is.null(mcmc$algo))
           {
               algo <- 1
		   }
           else
           {
              algo <- mcmc$algo
           }
           mcmcvec <- c(mcmc$nburn,mcmc$nskip,mcmc$ndisplay)
           nsave <- mcmc$nsave

         #########################################################################################
         # output
         #########################################################################################
           acrate <- 0
           cpo <- matrix(0,nrow=nsubject,ncol=p)
           cpov <- rep(0,nsubject)
           ngrid <- length(grid)
	       densave <- matrix(0,nrow=nsave,ncol=ngrid)
           cdfsave <- matrix(0,nrow=nsave,ncol=ngrid)
           thetasave <- matrix(0,nrow=nsave,ncol=p+4)
           randsave <- matrix(0,nrow=nsave,ncol=nsubject+1)
           bf <- 0

         #########################################################################################
         # MLE estimation
         #########################################################################################
         
           RaschMLE <- function(y,nitem,nsubject,offset)
           {
             ywork2 <- NULL
             roffset <- NULL
             id <- NULL
             x <- NULL
             count <- 0
             for(i in 1:nsubject)
             {
				 ywork2 <- c(ywork2,y[i,])
				 roffset <- c(roffset,offset[i,])
				 id <- c(id,rep(i,nitem))

                 aa <- diag(-1,nitem)
				 aa[,1] <- 1
                 x <- rbind(x,aa)
             }
             out <- NULL
             #library(nlme)
	#		 library(MASS)
             fit0 <- glmmPQL(ywork2~x-1+offset(roffset),random = ~ 1 | id,family=binomial(logit), verbose = FALSE) 

             beta <- as.vector(fit0$coeff$fixed[2:nitem])
             b <- as.vector(fit0$coeff$fixed[1]+fit0$coeff$random$id)
			 out$beta <- beta
			 out$b <- b
             out$mu <- fit0$coeff$fixed[1]
             out$sigma2 <- getVarCov(fit0)[1]
             return(out)
		   }
	 
		   if(is.null(offset))
	       {
			  roffset <- matrix(0,nrow=nsubject,ncol=p)
		   }
  	       else
		   {
			  roffset <- offset
		   }
	 
		   fit0 <- RaschMLE(ywork,p,nsubject,roffset)

         #########################################################################################
         # parameters depending on status
         #########################################################################################
       
    	   if(status==TRUE)
	       {
			  beta <- fit0$beta
			  b <- fit0$b
			  if(murand==1) mu <- fit0$mu
			  if(sigmarand==1) sigma2 <- fit0$sigma2
              probmat <- matrix(0.5,nrow=ntsets,ncol=maxm)
		   }
	 
      	   if(status==FALSE)
		   {
	          alpha <- state$alpha
	          b <- state$b
	          beta <- state$beta
			  mu <- state$mu
			  sigma2 <- state$sigma2
              probmat <- state$probmat
	       }    

         #########################################################################################
         # working space
         #########################################################################################

		   prob <- rep(0,ntsets)
           kvec <- rep(0,maxm)
           ptcount <- rep(0,ntprob)

		   betac <- rep(0,p-1)

           iflagp <- rep(0,p-1)
		   seed1 <- sample(1:29000,1)
           seed2 <- sample(1:29000,1)
           seed <- c(seed1,seed2)
           workmhp <- rep(0,(p-1)*p/2)
           workvp <- rep(0,p-1)
           xtx <- matrix(0,nrow=p-1,ncol=p-1)
           xty <- rep(0,p-1)

         #########################################################################################
         # calling the fortran code
         #########################################################################################

		   foo <- .Fortran("ptrasch",
					datastr    =as.integer(datastrm),
					imiss      =as.integer(imiss),
					nmissing   =as.integer(nmissing),
					nsubject   =as.integer(nsubject),
					p          =as.integer(p),
					y          =as.integer(ywork),
                    roffset    =as.double(roffset),  	 	
                    ngrid      =as.integer(ngrid),
                    grid       =as.double(grid),
                    maxm       =as.integer(maxm),
                    ntprob     =as.integer(ntprob),
                    ntsets     =as.integer(ntsets),
					a0b0       =as.double(a0b0),
					b0         =as.double(b0),
					prec       =as.double(prec),	
					sb         =as.double(sb),
					tau1       =as.double(tau1),
					tau2       =as.double(tau2),
					m          =as.double(m),
					s          =as.double(s),
					mcmc       =as.integer(mcmcvec),
					nsave      =as.integer(nsave),
                    algo       =as.integer(algo),
					acrate     =as.double(acrate),
					cpo        =as.double(cpo),
					cpov	   =as.double(cpov),
					densave    =as.double(densave),
					cdfsave    =as.double(cdfsave), 		
					randsave   =as.double(randsave),
					thetasave  =as.double(thetasave),
                    bf         =as.double(bf),
					alpha      =as.double(alpha),		
					b          =as.double(b),		
					beta       =as.double(beta),	
					mu         =as.double(mu),
					sigma2     =as.double(sigma2),
					probmat    =as.double(probmat),
                    seed       =as.integer(seed),
                    ptcount    =as.integer(ptcount),
                    kvec       =as.integer(kvec),
                    prob       =as.double(prob),
					betac      =as.double(betac),		
					workvp     =as.double(workvp),
					workmhp    =as.double(workmhp),
					iflagp     =as.integer(iflagp),
					xtx        =as.double(xtx),
					xty        =as.double(xty),
					PACKAGE    ="DPpackage")


         #########################################################################################
         # save state
         #########################################################################################

           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]))
           }

           model.name<-"Bayesian Rasch Poisson Model using a FPT prior"		
                
           state <- list(alpha=foo$alpha,
						 b=foo$b,
						 beta=foo$beta,
	                     mu=foo$mu,
	                     sigma2=foo$sigma2,
                         probmat=matrix(foo$probmat,nrow=ntsets,ncol=maxm))

           cpo <- matrix(foo$cpo,nrow=nsubject,ncol=p)
           randsave <- matrix(foo$randsave,nrow=nsave,ncol=nsubject+1)
           thetasave <- matrix(foo$thetasave,nrow=nsave,ncol=p+4) 
           densave <- matrix(foo$densave,nrow=nsave,ncol=ngrid)
           cdfsave <- matrix(foo$cdfsave,nrow=nsave,ncol=ngrid)
 
           dens.m <- apply(densave,2,mean)
           dens.l <- NULL
           dens.u <- NULL
           if(compute.band)
           {
              limm <- apply(densave, 2, hpdf)
              dens.l <- limm[1,]
              dens.u <- limm[2,]
           }

           cdf.m <- apply(cdfsave,2,mean)
           cdf.l <- NULL
           cdf.u <- NULL
           if(compute.band)
           {
              limm <- apply(cdfsave, 2, hpdf)
              cdf.l <- limm[1,]
              cdf.u <- limm[2,]
           }

           pnames<-NULL
           for(i in 2:p)
           {
               pnames <- c(pnames,paste("beta",i,sep=""))
           }
           pnames <- c(pnames,"mean","variance","mu","sigma2","alpha")
           colnames(thetasave) <- pnames
         
           qnames <- NULL
           for(i in 1:nsubject)
           {
               temp <- paste("theta(ID=",i,sep="")
               temp <- paste(temp,")",sep="")
               qnames <- c(qnames,temp)
           }
           qnames <- c(qnames,"theta(Prediction)")
           dimnames(randsave) <- list(NULL,qnames)
         
           coeff <- apply(thetasave, 2, mean)
         
           save.state <- list(thetasave=thetasave,
                              randsave=randsave,
							  densave=densave,
                              cdfsave=cdfsave)

         
		   acrate <- foo$acrate

		   z <- list(call=cl,
                     y=y,
                     modelname=model.name,
                     cpo=cpo,
					 prior=prior,
                     mcmc=mcmc,
                     state=state,
                     save.state=save.state,
					 nrec=nrec,
                     nsubject=nsubject, 
                     p=p,
                     alpharand=alpharand,
                     murand=murand,
                     sigmarand=sigmarand,
                     acrate=acrate,
                     coefficients=coeff,
                     dens=dens.m,
                     dens.l=dens.l,
                     dens.u=dens.u,
					 cdf=cdf.m,
                     cdf.l=cdf.l,
                     cdf.u=cdf.u,
                     grid=grid,
                     bf=foo$bf,
                     algo=algo,
                     cpov=foo$cpov)
                 
           cat("\n\n")
 	       class(z)<-c("FPTrasch")
  	       return(z)
}



###                    
### Tools
###
### Copyright: Alejandro Jara Vallejos, 2006
### Last modification: 24-09-2006.
###



"print.FPTrasch" <- function (x, digits = max(3, getOption("digits") - 3), ...) 
{
    cat("\n",x$modelname,"\n\nCall:\n", sep = "")
    print(x$call)
    cat("\n")

    if (length(x$coefficients)) {
        cat("Posterior Inference of Parameters:\n")
        if(x$alpharand==1){
        print.default(format(x$coefficients, digits = digits), print.gap = 2, 
            quote = FALSE)}
        if(x$alpharand==0){
        print.default(format(x$coefficients[1:(length(x$coefficients)-1)], digits = digits), print.gap = 2, 
            quote = FALSE)}

    }

    if(x$algo==1)
    {
       cat("\nAcceptance Rate for Metropolis Steps = ",x$acrate,"\n")    
    }
    cat("\nNumber of Observations:",x$nrec)
    cat("\nNumber of Groups:",x$nsubject,"\n")    
    cat("\n\n")
    invisible(x)
}



"summary.FPTrasch"<-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


### Difficulty parameters

    dimen1<-object$p-1

    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,]
    }

    names(coef.m)<-names(object$coefficients[1:dimen1])
    names(coef.sd)<-names(object$coefficients[1:dimen1])
    names(coef.se)<-names(object$coefficients[1:dimen1])
    names(coef.l)<-names(object$coefficients[1:dimen1])
    names(coef.u)<-names(object$coefficients[1:dimen1])

    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


### functionals

    mat<-thetasave[,(dimen1+1):(dimen1+2)]

    coef.p<-object$coefficients[(dimen1+1):(dimen1+2)]
    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,]
    }

    names(coef.m)<-names(object$coefficients[(dimen1+1):(dimen1+2)])
    names(coef.sd)<-names(object$coefficients[(dimen1+1):(dimen1+2)])
    names(coef.se)<-names(object$coefficients[(dimen1+1):(dimen1+2)])
    names(coef.l)<-names(object$coefficients[(dimen1+1):(dimen1+2)])
    names(coef.u)<-names(object$coefficients[(dimen1+1):(dimen1+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$functionals <-coef.table


### CPO
    ans$cpo<-object$cpo

### Baseline Information

	dimen1 <- dimen1 + 2

    dimen2 <- object$murand+object$sigmarand
 
    if(dimen2>0){
    
       if(dimen2==1)
       {
          if(object$murand==1)
          {
             mat<-matrix(thetasave[,dimen1+1],ncol=1) 
             coef.p<-object$coefficients[dimen1+1]
          }
          else
          {
             mat<-matrix(thetasave[,dimen1+2],ncol=1) 
             coef.p<-object$coefficients[dimen1+2]
          }
       }
       else
       {
          mat<-thetasave[,(dimen1+1):(dimen1+2)]
          coef.p<-object$coefficients[(dimen1+1):(dimen1+2)]
       }
    
       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))
    {
    }
    else
    {
      dimen3<-1
      coef.p<-object$coefficients[(dimen1+2+1)]
      mat<-matrix(thetasave[,(dimen1+2+1)],ncol=1)
      
      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
    }  


    ans$nrec <- object$nrec
    ans$nsubject <- object$nsubject
    ans$acrate <- object$acrate
    ans$algo <- object$algo  

    class(ans) <- "summaryFPTrasch"
    return(ans)
}


"print.summaryFPTrasch"<-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(as.vector(x$cpo))), digits = digits), print.gap = 2, 
            quote = FALSE) 
            
    if (length(x$coefficients)) {
        cat("\nDifficulty parameters:\n")
        print.default(format(x$coefficients, digits = digits), print.gap = 2, 
            quote = FALSE)
    }

    if (length(x$functionals)) {
        cat("\nFunctionals of the Random Effects:\n")
        print.default(format(x$functionals, 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)
    }

    if(x$algo==1)
    {
       cat("\nAcceptance Rate for Metropolis Steps = ",x$acrate,"\n")    
    }

    cat("\nNumber of Observations:",x$nrec)
    cat("\nNumber of Groups:",x$nsubject,"\n")
    cat("\n\n")
    invisible(x)
}


"plot.FPTrasch"<-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, "FPTrasch"))
   {
        if(is.null(param))
        {
           coef.p <- x$coefficients[1:(x$p+1)]
           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)
           {
               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=" ")
               fancydensplot1(x$save.state$thetasave[,i],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
           }

           if(x$murand==1)
           {
               title1 <- paste("Trace of","mu",sep=" ")
               title2 <- paste("Density of","mu",sep=" ")       
               plot(ts(x$save.state$thetasave[,x$p+2]),main=title1,xlab="MCMC scan",ylab=" ")
               fancydensplot1(x$save.state$thetasave[,x$p+2],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
           }

           if(x$sigmarand==1)
           {
               title1 <- paste("Trace of","sigma2",sep=" ")
               title2 <- paste("Density of","sigma2",sep=" ")       
               plot(ts(x$save.state$thetasave[,x$p+3]),main=title1,xlab="MCMC scan",ylab=" ")
               fancydensplot1(x$save.state$thetasave[,x$p+3],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
           }

           if(x$alpharand==1)
           {
               title1 <- paste("Trace of","alpha",sep=" ")
               title2 <- paste("Density of","alpha",sep=" ")       
               plot(ts(x$save.state$thetasave[,x$p+4]),main=title1,xlab="MCMC scan",ylab=" ")
               fancydensplot1(x$save.state$thetasave[,x$p+4],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
           }

           title1 <- c("Density Estimate")
           title2 <- c("CDF Estimate")
           plot(x$grid,x$dens,ylab="density",main=title1,lty=1,type='l',lwd=2,xlab="theta")
           plot(x$grid,x$cdf,ylab="probability",main=title2,lty=1,type='l',lwd=2,ylim=c(0,1),xlab="theta")

        }
   
        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 && param !="predictive")             
			{
				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))

			if(param !="predictive")
			{
				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=" ")
				fancydensplot1(x$save.state$thetasave[,poss],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
            }
            else
            {
				title1<-c("Density Estimate")
				title2<-c("CDF Estimate")
				plot(x$grid,x$dens,ylab="density",main=title1,lty=1,type='l',lwd=2,xlab="theta")
				plot(x$grid,x$cdf,ylab="probability",main=title2,lty=1,type='l',lwd=2,ylim=c(0,1),xlab="theta")
            }                

        }
   }

}