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FilconModelCompPseudoPriorBrugs.R
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graphics.off()
rm(list=ls(all=TRUE))
library(BRugs) # Kruschke, J. K. (2010). Doing Bayesian data analysis:
# A Tutorial with R and BUGS. Academic Press / Elsevier.
#------------------------------------------------------------------------------
# THE MODEL.
modelstring = "
# BUGS model specification begins here...
model {
for ( i in 1:nSubj ) {
# Likelihood:
nCorrOfSubj[i] ~ dbin( theta[i] , nTrlOfSubj[i] )
# Prior on theta: Notice nested indexing.
theta[i] ~ dbeta( aBeta[ CondOfSubj[i] ] ,
bBeta[ CondOfSubj[i] ] )I(0.0001,0.9999)
}
# Hyperprior on mu and kappa:
kappa0 ~ dgamma( shk0[mdlIdx] , rak0[mdlIdx] )
for ( j in 1:nCond ) {
mu[j] ~ dbeta( aHyperbeta , bHyperbeta )
kappa[j] ~ dgamma( shk[j,mdlIdx] , rak[j,mdlIdx] )
}
for ( j in 1:nCond ) {
aBeta[j] <- mu[j] * ((kappa[j]*(2-mdlIdx))+(kappa0*(mdlIdx-1)))
bBeta[j] <- (1-mu[j]) * ((kappa[j]*(2-mdlIdx))+(kappa0*(mdlIdx-1)))
# BUGS equals(,) won't work here, for no apparent reason.
# Took me hours to isolate this problem (argh!). So, DO NOT use:
# aBeta[j] <- mu[j] * (kappa[j]*equals(mdlIdx,1)+kappa0*equals(mdlIdx,2))
# bBeta[j] <- (1-mu[j]) * (kappa[j]*equals(mdlIdx,1)+kappa0*equals(mdlIdx,2))
}
# Constants for hyperprior:
aHyperbeta <- 1
bHyperbeta <- 1
# Actual priors:
shP <- 1.0 # shape for prior
raP <- 0.1 # rate for prior
# shape, rate kappa0[ model ]
shk0[2] <- shP
rak0[2] <- raP
# shape kappa[ condition , model ]
shk[1,1] <- shP
shk[2,1] <- shP
shk[3,1] <- shP
shk[4,1] <- shP
# rate kappa[ condition , model ]
rak[1,1] <- raP
rak[2,1] <- raP
rak[3,1] <- raP
rak[4,1] <- raP
# Pseudo priors:
# shape, rate kappa0[ model ]
shk0[1] <- 54.0
rak0[1] <- 4.35
# shape kappa[ condition , model ]
shk[1,2] <- 11.8
shk[2,2] <- 11.9
shk[3,2] <- 13.6
shk[4,2] <- 12.6
# rate kappa[ condition , model ]
rak[1,2] <- 1.34
rak[2,2] <- 1.11
rak[3,2] <- 0.903
rak[4,2] <- 0.748
# Hyperprior on model index:
mdlIdx ~ dcat( modelProb[] )
modelProb[1] <- .5
modelProb[2] <- .5
}
# ... end BUGS model specification
" # close quote for modelstring
# Write model to a file:
.temp = file("model.txt","w") ; writeLines(modelstring,con=.temp) ; close(.temp)
# Load model file into BRugs and check its syntax:
modelCheck( "model.txt" )
#------------------------------------------------------------------------------
# THE DATA.
# For each subject, specify the condition s/he was in,
# the number of trials s/he experienced, and the number correct.
# (These lines intentionally exceed the margins so that they don't take up
# excessive space on the printed page.)
CondOfSubj = c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4)
nTrlOfSubj = c(64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64)
nCorrOfSubj = c(45,63,58,64,58,63,51,60,59,47,63,61,60,51,59,45,61,59,60,58,63,56,63,64,64,60,64,62,49,64,64,58,64,52,64,64,64,62,64,61,59,59,55,62,51,58,55,54,59,57,58,60,54,42,59,57,59,53,53,42,59,57,29,36,51,64,60,54,54,38,61,60,61,60,62,55,38,43,58,60,44,44,32,56,43,36,38,48,32,40,40,34,45,42,41,32,48,36,29,37,53,55,50,47,46,44,50,56,58,42,58,54,57,54,51,49,52,51,49,51,46,46,42,49,46,56,42,53,55,51,55,49,53,55,40,46,56,47,54,54,42,34,35,41,48,46,39,55,30,49,27,51,41,36,45,41,53,32,43,33)
nSubj = length(CondOfSubj)
nCond = length(unique(CondOfSubj))
# Specify the data in a form that is compatible with BRugs model, as a list:
datalist = list(
nCond = nCond ,
nSubj = nSubj ,
CondOfSubj = CondOfSubj ,
nTrlOfSubj = nTrlOfSubj ,
nCorrOfSubj = nCorrOfSubj
)
# Get the data into BRugs:
# Function bugsData stores the data file (default filename is data.txt).
# Function modelData loads data file into BRugs (default filename is data.txt).
modelData( bugsData( datalist ) )
#------------------------------------------------------------------------------
# INTIALIZE THE CHAINS.
nchain = 1
modelCompile( numChains=nchain )
modelGenInits()
#------------------------------------------------------------------------------
# RUN THE CHAINS.
burninSteps = 1000
modelUpdate( burninSteps )
samplesSet( c("mu","kappa","kappa0","theta","mdlIdx") )
nPerChain = 10000
modelUpdate( nPerChain , thin=1 ) # takes nPerChain * thin steps
#------------------------------------------------------------------------------
# EXAMINE THE RESULTS.
filenamebase = "FilconModelCompPseudoPriorBrugs"
modelIdxSample = samplesSample( "mdlIdx" )
pM1 = sum( modelIdxSample == 1 ) / length( modelIdxSample )
pM2 = 1 - pM1
string1 =paste("p(M1|D)=",round(pM1,3),sep="")
string2 =paste("p(M2|D)=",round(pM2,3),sep="")
windows(10,4)
plot( 1:length(modelIdxSample) , modelIdxSample , type="l" ,
xlab="Step in Markov chain" , ylab="Model Index (1, 2)" ,
main=paste(string1,", ",string2,sep="") )
dev.copy2eps(file=paste(filenamebase,"_mdlIdx",".eps",sep=""))
kappa0sampleM1 = samplesSample( "kappa0" )[ modelIdxSample == 1 ]
kappa0sampleM2 = samplesSample( "kappa0" )[ modelIdxSample == 2 ]
windows()
layout( matrix(1:2,nrow=2) )
hist( kappa0sampleM1 , main="Post. kappa0 for M = 1" ,
xlab=expression(kappa[0]) , xlim=c(0,30) , freq=F , ylab="" ,
col="grey" , border="white" , cex.lab=1.75 , breaks=c(seq(0,30,len=19),10000) )
lines( seq(0,30,.1) , dgamma( seq(0,30,.1) , 1 , .1 ) )
hist( kappa0sampleM2 , main="Post. kappa0 for M = 2" ,
xlab=expression(kappa[0]) , xlim=c(0,30) , freq=F , ylab="" ,
col="grey" , border="white" , cex.lab=1.75 , breaks=c(seq(0,30,len=19),10000) )
dev.copy2eps(file=paste(filenamebase,"_k0",".eps",sep=""))
kappa1sampleM1 = samplesSample( "kappa[1]" )[ modelIdxSample == 1 ]
kappa2sampleM1 = samplesSample( "kappa[2]" )[ modelIdxSample == 1 ]
kappa3sampleM1 = samplesSample( "kappa[3]" )[ modelIdxSample == 1 ]
kappa4sampleM1 = samplesSample( "kappa[4]" )[ modelIdxSample == 1 ]
kappa1sampleM2 = samplesSample( "kappa[1]" )[ modelIdxSample == 2 ]
kappa2sampleM2 = samplesSample( "kappa[2]" )[ modelIdxSample == 2 ]
kappa3sampleM2 = samplesSample( "kappa[3]" )[ modelIdxSample == 2 ]
kappa4sampleM2 = samplesSample( "kappa[4]" )[ modelIdxSample == 2 ]
windows(10,5)
layout( matrix(1:8,nrow=2,byrow=T) )
hist( kappa1sampleM1 , main="Post. kappa[1] for M = 1" ,
xlab=expression(kappa[1]) , xlim=c(0,30) , freq=F , ylab="" ,
col="grey" , border="white" , cex.lab=1.75 , breaks=c(seq(0,30,len=19),10000) )
hist( kappa2sampleM1 , main="Post. kappa[2] for M = 1" ,
xlab=expression(kappa[2]) , xlim=c(0,30) , freq=F , ylab="" ,
col="grey" , border="white" , cex.lab=1.75 , breaks=c(seq(0,30,len=19),10000) )
hist( kappa3sampleM1 , main="Post. kappa[3] for M = 1" ,
xlab=expression(kappa[3]) , xlim=c(0,30) , freq=F , ylab="" ,
col="grey" , border="white" , cex.lab=1.75 , breaks=c(seq(0,30,len=19),10000) )
hist( kappa4sampleM1 , main="Post. kappa[4] for M = 1" ,
xlab=expression(kappa[4]) , xlim=c(0,30) , freq=F , ylab="" ,
col="grey" , border="white" , cex.lab=1.75 , breaks=c(seq(0,30,len=19),10000) )
hist( kappa1sampleM2 , main="Post. kappa[1] for M = 2" ,
xlab=expression(kappa[1]) , xlim=c(0,30) , freq=F , ylab="" ,
col="grey" , border="white" , cex.lab=1.75 , breaks=c(seq(0,30,len=19),10000) )
lines( seq(0,30,.1) , dgamma( seq(0,30,.1) , 1 , .1 ) )
hist( kappa2sampleM2 , main="Post. kappa[2] for M = 2" ,
xlab=expression(kappa[2]) , xlim=c(0,30) , freq=F , ylab="" ,
col="grey" , border="white" , cex.lab=1.75 , breaks=c(seq(0,30,len=19),10000) )
lines( seq(0,30,.1) , dgamma( seq(0,30,.1) , 1 , .1 ) )
hist( kappa3sampleM2 , main="Post. kappa[3] for M = 2" ,
xlab=expression(kappa[3]) , xlim=c(0,30) , freq=F , ylab="" ,
col="grey" , border="white" , cex.lab=1.75 , breaks=c(seq(0,30,len=19),10000) )
lines( seq(0,30,.1) , dgamma( seq(0,30,.1) , 1 , .1 ) )
hist( kappa4sampleM2 , main="Post. kappa[4] for M = 2" ,
xlab=expression(kappa[4]) , xlim=c(0,30) , freq=F , ylab="" ,
col="grey" , border="white" , cex.lab=1.75 , breaks=c(seq(0,30,len=19),10000) )
lines( seq(0,30,.1) , dgamma( seq(0,30,.1) , 1 , .1 ) )
dev.copy2eps(file=paste(filenamebase,"_kcond",".eps",sep=""))
source("plotPost.R")
windows(10,5)
layout( matrix(1:6,nrow=2,byrow=T) )
histInfo = plotPost( kappa1sampleM1 - kappa2sampleM1 , cex.lab=2 ,
xlab=bquote(kappa[1] -kappa[2]) , compVal=0 , breaks=20 )
histInfo = plotPost( kappa1sampleM1 - kappa3sampleM1 , cex.lab=2 ,
xlab=bquote(kappa[1] -kappa[3]) , compVal=0 , breaks=20 )
histInfo = plotPost( kappa1sampleM1 - kappa4sampleM1 , cex.lab=2 ,
xlab=bquote(kappa[1] -kappa[4]) , compVal=0 , breaks=20 )
histInfo = plotPost( kappa2sampleM1 - kappa3sampleM1 , cex.lab=2 ,
xlab=bquote(kappa[2] -kappa[3]) , compVal=0 , breaks=20 )
histInfo = plotPost( kappa2sampleM1 - kappa4sampleM1 , cex.lab=2 ,
xlab=bquote(kappa[2] -kappa[4]) , compVal=0 , breaks=20 )
histInfo = plotPost( kappa3sampleM1 - kappa4sampleM1 , cex.lab=2 ,
xlab=bquote(kappa[3] -kappa[4]) , compVal=0 , breaks=20 )
dev.copy2eps(file=paste(filenamebase,"_kdiff",".eps",sep=""))