gammaSample: Function gammaSample

Description

Runs MCMC for the hierarchical Gamma model

Usage

gammaSample(dat, M = 10000, keep = (M/10):M, getDIC = TRUE,
freeCrit=TRUE,shape=2,jump=.005)

Arguments

dat

Data frame that must include variables cond,sub,item,lag,resp. Indexes for cond, sub, item, and respone must start at zero and have no gapes (i.e., no skipped subject numbers). Lags must be zero-centered.

Number of MCMC iterations.

keep

Which MCMC iterations should be included in estimates and returned. Use keep to both get ride of burn-in, and thin chains if necessary

getDIC

Logical. should the function compute DIC value? This takes a while if M is large.

freeCrit

Logical. If TRUE (default) individual criteria vary across people. If false, all participants have the same criteria (but note that overall response biases are still modeled in the means)

shape

Fixed shape across both new and studied distributuions.

jump

The criteria and decorrelating steps utilize Matropolis-Hastings sampling routines, which require tuning. All MCMC functions should self tune during the burnin perior (iterations before keep), and they will alert you to the success of tuning.

Value

The function returns an internally defined "uvsd" S4 class that includes the following components
muIndexes which element of blocks contain grand means, mu
alphaIndexes which element of blocks contain participant effects, alpha
betaIndexes which element of blocks contain item effects, beta
s2alphaIndexes which element of blocks contain variance of participant effects (alpha).
s2betaIndexes which element of blocks contain variance of item effects (beta).
thetaIndexes which element of blocks contain theta, the slope of the lag effect
estNPosterior means of block parameters for new-item means
estSPosterior means of block parameters for studied-item means
estS2Not used for gamma model.
estCritPosterior means of criteria
blockNEach iteration for each parameter in the new-item mean block. Rows index iteration, columns index parameter.
blockSSame as blockN, but for the studied-item means
blockS2Not used for gamma model.
s.critSamples of each criteria.
pDNumber of effective parameters used in DIC. Note that this should be smaller than the actual number of parameters, as constraint from the hierarchical structure decreases the number of effective parameters.
DICDIC value. Smaller values indicate better fits. Note that DIC is notably biased toward complexity.
MNumber of MCMC iterations run
keepMCMC iterations that were used for estimation and returned
b0Metropolis-Hastings acceptance rates for new-item distribution parameters. These should be between .2 and .6. If they are not, the M, keep, or jump need to be adjusted.
b0S2Metropolis-Hastings acceptance rates for studied-item distribution parameters.
b0CritMetropolis-Hastings acceptance rates for criteria.

Examples

Run this code

#make data from gamma model
library(hbmem)
sim=gammaSim(I=30,J=200)
dat=as.data.frame(cbind(sim@subj,sim@item,sim@cond,sim@Scond,sim@lag,sim@resp))
colnames(dat)=c("sub","item","cond","Scond","lag","resp")

M=200 #set very small for demo speed
keep=50:M
gamma=gammaSample(dat,M=M,keep=keep,jump=.01)

par(mfrow=c(3,2),pch=19,pty='s')
#Look at chains of MuN and MuS
matplot(gamma@blockN[,gamma@muN],t='l',xlab="Iteration",ylab="Mu-N")
abline(h=sim@muN,col="blue")
matplot(gamma@blockS[,gamma@muS],t='l',xlab="Iteration",ylab="Mu-S")
abline(h=sim@muS,col="blue")

#Estimates of Alpha as function of true values
plot(gamma@estN[gamma@alphaN]~sim@alphaN,xlab="True
Alpha-N",ylab="Est. Alpha-N");abline(0,1,col="blue")
plot(gamma@estS[gamma@alphaS]~sim@alphaS,xlab="True
Alpha-S",ylab="Est. Alpha-S");abline(0,1,col="blue")
#Estimates of Beta as function of true values
plot(gamma@estN[gamma@betaN]~sim@betaN,xlab="True
Beta-N",ylab="Est. Beta-N");abline(0,1,col="blue")
plot(gamma@estS[gamma@betaS]~sim@betaS,xlab="True
Beta-S",ylab="Est. Beta-S");abline(0,1,col="blue")

gamma@estN[c(gamma@s2alphaN,gamma@s2betaN)]
gamma@estS[c(gamma@s2alphaS,gamma@s2betaS)]


#Look at some criteria
par(mfrow=c(2,2))
for(i in 1:4)
matplot(t(gamma@s.crit[i,,]),t='l')

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Description

Usage

Arguments

Value

See Also

Examples