hbmem (version 0.3-4)

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)

Value

The function returns an internally defined "uvsd" S4 class that includes the following components

mu

Indexes which element of blocks contain grand means, mu

alpha

Indexes which element of blocks contain participant effects, alpha

beta

Indexes which element of blocks contain item effects, beta

s2alpha

Indexes which element of blocks contain variance of participant effects (alpha).

s2beta

Indexes which element of blocks contain variance of item effects (beta).

theta

Indexes which element of blocks contain theta, the slope of the lag effect

estN

Posterior means of block parameters for new-item means

estS

Posterior means of block parameters for studied-item means

estS2

Not used for gamma model.

estCrit

Posterior means of criteria

blockN

Each iteration for each parameter in the new-item mean block. Rows index iteration, columns index parameter.

blockS

Same as blockN, but for the studied-item means

blockS2

Not used for gamma model.

s.crit

Samples of each criteria.

pD

Number 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.

DIC

DIC value. Smaller values indicate better fits. Note that DIC is notably biased toward complexity.

M

Number of MCMC iterations run

keep

MCMC iterations that were used for estimation and returned

b0

Metropolis-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.

b0S2

Metropolis-Hastings acceptance rates for studied-item distribution parameters.

b0Crit

Metropolis-Hastings acceptance rates for criteria.

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.

M

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. If acceptance rates are too low, "jump" should be decreased, if they are too hight, "jump" should be increased. Alternatively, or in addition to adjusting "jump", simply increase the burnin period which will allow the function more time to self-tune.

Author

Michael S. Pratte

See Also

hbmem

Examples

#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=10 #set very small for demo speed
keep=2: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([e-mail][i,,]),t='l')