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Runs MCMC for the hierarchical Gamma model
gammaSample(dat, M = 10000, keep = (M/10):M, getDIC = TRUE,
freeCrit=TRUE,shape=2,jump=.005)The function returns an internally defined "uvsd" S4 class that includes the following components
Indexes which element of blocks contain grand means, mu
Indexes which element of blocks contain participant effects, alpha
Indexes which element of blocks contain item effects, beta
Indexes which element of blocks contain variance of participant effects (alpha).
Indexes which element of blocks contain variance of item effects (beta).
Indexes which element of blocks contain theta, the slope of the lag effect
Posterior means of block parameters for new-item means
Posterior means of block parameters for studied-item means
Not used for gamma model.
Posterior means of criteria
Each iteration for each parameter in the new-item mean block. Rows index iteration, columns index parameter.
Same as blockN, but for the studied-item means
Not used for gamma model.
Samples of each criteria.
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 value. Smaller values indicate better fits. Note that DIC is notably biased toward complexity.
Number of MCMC iterations run
MCMC iterations that were used for estimation and returned
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.
Metropolis-Hastings acceptance rates for studied-item distribution parameters.
Metropolis-Hastings acceptance rates for criteria.
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.
Which MCMC iterations should be included in estimates and returned. Use keep to both get ride of burn-in, and thin chains if necessary
Logical. should the function compute DIC value? This takes a while if M is large.
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)
Fixed shape across both new and studied distributuions.
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.
Michael S. Pratte
hbmem
#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(gamma@s.crit[i,,]),t='l')
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