hbmem (version 0.3-4)

uvsdSample: Function uvsdSample

Description

Runs MCMC estimation for the hierarchical UVSD model.

Usage

uvsdSample(dat, M = 10000, keep = (M/10):M, getDIC = TRUE,
freeCrit=TRUE, equalVar=FALSE, freeSig2=FALSE, Hier=TRUE,jump=.0001)

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

Posterior means of block for studied-item variances.

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

Same as blockN, but for variances of studied-item distribution. If equalVar=TRUE, then these values are all zero. If UVSD is fit but freeSig2=FALSE, then only the first element is non-zero (mu).

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 decorrelating steps. These should be between .2 and .6. If they are not, the M, keep, or jump need to be adjusted.

b0S2

If additive model is placed on Sigma2 (i.e., freeSigma2=TRUE), then all parameters on S2 must be tuned. b0S2 are the acceptance probabilities for these parameters.

Arguments

dat

Data frame that must include variables Scond,cond,sub,item,lag,resp. Scond indexes studied/new, whereas cond indexes conditions nested within the studied or new conditions. Indexes for Scond,cond, sub, item, and response must start at zero and have no gaps (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. This should be set to false if there is only one participant, e.g., if averaging data over subjects.

equalVar

Logical. If FALSE (default), unequal-variance model is fit. If TRUE, equal-variance model is fit.

freeSig2

Logical. If FALSE (default), one sigma is fit for all participants and items (as in Pratte, et al., 2009). If TRUE, then an additive model is placed on the log of sigma2 (as in Pratte and Rouder (2010).

Hier

Logical. If TRUE then the variances of effects (e.g., item effects) are estimated from the data, i.e., effects are treated as random. If FALSE then these variances are fixed to 2.0 (.5 for recollection effects), thus treating these effects as fixed. This option is there to allow for compairson with more traditional approaches, and to see the effects of imposing hierarcical structure. It should always be set to TRUE in real analysis, and is not even guaranteed to work if set to false.

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

References

See Pratte, Rouder, & Morey (2009)

See Also

hbmem

Examples

#In this example we generate data from UVSD with a different muN,muS,and
#Sigma2 for every person and item. These data are then fit with 
#hierarchical UVSD allowing participant or item effects on log(sigma2).

library(hbmem)
sim=uvsdSim(NN=1,muN=-.5,NS=2,muS=c(.5,1),I=30,J=300,s2aN = .2, s2bN = .2,
muS2=log(c(1.3,1.5)),s2aS=.2,s2bS=.2,s2aS2=.2,s2bS2=.2)
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 #Way too low for real analysis
keep=2:M
uvsd=uvsdSample(dat,M=M,keep=keep,equalVar=FALSE,freeSig2=TRUE,jump=.0001,Hier=1)

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

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

#Sigma^2 effects
#Note that Sigma^2 is biased high with
#few participants and items.  This bias
#goes away with larger sample sizes.
par(mfrow=c(2,2),pch=19,pty='s')
matplot(sqrt(exp(uvsd@blockS2[,uvsd@muS])),t='l',xlab="Iteration",ylab="Mu-Sigma2")
abline(h=sqrt(exp(sim@muS2)),col="blue")
plot(uvsd@blockS2[,uvsd@thetaS],t='l')

plot(uvsd@estS2[uvsd@alphaS]~sim@alphaS2,xlab="True
Alpha-Sigma2",ylab="Est. Alpha-Sigma2");abline(0,1,col="blue")
plot(uvsd@estS2[uvsd@betaS]~sim@betaS2,xlab="True
Beta-Sigma2",ylab="Est. Beta-Sigma2");abline(0,1,col="blue")

#Look at some criteria
par(mfrow=c(2,2))
for(i in 1:4)
matplot(t([e-mail][i,,]),t='l')