sampleNormR {hbmem}R Documentation

Function sampleNormR

Description

Samples posterior of mean parameters of the hierarchical linear normal model with the effects a linear function of some other variable.

Usage

sampleNormR(sample, phi,blockD,y,subj, item, lag, I, J, R, nsub, nitem,
    s2mu, s2a, s2b, meta, metb, sigma2, sampLag)

Arguments

sample Block of linear model parameters from previous iteration.
y Vector of data
phi Vector of linear slopes on effects.
blockD Block of parameters that will serve as the means of random effects
subj Vector of subject index, starting at zero.
item Vector of item index, starting at zero.
lag Vector of lag index, zero-centered.
I Number of subjects.
J Number of items.
R Total number of trials.
nsub Vector of length (I) containing number of trials per each subject.
nitem Vector of length (J) containing number of trials per each item.
s2mu Prior variance on the grand mean mu; usually set to some large number.
s2a Shape parameter of inverse gamma prior placed on effect variances.
s2b Rate parameter of inverse gamma prior placed on effect variances. Setting both s2a AND s2b to be small (e.g., .01, .01) makes this an uninformative prior.
meta Matrix of tuning parameter for metropolis-hastings decorrelating step on mu and alpha. This hould be adjusted so that .2 < b0 < .6.
metb Tunning parameter for decorrelating step on alpha and beta.
sigma2 Variance of distribution.
sampLag Logical. Whether or not to sample the lag effect.

Value

The function returns a list. The first element of the list is the newly sampled block of parameters. The THIRD element contains a vector of 0s and 1s indicating which of the decorrelating steps were accepted.

Author(s)

Michael S. Pratte

References

Not published yet.

See Also

hbmem

Examples

library(hbmem)

I=50
J=100
M=500
B=I+J+4
mu=.5
muS2=0
s2a=.2
s2b=.2
s2aS2=0
s2bS2=0

phi=c(.2,.08)
blockD=rep(0,B)
blockD[2:(I+1)]=rnorm(I,0,.5)
blockD[(I+2):(I+J+1)]=rnorm(J,0,.5)

    R = I * J
    alpha = rnorm(I, phi[1]*blockD[2:(I+1)], sqrt(s2a))
    beta =  rnorm(J, phi[2]*blockD[(I+2):(I+J+1)], sqrt(s2b))
    alphaS2 = rnorm(I, 0, sqrt(s2aS2))
    betaS2 = rnorm(J, 0, sqrt(s2bS2))
    subj = rep(0:(I - 1), each = J)
    item = rep(0:(J - 1), I)
    lag = rep(0, R)
    resp = 1:R
    for (r in 1:R) {
        mean = mu + alpha[subj[r] + 1] + beta[item[r] + 1]
        sd = sqrt(exp(muS2 + alphaS2[subj[r] + 1] + betaS2[item[r] + 1]))
        resp[r] = rnorm(1, mean, sd)
    }
    sim=(as.data.frame(cbind(subj, item, lag, resp)))


blockR=matrix(0,M,B)
blockR[1,c(I+J+2,I+J+3)]=c(.1,.1)
met=c(.1,.1)
b0=c(0,0)

for(m in 2:M)
  {
tmp=sampleNormR(blockR[m-1,],phi,blockD,sim$resp,sim$subj,sim$item,sim$lag,I,J,I*J,table(sim$sub),table(sim$item),10,.01,.01,met[1],met[2],1,1)
blockR[m,]=tmp[[1]]
b0=b0+tmp[[3]]
}

est=colMeans(blockR)

par(defpar(2,3))
plot(blockR[,1],t='l')
abline(h=mu,col="blue")
plot(blockR[,I+J+2],t='l')
abline(h=s2a,col="blue")
plot(blockR[,I+J+3],t='l')
abline(h=s2b,col="blue")

plot(est[2:(I+1)]~alpha);abline(0,1,col="blue")
plot(est[(I+2):(I+J+1)]~beta);abline(0,1,col="blue")

#Compare estimates from regular normal ones:

s.block=matrix(0,nrow=M,ncol=B)
met=c(.1,.1);b0=c(0,0)
for(m in 2:M)
{
tmp=sampleNorm(s.block[m-1,],sim$resp,rep(0,length(sim$resp)),sim$subj,sim$item,sim$lag,1,I,J,R,R,table(sim$subj),
table(sim$item),100,.01,.01,met[1],met[2],1,1)
s.block[m,]=tmp[[1]]
b0=b0 + tmp[[2]]
}

est2=colMeans(s.block)

par(defpar(1,2))
plot(est[2:(I+1)]~est2[2:(I+1)]);abline(0,1,col="blue")
plot(est[(I+2):(I+J+1)]~est2[(I+2):(I+J+1)]);abline(0,1,col="blue")



[Package hbmem version 0.2 Index]