vasishth

data {
int<lower=1> N;
real rt[N];                         //outcome
real c1[N];                         //predictor
real c2[N];                         //predictor
real c3[N];                         //predictor
int<lower=1> I;                     //number of subjects
int<lower=1, upper=I> id[N];        //subject id
vector[4] mu_prior;                 //vector of zeros passed in from R
}

vasishth

Details:

key:
beta[1] = Intercept
beta[2] = c1
beta[3] = c2
beta[4] = c3

1. Fixed effects, Stan vs lmer:
Stan:

vasishth

model
{
# The model for each observational unit 
# (each row is a subject's data point)
for( j in 1:N )
{
mu[j] <- beta[1] + beta[2] * ( so[j] ) + u[subj[j]] + w[item[j]]
rt[j] ~ dnorm( mu[j], tau.e )
##change the above line to:
#rt[j] ~ dt(mu[j],tau.e, 2)

vasishth

newcomb <-
c(28,26,33,24,34,-44,27,16,40,-2,
29,22,24,21,25,30,23,29,31,19,
24,20,36,32,36,28,25,21,28,29,
37,25,28,26,30,32,36,26,30,22,
36,23,27,27,28,27,31,27,26,33,
26,32,32,24,39,28,24,25,32,25,
29,27,28,29,16,23)

# Data as a list

vasishth

> # Calculate the predicted random effects by hand for the ergoStool data
> (fm1<-lmer(effort~Type-1 + (1|Subject),ergoStool))
Linear mixed model fit by REML 
Formula: effort ~ Type - 1 + (1 | Subject) 
   Data: ergoStool 
 AIC BIC logLik deviance REMLdev
 133 143  -60.6      122     121
Random effects:
 Groups   Name        Variance Std.Dev.
 Subject  (Intercept) 1.78     1.33    

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> summary(lm<-lm(wear~material-1,BHHshoes))
> X<-model.matrix(lm)
> 2.49^2*solve(t(X)%*%X)
          materialA materialB
materialA   0.62001   0.00000
materialB   0.00000   0.62001

vasishth

> b1.vals<-subset(BHHshoes,material=="A")$wear
> b2.vals<-subset(BHHshoes,material=="B")$wear
> 
> vcovmatrix<-var(cbind(b1.vals,b2.vals))
> 
> covar<-vcovmatrix[1,2]
> sds<-sqrt(diag(vcovmatrix))
> covar/(sds[1]*sds[2])
b1.vals 
0.98823 

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> (lm.full<-lmer(wear~material-1+(1|Subject), data = BHHshoes))
Linear mixed model fit by REML 
Formula: wear ~ material - 1 + (1 | Subject) 
   Data: BHHshoes 
  AIC  BIC logLik deviance REMLdev
 62.9 66.9  -27.5     53.8    54.9
Random effects:
 Groups   Name        Variance Std.Dev.
 Subject  (Intercept) 6.1009   2.470   
 Residual             0.0749   0.274