===== Bayesian exploratory factor analysis using informative priors =====
==== Data generation ====
<code>
model{
   for (i in 1:N){
     f[i,1:2]~dmnorm(muf[1:2], pre.phi[1:2,1:2])
     for (j1 in 1:6){
         muy[i,j1]<-l1[j1]*f[i,1]+l2[j1]*f[i,2]
         y[i,j1]~dnorm(muy[i,j1],pre.p[j1])
     }
   }
}
list(N=200, l1=c(.6,.6,.6,0,0,0), l2=c(0,0,0, .6,.6,.6),
muf=c(0,0),
pre.p=c(1.5625,1.5625, 1.5625, 2.78, 2.78, 2.78),
pre.phi=structure(.Data =c(1.33, -0.67, -.67, 1.33), .Dim = c(2,2)))
</code>
==== Data analysis ====

<code>
model{
   for (i in 1:N){
     f[i,1:2]~dmnorm(muf[1:2], pre.phi[1:2,1:2])
     for (j1 in 1:6){
         muy[i,j1]<-l1[j1]*f[i,1]+l2[j1]*f[i,2]
         y[i,j1]~dnorm(muy[i,j1],pre.p[j1])
     }
   }
muf[1]<-0
muf[2]<-0
for (i in 1:6){
  l1[i]~dbeta(.5, .5)
  l2[i]~dbeta(.5,.5)
  pre.p[i]~dgamma(.001,.001)
}

pre.phi[1:2,1:2]<-inverse(phi[1:2,1:2])
   phi[1,1]<-1
   phi[2,2]<-1
   phi[1,2]~dunif(0,1)
   phi[2,1]<-phi[1,2]
}

list( 
pre.p=c(1.5625,1.5625, 1.5625, 2.78, 2.78, 2.78),
phi=structure(.Data =c(NA, 0, NA, NA), .Dim = c(2,2)))

list(N=200, y = structure(.Data = c(
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.Dim = c(200,6)))
</code>