JAGS - hierarchical model comparison, not jumping between models even with pseudo-welds

Question

I use the hierarchical modeling framework described by Kruschke to establish a comparison between the two models in JAGS. The idea in this structure is to run and compare several versions of a model, indicating each version as one level of a categorical variable. Then the subsequent distribution of this categorical variable can be interpreted as the relative probability of various models.

In the code below, I am comparing two models. Models are identical in shape. Each of them has a single parameter to be estimated mE. As you can see, the models differ in their priorities. Both priorities are distributed as beta distributions, which have a mode of 0.5. However, the preliminary distribution for model 2 is much more concentrated. Please also note that I used pseudo-primers, which, I hoped, made the chains get stuck on one of the models. But the model is still stuck.

Here is the model:

 model {

  m ~ dcat( mPriorProb[] )
  mPriorProb[1] <- .5
  mPriorProb[2] <- .5

  omegaM1[1] <- 0.5      #true prior
  omegaM1[2] <- 0.5      #psuedo prior 
  kappaM1[1] <- 3        #true prior for Model 1
  kappaM1[2] <- 5        #puedo prior for Model 1

  omegaM2[1] <- 0.5      #psuedo prior
  omegaM2[2] <- 0.5      #true prior
  kappaM2[1] <- 5        #puedo  prior for Model 2
  kappaM2[2] <- 10        #true prior for Model 2

  for ( s in 1:Nsubj ) {

    mE1[s] ~ dbeta(omegaM1[m]*(kappaM1[m]-2)+1 , (1-omegaM1[m])*(kappaM1[m]-2)+1 )
    mE2[s] ~ dbeta(omegaM2[m]*(kappaM2[m]-2)+1 , (1-omegaM2[m])*(kappaM2[m]-2)+1 )

    mE[s] <- equals(m,1)*mE1[s] + equals(m,2)*mE2[s]

    z[s] ~ dbin( mE[s] , N[s] )

  }
}

Here is the R code for the relevant data:

dataList = list(
  z = c(81, 59, 36, 18, 28, 59, 63, 57, 42, 28, 47, 55, 38, 
        30, 22, 32, 31, 30, 32, 33, 32, 26, 13, 33, 30), 
  N = rep(96, 25),
  Nsubj = 25
)

, MCMC m = 1 m = 2. priors pseudo priors , MCMC m = 2. 1 2, . , MCMC , , , . , JAGS m = 1. 6000 , .

, - , .

Cheers,

Answer 1

, , , , , R rjags ( JAGS).

: , m ~ dcat() m ~ dbern(), m m+1 . , , . , m, , , m ( , ). ; http://sourceforge.net/p/mcmc-jags/discussion/

library(rjags)
load.module('glm')

dataList = list(
  z = c(81, 59, 36, 18, 28, 59, 63, 57, 42, 28, 47, 55, 38, 
        30, 22, 32, 31, 30, 32, 33, 32, 26, 13, 33, 30), 
  N = rep(96, 25),
  Nsubj = 25
)

sink("mymodel.txt")
cat("model {

  m ~ dbern(.5)

  omegaM1[1] <- 0.5      #true prior
  omegaM1[2] <- 0.5      #psuedo prior 
  kappaM1[1] <- 3        #true prior for Model 1
  kappaM1[2] <- 5        #puedo prior for Model 1

  omegaM2[1] <- 0.5      #psuedo prior
  omegaM2[2] <- 0.5      #true prior
  kappaM2[1] <- 5        #puedo  prior for Model 2
  kappaM2[2] <- 10        #true prior for Model 2

    for ( s in 1:Nsubj ) {

    mE1[s] ~ dbeta(omegaM1[m+1]*(kappaM1[m+1]-2)+1 , (1-omegaM1[m+1])*(kappaM1[m+1]-2)+1 )
    mE2[s] ~ dbeta(omegaM2[m+1]*(kappaM2[m+1]-2)+1 , (1-omegaM2[m+1])*(kappaM2[m+1]-2)+1 )


    z[s] ~ dbin( (1-m)*mE1[s] + m*mE2[s] , N[s] )

    }
    }
    ", fill=TRUE)
sink()
inits <- function(){list(m=0)}

params <- c("m")

nc <- 1
n.adapt <-100
n.burn <- 200
n.iter <- 5000
thin <- 1
mymodel <- jags.model('mymodel.txt', data = dataList, inits=inits, n.chains=nc, n.adapt=n.adapt)
update(mymodel, n.burn)
mymodel_samples <- coda.samples(mymodel,params,n.iter=n.iter, thin=thin)
summary(mymodel_samples)

Answer 2

, (phi ) . phi, 2 (.. "" m = 1; Pr ( 1) = 1-phi).

sink("mymodel.txt")
cat("model {

  m ~ dbern(phi)
  phi ~ dunif(0,1)

  omegaM1[1] <- 0.5      #true prior
  omegaM1[2] <- 0.5      #psuedo prior 
  kappaM1[1] <- 3        #true prior for Model 1
  kappaM1[2] <- 5        #puedo prior for Model 1

  omegaM2[1] <- 0.5      #psuedo prior
  omegaM2[2] <- 0.5      #true prior
  kappaM2[1] <- 5        #puedo  prior for Model 2
  kappaM2[2] <- 10       #true prior for Model 2

  for ( s in 1:Nsubj ) {

    mE1[s] ~ dbeta(omegaM1[m+1]*(kappaM1[m+1]-2)+1 , (1-omegaM1[m+1])*(kappaM1[m+1]-2)+1 )
    mE2[s] ~ dbeta(omegaM2[m+1]*(kappaM2[m+1]-2)+1 , (1-omegaM2[m+1])*(kappaM2[m+1]-2)+1 )

    z[s] ~ dbin( (1-m)*mE1[s] + m*mE2[s] , N[s] )

    }
  }
", fill=TRUE)
sink()
inits <- function(){list(m=0)}

params <- c("phi")

Answer 3

. .

, m, phi.

, ,

data <- c(-1, 0, 1, .5, .1)

m~dbern(phi)
data[i] ~ m*dnorm(0, 1) + (1-m)*dnorm(100, 1)

, , m 1. phi? , phi , , phi. , phi = 0.1 10% m = 1; phi = 0,5 50% m = 1. , phi, , m = 1. m.