How to obtain new samples from ZIP or ZINB-model for bayesian p-value

Question

Hopefully someone can help me with this one, because I am really stuck and do not find my coding error!

I am fitting zero-inflated poisson / negative binomial GLMs (no random effects) in JAGS (with R2Jags) and everything is fine with the parameter estimates, priors, initial values and chains convergence. All results are perfectly in line with, e.g., the estimates from the pscl-package, including my calculation of pearson residuals in the model...

The only thing I cannot get to work is to sample from the model a new sample to obtain a bayesian p-value for evaluating the model fit. The "normal" poisson and negative binomial models I fit before all gave the expected replicated samples and no problems occured.

Here's my code so far, but the important part is "#New Samples":

model{
# 1. Priors
beta  ~ dmnorm(b0[], B0[,])   
aB    ~ dnorm(0.001, 1)

    #2. Likelihood function
    for (i in 1:N){  

    # Logistic part
    W[i]           ~ dbern(psi.min1[i])
    psi.min1[i]   <- 1 - psi[i]
    eta.psi[i]    <- aB
    logit(psi[i]) <- eta.psi[i]

    # Poisson part
    Y[i]           ~ dpois(mu.eff[i])
    mu.eff[i]     <- W[i] * mu[i]
    log(mu[i])    <- max(-20, min(20, eta.mu[i]))
    eta.mu[i]     <- inprod(beta[], X[i,])

    # Discrepancy measures:
    ExpY[i]       <- mu [i] * (1 - psi[i])
    VarY[i]       <- (1- psi[i]) * (mu[i] + psi[i] * pow(mu[i], 2))
    PRes[i]       <- (Y[i] - ExpY[i]) / sqrt(VarY[i])
    D[i]          <- pow(PRes[i], 2)

    # New Samples:
    YNew[i]        ~ dpois(mu.eff[i])
    PResNew[i]    <- (YNew[i] - ExpY[i]) / sqrt(VarY[i])
    DNew[i]       <- pow(PResNew[i], 2)
    } 
Fit         <- sum(D[1:N])
FitNew      <- sum(DNew[1:N])
}

The big problem is, that I really tried all combinations and alterations I think could/should work, but when I look at the simulated samples, I get this here:

> all.equal( Jags1$BUGSoutput$sims.list$YNew, Jags1$BUGSoutput$sims.list$Y )

[1] TRUE

And, to make it really weird, when using the means of Fit and FitNew:

> Jags1$BUGSoutput$mean$Fit
[1] 109.7883
> Jags1$BUGSoutput$mean$FitNew
[1] 119.2111

Has anyone a clue what I am doing wrong? Any help would be deeply appreciated!

Kind regards, Ulf

you are using Jags1$BUGSoutput$sims.list$Y, but this does not make sense, since Y is data, not output parameter, so it shouldn't have any simulations. — Tomas

Matt Denwood Matt Denwood · Accepted Answer · 2014-09-04T06:59:31

I suspect this isn't the case, but the only obvious reason I can suspect for Y[i] and YNew[i] being always identical is if mu.eff[i] is ~zero, either because W[i] is 0 or mu[i] is close to zero. This implies that Y[] is always zero, which is easy to check from your data, but as I said it does seem odd that you would be trying to model this... Otherwise, I'm not sure what is going on ... try simplifying the code to see if that solves the problem, and then add things back in until it breaks again. Some other suggestions:

It may be helpful for debugging to look at the absolute values of Y and YNew rather than just Y==YNew
If you want a negative binomial (= gamma-Poisson) try sampling mu[i] from a gamma distribution - I have used this formulation for ZINB models extensively, so am sure it works
Your prior for aB looks odd to me - it gives a prior 95% CI for zero inflation around 12-88% - is that what you intended? And why a mean of 0.001 not 0? If you have no predictors then a beta prior for psi.min seems more natural - and if you have no useful prior information a beta(1,1) prior would be an obvious choice.
Minor point but you are calculating a lot of deterministic functions of aB within the for loop - this is going to slow down your model...

Hope that helps,

Matt

How to obtain new samples from ZIP or ZINB-model for bayesian p-value

2 Answers