Deviance and DIC in missing data models

[Corey Sparks]

Hello,
I am using INLA to fit some space-time small area estimate models for poverty rates in the US.  I have lots of missing data, as many areas do not have annual estimates, so i'm trying to use INLA to estimate them. My question is about how INLA calculates Deviance or DIC in missing data models.  I assume that for missing data, no deviance is calculated for the missing element, for example of what I'm doing here are some fake data:

N<-rpois(n=1000, lambda=30000)
Y<-rbinom(n=1000, size=N,prob=.15 )
t<-c(rep(1,100),rep(2,100),rep(3,100),rep(4,100),rep(5,100),rep(6,100),rep(7,100),rep(8,100),rep(9,100),rep(10,100) )
id<-rep(1:100, 10)
test2<-data.frame(Y=Y, N=N, time=t, id=id)

missing<-sample(1:1000, size=100, replace=F)
test2$Y[missing]<-NA
test2$N[missing]<-NA

mod2<-Y~1+f(id, model="iid")+f(time, model="rw1")

fit2<-inla(formula=mod2, Ntrials=N, data=test2, family="binomial",
           control.compute=list(dic=1), control.predictor=list(compute=T, link=1))

summary(fit2)

which gives:

Model hyperparameters:
                   mean      sd        0.025quant 0.5quant  0.975quant
Precision for id   116872.86  36116.54  61522.23  111741.34 202038.93 
Precision for time  75770.56  35286.15  26385.42   69601.49 161624.15 

Expected number of effective parameters(std dev): 82.17(4.928)
Number of equivalent replicates : 10.95 

Deviance Information Criterion: 9931.07
Effective number of parameters: 82.41

Marginal Likelihood:  -4973.84 
Posterior marginals for linear predictor and fitted values computed

Does this DIC have any information from the missing data?  In Win/OpenBUGS missing data models can often give negative DIC values, or DIC is not interpretable, so how is INLA doing this, and is the DIC interpretable in missing data models?
I would be most grateful for any advice

Corey

[INLA help]

DIC only use the observed data, missing data are not used.

[Corey Sparks]

so if I had 2 models fit to estimate the missing data, with different parameterizations, would the DICs be comparable between them, as they would be normally in the non-missing case?

[INLA help]

On Fri, 2012-11-02 at 09:30 -0700, Corey Sparks wrote:
> so if I had 2 models fit to estimate the missing data, with different
> parameterizations, would the DICs be comparable between them, as they
> would be normally in the non-missing case?

if you estimate missing data within inla, which is sometimes possible
using a joint model, then the DIC is computed using the observed data
only. if you estimate missing data outsida inla, using some other
methods, and feed these also into inla together with the observed data,
then the DIC would use both of them.

Best
H


--
INLA help <he...@r-inla.org>
R-INLA

[wangji...@gmail.com]

Are there any examples available using INLA to build a joint model for sampling model and missing data?