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Hello

Below are responses to questions I posed about covariates, priors and
model selection. It seems there are few ways to choose the best model in
WinBugs.

The way I am approaching this problem is somewhat Bayesian-like in that
I look at how the univariate model behaves in terms of the density and
history plots for beta, clustering and heterogeneity components of the
model. Depending on or conditional on which univariate models have sig.
values for beta and good history and density plots for unknown
paramters, I use them to contruct the full model. In this way DIC was
reduced and the model behaved well in terms of exploring the paramter
space, mixing of markov chains, etc.

I have not found any reason to reject nor accept this method as a valid
one since no literature to my knowledge exists about it yet! So any
comments or criticisms are welcome.

Thanks

Ayaz


Thanks to Dr. Finn Krogstadt and Dr. Glen D. Johnson for responses
below.


Question I asked was how to prioritize selection of models either by
lower DIC or better history plots and other output from WinBugs of
parameter space.

WRT #2, your DICs are essentially equal, so choose the model with the
stable "time series"  (I believe you mean the "trace plots" for
monitoring convergence and behavior of a Markov Chain wrt to your
coefficient beta). Also, if you are talking about traces, then you
should be monitoring at least 3 independednt Markov Chains and run the
iterations until all of the traces converge, overlapping each other and
varying like white noise with no trend.  The Gelman-Rubin diagnostics
were designed to monitor aspects of these traces in order to assess
convergence, but just looking at the traces will pretty much tell you if
you have convergence. Also, I caution you, given that I've worked alot
with these hierarchical spatial Poisson models, convergence does not
happen readily for linear coefficients associated with covariates.  It
works great for producing smoothed response variables, but not for
making inference about these linear coefficients.

> 3. IS THIS APPROACH VALID? -->
> I ran univariate models for 12 variables using 3 different
> priors which makes 36 models in total. Full model was chosen
> based on following
> criteria:
> -beta value for covariate is significant
> -tau.h and tau.c for non-spatial and spatial random effects,
> respectively, and beta value of covariate have a time-series
> plot which shows good mixing and low variation, i.e. not a
> very narrow band of values with large spikes in the estimate
> occuring randomly throughout the simulation.

Ayaz,
For model selection, there really is no substitute for the model
likelihood or posterior probability.  You might want to take a look at
the PINES example (in some example sets but not others).

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