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Dear Allstat, I'm trying to identify an appropriate, calculable, Information criterion for model selection in the following circumstances. I've fitted a Markov disease progression model to a set of censored (several types) individual level data for patients with HIV. The transition rates are modeled on the log-rate scale and the baseline parameter allows for the possibility of tracking (i.e. where persons who's Cd4% has declined more quickly in the past are more likely to do so in the future). For each person, there is an estimated probability that his or her baseline rate is that of a fast tracker vs. a slow tracker. This means I have fitted a mixture model where the likelihood function for each observation includes multiple parameters that are nonlinearly correlated (due to censoring). I have a couple of questions relating to this problem: Firstly, Aside from the problem of mixing: - Because the data are censored, the likelihood function for each observation includes multiple non-linearly correlated parameters. This means, I think, that even if the mixing distribution is properly accounted for using the methods described in Celeux et al 2006, the DIC will still not be calculable. This is because when estimating the Deviance calculated at the posterior mean/median/mode (D.hat) the results are incorrect because of the non-linear correlations. Is this correct? If so does the same problem arise when estimating the BIC or the AIC? I have looked at the slideshow from IceBUGS and didn't quite understand how the first term in the BIC and AIC should be calculated for a model that is not hierarchical (D.Hat,D.Bar?). Also, is it reasonable to use the pV as an estimate of the parameters in the AIC or BIC. Secondly: Is a mixture model a type of hierarchical model? and are we expecting in this example for the effective number of parameters to be very high (1 per person for the mixture model + a few other covariates). Does the pV (or pD(2) in Gelman et al 2004) provide a useful estimate in a mixture model? I calculated it for the eyes Normal mixture model example and found that pV = 58. I was unsure if this is a robust estimate of the effective number of parameters for this model and entirely unsurprising, or if I have inappropriately used the statistic? Thirdly, I have found that all of these different measures are fairly disparately reported and I have not found a single source that explains everything fully. Does anyone know of a textbook that does this? As far as I can make out the only calculable statistics would be the posterior mean deviance + either the pV, or the total number of parameters in the linear predictors for the log-rates excluding the individual level mixing probabilities. Possibly adjusted to account for sample size as in the BIC. Thank you very much for any help you can offer Best Wishes Malcolm Price PHD Student University of Bristol - Dept. Social Medicine [log in to unmask] --