Dept Statistics, University of Auckland
University of Waikato, Room I.1.09 (I block, 1st floor)
The deviance information criterion (DIC) was found to be a potentially dangerous tool for comparison between hierarchical models of count data and the results herein show that it has been used inappropriately in several recent publications that have employed these models. DIC was
useful only when the likelihood was expressed at the subject level, and so it can be used for comparison between the Poisson and negative binomial.
In addition, despite zero-inflation being a form of mixture, the DIC also performed well for comparison of the Poisson and negative binomial with their zero-inflated counterparts.
However, DIC was not reliable for likelihoods expressed at the replicate level, and it can not be used to distinguish between Poisson-gamma (the negative binomial implemented at replicate level) and Poisson-lognormal models, or to assess whether these models require zero-inflation.
For example, when fitting Poisson-gamma and oisson-lognormal models to simulated Poisson-lognormal data, the oisson-gamma model always had lower DIC. Bayesian predictive checks (BPCs) were also investigated and were found to be extremely conservative.
For example, under 100 simulations of the Poisson model fitted to Poisson data, the lower 5% quantile of the BPC p-value for goodness of fit was approximately 0.3.