Generalizing the probability matrix decomposition model: An example of Bayesian model checking and model expansion
Probability matrix decomposition (PMD) models can be used to explain observed associations between two sets of elements. More speciically, observed associations are modeled as a deterministic function of B latent Bernoulli variables that are realized for each element. To estimate the parameters of this model, a sample of the posterior distribution is computed with a data augmentation algorithm. The obtained posterior sample can also be used to assess the t of the model with the technique of posterior predictive checks. In this paper a PMD model is applied to data on psychiatric diagnosis. In checking the model for this analysis, we focus on the appropriateness of the prior distribution for a set of latent parameters. Based on the posterior distribution for the values of the parameters corresponding to the observed data, we conclude that a relatively at prior distribution is inappropriate. In order to solve this problem, a mixture prior density with two beta distributed components is used to expand the model in a meaningful way.