Generalizing the probability matrix decomposition model: An example of Bayesian model checking and model expansion
Michel Meulders, Andrew Gelman, Iven Van Mechelen, Paul De Boeck · 1998
Probability matrix decomposition (PMD) models can be used to explain observed associations between two sets of elements. More specifically, 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 fit 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 flat prior distribution is inappropriate. In order to solve this problem, a mixture prior density with two beta distributed components ...