Title: Generalizing the probability matrix decomposition model: An example of Bayesian model checking and expansion
Authors: Meulders, Michel
Gelman, Andrew
Van Mechelen, Iven
De Boeck, Paul
Editors: Hox, Joop J
De Leeuw, Edith
Issue Date: 1998
Publisher: TT Publications
Host Document: Assumptions, robustness, and estimation methods in multivariate modeling pages:1-19
Conference: Working group on Structural Equation Modeling and the Netherlands Society for Statistics and Operations Research location:Utrecht date:1997
Abstract: 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 is used to expand the model in a meaningful way.
Publication status: published
KU Leuven publication type: IC
Appears in Collections:Faculty of Economics and Business (FEB) - miscellaneous
Quantitative Psychology and Individual Differences
Research Centre for Quantitative Business Processes, Campus Brussels (-)

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