AMS2003-7: Nonparametric Bayesian Modeling for Multivariate Ordinal Data

Athanasios Kottas, Peter Mueller and Fernando Quintana
12/31/2003 09:00 AM
Applied Mathematics & Statistics
We propose a probability model for k-dimensional ordinal outcomes, i.e., we consider inference for data recorded in k-dimensional contingency tables with ordinal factors. The proposed approach is based on full posterior inference, assuming a flexible underlying prior probability model for the contingency table cell probabilities. We use a variation of the traditional multivariate probit model, with latent scores that determine the observed data. In our model, a mixture of normals prior replaces the usual single multivariate normal model for the latent variables.

By augmenting the prior model to a mixture of normals we generalize inference in two important ways. First, we allow for different polychoric correlation coefficients across the contingency table. Second, inference in ordinal multivariate probit models is plagued by problems related to the choice and resampling of cutoffs defined for these latent variables.

We show how the proposed mixture model approach entirely removes these problems. We illustrate the methodology with two examples, one simulated data set and one data set of interrater agreement.

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