Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data

Authors:
Francesco Bartolucci;Luisa Scaccia;Alessio Farcomeni
Affiliations:
Department of Economics, Finance and Statistics, University of Perugia, Italy;Department of Economic and Financial Institutions, University of Macerata, Italy;Department of Public Health and Infectious Diseases, Sapienza - University of Rome, Italy
Venue:
Computational Statistics & Data Analysis
Year:
2012

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Abstract

A Bayesian approach is developed for selecting the model that is most supported by the data within a class of marginal models for categorical variables, which are formulated through equality and/or inequality constraints on generalized logits (local, global, continuation, or reverse continuation), generalized log-odds ratios, and similar higher-order interactions. For each constrained model, the prior distribution of the model parameters is specified following the encompassing prior approach. Then, model selection is performed by using Bayes factors estimated through an importance sampling method. The approach is illustrated by three applications based on different datasets, which also include explanatory variables. In connection with one of these examples, a sensitivity analysis to the prior specification is also performed.