SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

Contributions: Abstract

Testing models with inequality constraints in contingency tables using posterior predictive check distributions

Francisca Galindo-Garre Jeroen K. Vermunt
Tilburg University
The Netherlands

Assessing the goodness of fit of a model is a fundamental aspectof applied research. In contingency tables the likelihood-ratiostatistic is typically used to evaluate the discrepancy between theestimated frequencies and the data. In models with inequalityconstraints on the parameters the asymptotic distribution of thelikelihood-ratio statistic depends on unknown parameters and theassociated p values are not uniquely defined. Plug-in p valuesobtained by replacing the unknown parameters by their maximumlikelihood estimates may also be inconsistent if many of theconstraints imposed are not satisfied in the population.

In this paper, we describe the problems associated with the use ofclassical and plug-in p values. We propose posterior predictivecheck distributions as a better alternative to assess the modelfit when the model contains inequality constraints.