Inferential Implications of Over-Parametrization: A Case Study in Incomplete Categorical Data

Abstract

In the context of either Bayesian or classical sensitivity analyses of over-parametrized models for incomplete categorical data, it is well known that prior-dependence on posterior inferences of nonidentifiable parameters or that too parsimonious over-parametrized models may lead to erroneous conclusions. Nevertheless, some authors either pay no attention to which parameters are nonidentifiable or do not appropriately account for possible prior-dependence. We review the literature on this topic and consider simple examples to emphasize that in both inferential frameworks, the subjective components can influence results in nontrivial ways, irrespectively of the sample size. Specifically, we show that prior distributions commonly regarded as slightly informative or noninformative may actually be too informative for nonidentifiable parameters, and that the choice of over-parametrized models may drastically impact the results, suggesting that a careful examination of their effects should be considered before drawing conclusions.

Que ce soit dans un cadre Bay´esien ou classique, il est bien connu que la surparam´etrisation, dans les mod`eles pourdonn´ees cat´egorielles incompl`etes, peut conduire`a des conclusions erron´ees. Cependant, certains auteurs persistent`an´egliger les probl`emes li´es`alapr´esence de param`etres non identifi´es. Nous passons en revue la litt´erature dans cedomaine, et consid´erons quelques exemples surparam´etr´es simples dans lesquels les´el´ements subjectifs influencentde fac¸on non n´egligeable les r´esultats, ind´ependamment de la taille des´echantillons. Plus pr´ecis´ement, nous montronscomment des a priori consid´er´es comme peu ou non-informatifs peuvent se r´ev´eler extrˆemement informatifs en ce quiconcerne les param`etres non identifi´es, et que le recours`a des mod`eles surparam´etr´es peut avoir sur les conclusionsfinales un impact consid´erable. Ceci sugg`ere un examen tr`es attentif de l’impact potentiel des a priori.