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

P>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.Resume Que ce soit dans un cadre Bayesien ou classique, il est bien connu que la surparametrisation, dans les modeles pour donnees categorielles incompletes, peut conduire a des conclusions erronees. Cependant, certains auteurs persistent a negliger les problemes lies a la presence de parametres non identifies. Nous passons en revue la litterature dans ce domaine, et considerons quelques exemples surparametres simples dans lesquels les elements subjectifs influencent de facon non negligeable les resultats, independamment de la taille des echantillons. Plus precisement, nous montrons comment des a priori consideres comme peu ou non-informatifs peuvent se reveler extremement informatifs en ce qui concerne les parametres non identifies, et que le recours a des modeles surparametres peut avoir sur les conclusions finales un impact considerable. Ceci suggere un examen tres attentif de l`impact potentiel des a priori.