A Neyman-Scott phenomenon in model discrimination.

The aim of this paper is to show through simulation that a Neyman-Scott phenomenon may occur in discriminating among separate stratified models. We focus on models which are scale families in each stratum. We consider traditional model selection procedures, such as the Akaike and Takeuchi information criteria, together with procedures based on the marginal likelihood and its Laplace approximation. We perform two simulation studies. Results indicate that, when the sample size in each stratum is fixed and the number of strata increases, correct selection probabilities for traditional model selection criteria may approach zero. On the other hand, model selection based on exact or approximate marginal likelihoods, that exploit invariance, can behave far better.