On the Use of Marginal Likelihood in Model Selection

SUMMARY Based on the marginal likelihood approach, we develop a model selection criterion, MIC, for regression models with the general variance structure. These include weighted regression models, regression models with ARMA errors, growth curve models, and spatial correlation models. We show that MIC is a consistent criterion. For regression models with either constant or non-constant variance, simulation studies indicate that MIC not only provides better model order choices than the asymptotic eecient criteria AIC, AICC, FPE and C p , but is also superior to the consistent criteria BIC and FIC in both small and large sample sizes. These results also hold for regression models with AR(1) errors, except that BIC performs slightly better than MIC in the large sample size case. Finally, Monte Carlo studies show that the eeectiveness of model selection criteria decreases as the degree of heterogeneity (or the rst order autocorrelation) increases.