MODEL SELECTION CRITERIA - AN INVESTIGATION OF RELATIVE ACCURACY, POSTERIOR PROBABILITIES, AND COMBINATIONS OF CRITERIA

We investigate the performance of empirical criteria for comparing and selecting quantitative models from among a candidate set. A simulatio n based on empirically observed parameter values is used to determine which criterion is the most accurate at identifying the correct model specification. The simulation is composed of both nested and nonnested linear regression models. We then derive posterior probability estima tes of the superiority of the alternative models from each of the crit eria and evaluate the relative accuracy, bias, and information content of these probabilities. To investigate whether additional accuracy ca n be derived from combining criteria, a method for obtaining a joint p rediction from combinations of the criteria is proposed and the increm ental improvement in selection accuracy considered. Based on the simul ation, we conclude that most leading criteria perform well in selectin g the best model, and several criteria also produce accurate probabili ties of model superiority. Computationally intensive criteria failed t o perform better than criteria which were computationally simpler. Als o, the use of several criteria in combination failed to appreciably ou tperform the use of one model. The Schwarz criterion performed best ov erall in terms of selection accuracy, accuracy of posterior probabilit ies, and ease of use. Thus, we suggest that general model comparison, model selection, and model probability estimation be performed using t he Schwarz criterion, which can he implemented (given the model log li kelihoods) using only a hand calculator.