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 simulation 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 estimates of the superiority of the alternative models from each of the criteria and evaluate the relative accuracy, bias, and information content of these probabilities. To investigate whether additional accuracy can be derived from combining criteria, a method for obtaining a joint prediction from combinations of the criteria is proposed and the incremental improvement in selection accuracy considered. Based on the simulation, we conclude that most leading criteria perform well in selecting the best model, and several criteria also produce accurate probabilities of model superiority. Computationally intensive criteria failed to perform better than criteria which were computationally simpler. Also, the use of several criteria in combination failed to appreciably outperform the use of one model. The Schwarz criterion performed best overall in terms of selection accuracy, accuracy of posterior probabilities, and ease of use. Thus, we suggest that general model comparison, model selection, and model probability estimation be performed using the Schwarz criterion, which can be implemented (given the model log likelihoods) using only a hand calculator.