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 s...

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Bibliographic Details
Published in:	Management science Vol. 41; no. 2; pp. 322 - 333
Main Authors:	Rust, Roland T, Simester, Duncan, Brodie, Roderick J, Nilikant, V
Format:	Journal Article
Language:	English
Published:	Linthicum, MD INFORMS 01-02-1995 Institute for Operations Research and the Management Sciences
Series:	Management Science
Subjects:	Accuracy AIC Akaike's criterion Bayesian methods BCVL BIC combination of forecasts Criteria cross-validation Datasets Economic models Estimate reliability Exact sciences and technology Forecasting models Forecasts General topics Information content Linear programming Management science Mathematics model selection Modeling Parametric models Probabilities Probability Probability and statistics Probability forecasts Regression analysis Schwarz' criterion Sciences and techniques of general use Simulation Simulations Statistics Studies Posterior probability Statistical model Model specification Selection criterion Cross validation Statistical forecasting Bayes decision
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Summary:	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.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0025-1909 1526-5501
DOI:	10.1287/mnsc.41.2.322