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This study presents comparisons of subset selection criteria used to help determine the "best" regression model in multiple linear regression. No such criteria can replace a researcher's knowledge of theory to help choose useful models, but such criteria may help in exploratory research. Relationships among variables can be more complicated than expected and may require adjustment to theory based on empirical models. Knowing how well each subset selection method performs can be useful in such cases. Monte Carlo simulations were performed to compare a number of well-known criteria (e.g., AIC, BIC, PRESS, adjusted R2 ) to some less well-known criteria (e.g., AICc, AICu, GCV, cross-validity R2). We found that although none of the criteria work well to identify a single correct model across a large number of coefficient and multicollinearity patterns, AIC and adjusted R2 work reasonably well enough to recommend, in combination, to identify a model within-one of the correct model.

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Brooks, G. P., & Ruengvirayudh, P. (2016). Best-subset selection criteria for multiple linear regression. General Linear Model Journal, 42(2), 14-25.