Conventional statistical procedures, such as the likelihood ratio test, do not apply to comparisons of non-nested models. This paper describes three procedures for carrying out such comparisons and explores the ability of each to distinguish between correct and incorrect models. The abilities of the various procedures to reject incorrect models and accept correct ones are explored analytically and through numerical experiments. It is shown analytically that, in large sample, the modified likelihood ratio index has greater ability to distinguish between correct and incorrect models than do composite model procedures. The results of the numerical experiments suggest that the modified likelihood ratio index also has greater ability to distinguish correct and incorrect models than does the Cox test. The numerical results give encouraging indications of the ability of the modified likelihood ratio index to choose the correct model in comparisons of models whose choice probabilities differ by at least 10-15%.
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