Bias-corrected AIC for selecting variables in multinomial logistic regression models |
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| Authors: | Hirokazu Yanagihara Ken-ichi Kamo Shinpei Imori Kenichi Satoh |
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| Institution: | 1. Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8626, Japan;2. Department of Liberal Arts and Sciences, Sapporo Medical University, South 1, West 17, Chuo-ku, Sapporo 060-8543, Japan;3. Department of Environmetrics and Biometrics, Research Institute for Radiation Biology and Medicine, Hiroshima University, 1-2-3 Kasumi, Minami-ku, Hiroshima 734-8553, Japan |
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| Abstract: | In this paper, we consider the bias correction of Akaike’s information criterion (AIC) for selecting variables in multinomial logistic regression models. For simplifying a formula of the bias-corrected AIC, we calculate the bias of the AIC to a risk function through the expectations of partial derivatives of the negative log-likelihood function. As a result, we can express the bias correction term of the bias-corrected AIC with only three matrices consisting of the second, third, and fourth derivatives of the negative log-likelihood function. By conducting numerical studies, we verify that the proposed bias-corrected AIC performs better than the crude AIC. |
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