Bias-corrected AIC for selecting variables in multinomial logistic regression models

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.