Entropy coefficient of determination for generalized linear models

The objective of the present paper is to propose a predictive power measure for generalized linear models (GLMs). First, basic predictive power measures for GLMs are compared with respect to some desirable properties. We propose a generalized coefficient of determination for GLMs, which is referred to as the entropy coefficient of determination (ECD). The advantage of the measure is discussed in the GLM framework. Second, the asymptotic properties of the maximum likelihood estimator of ECD are discussed. Third, ECD is applied to GLMs with polytomous response variables. Finally, discussions and a conclusion to this study are provided.