Three predictive power measures for generalized linear models: The entropy coefficient of determination, the entropy correlation coefficient and the regression correlation coefficient

In this paper, three predictive power measures for generalized linear models (GLMs) are compared, and the utility of the entropy correlation coefficient (ECC) and the entropy coefficient of determination (ECD) is demonstrated. First, ECC, ECD and the regression correlation coefficient (RCC) are briefly explained. Second, relationships of the three measures are discussed, and the necessary and sufficient condition under which ECC and RCC are equal is deduced. Third, ECC and ECD are discussed for GLMs with canonical links and polytomous response variables, and an analysis of the effects of factors in GLMs is given. Finally, a discussion of the conclusions of this study is provided.