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.

► ECC and ECD are entropy-based explanatory power measures for GLMs. ► In GLMs, it is essential to assess the effects of factors on response variables. ► This paper shows the advantage of ECC and ECD theoretically. ► We propose a method of analysis of factor effects in GLMs by ECC and ECD. ► A numerical example is also given using a GLM with a polytomous response variable.