In a generalized linear model of binary data, we consider models based on a general link function including a logistic regression model and a probit model as special cases. For testing the null hypothesis H0 that the considered model is correct, we consider a family of ϕ-divergence...

In logistic regression models, we consider the deviance statistic (the log likelihood ratio statistic) D as a goodness-of-fit test statistic. In this paper, we show the derivation of an expression of asymptotic expansion for the distribution of D under a null hypothesis. Using the continuous...

We consider a class of statistics C[phi] based on [phi]-divergence for the test of independence in rxs contingency tables. The class of statistics C[phi] includes the statistics Ra based on the power divergence as a special case. Statistic R0 is the log likelihood ratio statistic and R1 is...

Cressie and Read (J. Roy. Statist. Soc. B 46 (1984) 440-464) introduced the power divergence statistics, Ra, as multinomial goodness-of-fit statistics. Each Ra has a limiting noncentral chi-square distribution under a local alternative and has a limiting normal distribution under a nonlocal...

N. Cressie and T. R. C. Read (1984, J. Roy. Statist. Soc. B46, 440-464) introduced a class of multinomial goodness-of-fit statistics Ra based on power divergence. All Ra have the same chi-square limiting distribution under null hypothesis and have the same noncentral chi-square limiting...