Log-linear modeling under generalized inverse sampling scheme

This article discusses the log-linear model for a multi-way contingency table, where the cell values represent the frequency counts that follow an extended negative multinomial distribution. This is an extension of the negative multinomial log-linear model described by Evans and Bonett (1989). The parameters of the new model are estimated by the maximum likelihood method. The likelihood ratio test for the general log-linear hypothesis is derived, and a practical application of the log-linear model under the generalized inverse sampling scheme is presented.