The choice of a log-linear model using a Cp-type statistic

Abstract

Most methods of selecting an appropriate log-linear model for categorical data are sensitive to the underlying distributional assumptions. However, there are many situations in which the assumption that the data are randomly chosen from an underlying Poisson, multinomial or product-multinomial distribution cannot be sustained. In these cases we propose a criterion to select among log-linear models that is an analogue of the Cp statistic for regression models and describe a method to estimate the denominator of this statistic.