Nonadditivity in loglinear models using φ-divergences and MLEs

In this paper three families of test statistics for testing nonadditivity in loglinear models are presented under the assumption of either Poisson, multinomial, or product-multinomial sampling. These new families are based on the φ-divergence measures. The standard method for testing nonadditivity is used, i.e., the two-stage tests procedure. In this procedure the parameters are first estimated using an additive model and then the estimates are treated as known constants for the second stage of the procedure. These test statistics, which are asymptotically chi-squared, generalize the likelihood ratio test for this problem given by Christensen and Utts (J. Statist. Plann. Inference 33 (1992) 333). An example and a simulation study are included.