Nonadditivity in loglinear models using and under product-multinomial sampling

Based on ϕ - divergence measures and minimum ϕ - divergence estimators ( M ϕ Es ) , we present three families of test statistics for testing nonadditivity in loglinear models. The minimum ϕ - divergence estimator can be seen to be a generalization of the maximum likelihood estimator. In the process of testing nonadditivity, the two-stage tests procedure is usually used as the standard method. The unknown parameters are first estimated by some method (here M ϕ Es ) and then these estimators which are treated as known constants are applied in the second-stage of this procedure. These three families of statistics which generalize the conclusions in Pardo and Pardo (2005) are asymptotically chi-squared. In the last section, we apply our method to a practical example and do a simulation study.