Nonadditivity in loglinear models using φ-divergences and MφEs under product-multinomial sampling

Based on phi-divergence measures and minimum phi-divergence estimators (M phi Es), we present three families of test statistics for testing nonadditivity in loglinear models. The minimum phi-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 phi 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. (C) 2012 Elsevier B.V. All rights reserved.