Using power-divergence statistics to test for homogeneity in product-multinomial distributions
Testing for homogeneity in the product-multinomial distribution, where the hypotheses are hierarchical, uses maximum likelihood estimation and the loglikelihood ratio statistic G 2. We extend these ideas to the power-divergence family of test statistics, which is a one-parameter family of goodness-of-fit statistics that includes the loglikelihood ratio statistic G 2, Pearson's X 2, the Freeman-Tukey statistic, the modified loglikelihood ratio statistic, and the Neyman-modified chi-squared statistic. Explicit minimum-divergence estimators can be obtained for all members of the one-parameter family, which allows a straightforward analysis of divergence. An analysis of fourteen retrospective studies on the association between smoking and lung cancer demonstrates the ease of interpretation of the resulting analysis of divergence.
Cressie, N. & Medak, F. M. (2011). Using power-divergence statistics to test for homogeneity in product-multinomial distributions. In L. Pardo, N. Balakrishnan & M. Gil (Eds.), Modern Mathematical Tools and Techniques in Capturing Complexity (pp. 157-175). United States: Springer.