A Comparison of Minimum Logit Chi-Square Estimation and Maximum Likelihood Estimation in 2×2×2 and 3×2×2 Contingency Tables: Tests for Interaction

Abstract This article compares small sample properties of 12 goodness of fit tests for interaction in 2×2×2 and 3×2×2 contingency tables. The 12 tests are constructed by-combining three tests (the minimum logit chi-square test, the Pearson chi-square test, and the likelihood ratio test) and four methods of estimation (the iterative maximum likelihood estimator and three variants of the non-iterative minimum logit chi-square estimator). An evaluation is made of the adequacy of the tabular chi-square distribution in approximating the exact levels, the power, and computational simplicity of the tests. The exact level and power of the tests were computed by enumeration for 2×2×2 tables and by enumeration and Monte Carlo sampling for 3×2×2 tables. In general, the exact levels of the minimum logit chi-square tests and the Pearson chi-square tests are better approximated by the tabular chi-square. distribution than are the levels of the likelihood ratio tests. The exact levels of tests based on minimum logit chi-square estimation are better approximated than the exact levels of tests based on maximum likelihood estimation. No important differences in power were observed.