Testing Simultaneous Marginal Homogeneity for Clustered Matched-Pair Multinomial Data

摘要

For matched-pair data with a polychotomous outcome, the Stuart-Maxwell test (1955) and the Bhapkar test(1966) are commonly used to test marginal homogeneity. When the outcome is ordinal, the test proposed by Agresti (1983) can be used to test the marginal homogeneity against stochastic order. In practice, we often face the need to consider multiple categorical outcomes simultaneously to insure Type I error protection. In this paper, we propose three statistics to test simultaneous marginal homogeneity for multiple multinomial outcomes in two dependent samples. Furthermore, when the outcome is ordinal, we also propose a transformed version of the three statistics for testing simultaneous marginal homogeneity against stochastic order in two dependent samples. We then prove their asymptotic properties. Finally, Monte Carlo simulations are conducted to evaluate their performance in small samples with respect to empirical size and power.