Score and Wald Tests for Antedependence in Categorical Longitudinal Data

Abstract

Three standard hypothesis testing procedures exist based on likelihood functions: the likelihood ratio, score, and Wald tests. For unstructured antedependence models for categorical longitudinal data, Xie and Zimmerman derived the likelihood ratio test for the order of antedependence as well as likelihood ratio tests for time-invariance of transition probabilities and strict stationarity. In this article, we derive score tests (of Pearson’s chi-square form) and Wald tests for all the same purposes. Via simulation, we show that for testing for order of antedependence, a modified likelihood ratio test performs best if the sample is of size 50 or smaller, but otherwise the score test is superior. The Wald test is markedly inferior to both. We also show that the likelihood ratio and score tests for time-invariant transition probabilities and strict stationarity perform about equally well. The methods are applied to data from a longitudinal study of labor force participation of married women, indicating that these data are third-order antedependent with time-invariant transition probabilities of this order.