Score and Wald Tests for Antedependence in Categorical Longitudinal DataYunlong Xie1 and Dale L Zimmerman2*
1Division of Intramural Population Health Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, 6100 Executive Boulevard, Bethesda, MD 20892, USA
- *Corresponding Author:
- Dale L. Zimmerman
Department of Statistics and Actuarial Science
241 Schaeffer Hall, University of Iowa, Iowa City, IA 52242, USA
E-mail: [email protected]
Received date: February 19, 2014; Accepted date: March 27, 2014; Published date: March 31, 2014
Citation: Xie Y, Zimmerman DL (2014) Score and Wald Tests for Antedependence in Categorical Longitudinal Data. J Biomet Biostat 5:188. doi:10.4172/2155-6180.1000188
Copyright: © 2014 Xie Y, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are are credited.
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.