Power Computation for Likelihood Ratio Tests for the Transition Parameters in Latent Markov Models

Abstract

Latent Markov (LM) models are increasingly used in a wide range of research areas including psychological, sociological, educational, and medical sciences. Methods to perform power computations are lacking, however. This article presents methods for preforming power analysis in LM models. Two cases of tests of hypotheses on the transition parameters of LM models are considered. The first case concerns the situation where the likelihood ratio test statistic follows a chi-square distribution, implying that the power computation can also be based on this theoretical distribution. In the second case, power needs to be computed based on empirical distributions constructed via Monte Carlo methods. Numerical studies are conducted to illustrate the proposed power computation methods and to investigate design factors affecting the power of this test.

Keywords:

• likelihood ratio, Monte Carlo methods, transition probabilities, design factors, power computation

Notes

¹ For the three-state LM model, we do not show the results of the power calculation, as they provide similar information with the two-state LM model shown in Table 2. We should, however, note that the power to demonstrate differences in the transition probabilities for the three-state LM model is in general lower than its corresponding power value for the two-state LM model, implying that the power depends on the number of states as well.