Power computation for likelihood ratio tests for the transition parameters in latent Markov models

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. Power computations can help 1) to make an informed decision on the sample size or the number of measurement occasions required to achieve a prespecified power level of a statistical test, and 2) to evaluate the ability of this test in detecting a statistically meaningful effect when indeed there is such an effect in a population. This paper 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 also the power computation can 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.