Dereje W Gudicha
Tilburg University
The Netherlands
Title: Power Analysis for the Likelihood Ratio Test in Latent Markov Models: Short-cutting the bootstrap p-value based method
Biography
Biography: Dereje W Gudicha
Abstract
In recent years, the latent Markov (LM) model has proven useful to identify distinct unobserved states and transitions between these states over time in longitudinally observed responses. The bootstrap likelihood ratio (BLR) test is becoming a gold standard for testing the number of states, yet little is known about power analysis methods for this test. This paper presents a short-cut to a p-value based power computation for the BLR test. The p-value based power computation involves computing the power as the proportion of the bootstrap p-value (PBP) for which the null hypothesis is rejected. This requires to perform the full bootstrap for multiple samples of the model under the alternative hypothesis. Power computation using the short-cut method involves the following simple steps: obtain the parameter estimates of the model under the null hypothesis, construct the empirical distributions of the likelihood ratio under the null and alternative hypotheses via Monte Carlo simulations, and use these empirical distributions to compute the power. The advantage of this short-cut method is that it is computationally cheaper and is simple to apply for sample size determination.