Power analysis for the likelihood-ratio test in latent Markov models

Shortcutting the bootstrap p-value-based method

D.W. Gudicha, V.D. Schmittmann, F.B. Tekle, J.K. Vermunt

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Abstract

The latent Markov (LM) model is a popular method for identifying distinct unobserved states and transitions between these states over time in longitudinally observed responses. The bootstrap likelihood-ratio (BLR) test yields the most rigorous test for determining the number of latent states, yet little is known about power analysis for this test. Power could be computed as the proportion of the bootstrap p values (PBP) for which the null hypothesis is rejected. This requires performing the full bootstrap procedure for a large number of samples generated from the model under the alternative hypothesis, which is computationally infeasible in most situations. This article presents a computationally feasible shortcut method for power computation for the BLR test. The shortcut method involves the following simple steps: (1) obtaining the parameters of the model under the null hypothesis, (2) constructing the empirical distributions of the likelihood ratio under the null and alternative hypotheses via Monte Carlo simulations, and (3) using these empirical distributions to compute the power. We evaluate the performance of the shortcut method by comparing it to the PBP method and, moreover, show how the shortcut method can be used for sample-size determination.
Keywords: Latent Markov, number of states, Likelihood Ratio, bootstrap, Monte Carlo simulation, longitudinal data, Power Analysis
Original languageEnglish
Pages (from-to)649-660
JournalMultivariate Behavioral Research
Volume51
Issue number5
DOIs
Publication statusPublished - 2 Sep 2016

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Power Analysis
Likelihood Ratio Test
p-Value
Bootstrap
Markov Model
Empirical Distribution
Likelihood Ratio
Null hypothesis
Proportion
Monte Carlo Simulation
Sample Size Determination
Alternatives
Longitudinal Data
Null
Distinct
Evaluate
Model

Cite this

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title = "Power analysis for the likelihood-ratio test in latent Markov models: Shortcutting the bootstrap p-value-based method",
abstract = "The latent Markov (LM) model is a popular method for identifying distinct unobserved states and transitions between these states over time in longitudinally observed responses. The bootstrap likelihood-ratio (BLR) test yields the most rigorous test for determining the number of latent states, yet little is known about power analysis for this test. Power could be computed as the proportion of the bootstrap p values (PBP) for which the null hypothesis is rejected. This requires performing the full bootstrap procedure for a large number of samples generated from the model under the alternative hypothesis, which is computationally infeasible in most situations. This article presents a computationally feasible shortcut method for power computation for the BLR test. The shortcut method involves the following simple steps: (1) obtaining the parameters of the model under the null hypothesis, (2) constructing the empirical distributions of the likelihood ratio under the null and alternative hypotheses via Monte Carlo simulations, and (3) using these empirical distributions to compute the power. We evaluate the performance of the shortcut method by comparing it to the PBP method and, moreover, show how the shortcut method can be used for sample-size determination.Keywords: Latent Markov, number of states, Likelihood Ratio, bootstrap, Monte Carlo simulation, longitudinal data, Power Analysis",
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Power analysis for the likelihood-ratio test in latent Markov models : Shortcutting the bootstrap p-value-based method. / Gudicha, D.W.; Schmittmann, V.D.; Tekle, F.B.; Vermunt, J.K.

In: Multivariate Behavioral Research, Vol. 51, No. 5, 02.09.2016, p. 649-660.

Research output: Contribution to journalArticleScientificpeer-review

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