### Abstract

Keywords: Latent Markov, number of states, Likelihood Ratio, bootstrap, Monte Carlo simulation, longitudinal data, Power Analysis

Original language | English |
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Pages (from-to) | 649-660 |

Journal | Multivariate Behavioral Research |

Volume | 51 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2 Sep 2016 |

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*Multivariate Behavioral Research*,

*51*(5), 649-660. https://doi.org/10.1080/00273171.2016.1203280

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*Multivariate Behavioral Research*, vol. 51, no. 5, pp. 649-660. https://doi.org/10.1080/00273171.2016.1203280

**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.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Power analysis for the likelihood-ratio test in latent Markov models

T2 - Shortcutting the bootstrap p-value-based method

AU - Gudicha, D.W.

AU - Schmittmann, V.D.

AU - Tekle, F.B.

AU - Vermunt, J.K.

PY - 2016/9/2

Y1 - 2016/9/2

N2 - 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

AB - 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

U2 - 10.1080/00273171.2016.1203280

DO - 10.1080/00273171.2016.1203280

M3 - Article

VL - 51

SP - 649

EP - 660

JO - Multivariate Behavioral Research

JF - Multivariate Behavioral Research

SN - 0027-3171

IS - 5

ER -