Gudicha Dereje W, Schmittmann Verena D, Tekle Fetene B, Vermunt Jeroen K
a Department of Methodology and Statistics , Tilburg University.
Multivariate Behav Res. 2016 Sep-Oct;51(5):649-660. doi: 10.1080/00273171.2016.1203280.
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.
隐马尔可夫（LM）模型是一种常用方法，用于在纵向观测响应中识别不同的未观测状态以及这些状态随时间的转变。自举似然比（BLR）检验是确定潜在状态数量的最严格检验，但对于该检验的功效分析却知之甚少。功效可以计算为拒绝原假设的自举p值（PBP）的比例。这需要针对在备择假设下从模型生成的大量样本执行完整的自举过程，而这在大多数情况下在计算上是不可行的。本文提出了一种用于BLR检验功效计算的计算可行的捷径方法。该捷径方法包括以下简单步骤：（1）获取原假设下模型的参数，（2）通过蒙特卡罗模拟构建原假设和备择假设下似然比的经验分布，以及（3）使用这些经验分布来计算功效。我们通过将捷径方法与PBP方法进行比较来评估其性能，此外，还展示了如何使用捷径方法进行样本量确定。
