Kohli Nidhi, Hughes John, Wang Chun, Zopluoglu Cengiz, Davison Mark L
Department of Educational Psychology.
The Division of Biostatistics, University of Minnesota.
Psychol Methods. 2015 Jun;20(2):259-75. doi: 10.1037/met0000034. Epub 2015 Apr 13.
A linear-linear piecewise growth mixture model (PGMM) is appropriate for analyzing segmented (disjointed) change in individual behavior over time, where the data come from a mixture of 2 or more latent classes, and the underlying growth trajectories in the different segments of the developmental process within each latent class are linear. A PGMM allows the knot (change point), the time of transition from 1 phase (segment) to another, to be estimated (when it is not known a priori) along with the other model parameters. To assist researchers in deciding which estimation method is most advantageous for analyzing this kind of mixture data, the current research compares 2 popular approaches to inference for PGMMs: maximum likelihood (ML) via an expectation-maximization (EM) algorithm, and Markov chain Monte Carlo (MCMC) for Bayesian inference. Monte Carlo simulations were carried out to investigate and compare the ability of the 2 approaches to recover the true parameters in linear-linear PGMMs with unknown knots. The results show that MCMC for Bayesian inference outperformed ML via EM in nearly every simulation scenario. Real data examples are also presented, and the corresponding computer codes for model fitting are provided in the Appendix to aid practitioners who wish to apply this class of models.
线性-线性分段增长混合模型（PGMM）适用于分析个体行为随时间的分段（不连续）变化，其中数据来自两个或更多潜在类别的混合，并且每个潜在类别内发育过程不同段的潜在增长轨迹是线性的。PGMM允许估计节点（变化点），即从一个阶段（段）过渡到另一个阶段的时间（当它不是先验已知时）以及其他模型参数。为了帮助研究人员确定哪种估计方法对于分析这类混合数据最有利，当前研究比较了两种用于PGMM推理的流行方法：通过期望最大化（EM）算法的最大似然（ML），以及用于贝叶斯推理的马尔可夫链蒙特卡罗（MCMC）。进行了蒙特卡罗模拟，以研究和比较这两种方法在具有未知节点的线性-线性PGMM中恢复真实参数的能力。结果表明，在几乎每个模拟场景中，用于贝叶斯推理的MCMC都优于通过EM的ML。还给出了实际数据示例，并在附录中提供了用于模型拟合的相应计算机代码，以帮助希望应用这类模型的从业者。
