title: Fitting a linear-linear piecewise growth mixture model with unknown knots: A comparison of two common approaches to inference.
abstract: 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.
authors: Department of Educational Psychology.
authors: Nidhi
authors: N
authors: Kohli
authors: The Division of Biostatistics, University of Minnesota.
authors: John
authors: J
authors: Hughes
authors: Department of Psychology, University of Minnesota.
authors: Chun
authors: C
authors: Wang
authors: Department of Educational and Psychological Studies, University of Miami.
authors: Cengiz
authors: C
authors: Zopluoglu
authors: Department of Educational Psychology.
authors: Mark L
authors: ML
authors: Davison
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D016013:Likelihood Functions; D016014:Linear Models; D008137:Longitudinal Studies; D008390:Markov Chains; D015233:Models, Statistical; D009010:Monte Carlo Method