关键词:  追踪数据, 混合增长模型, 多阶段混合增长模型, 参数估计方法

Abstract:  Piecewise growth mixture models (PGMM) can be used to analyze multi-phase longitudinal data with unobserved heterogeneity in a population, and are widely applied in fields such as ability growth, social behaviors development and intervention, and clinical psychology. PGMM can be defined within both the structural equation modeling framework and the random coefficient modeling framework. Maximum likelihood via an expectation–maximization algorithm (EM-ML) and Markov Chain Monte Carlo for Bayesian inference (MCMC-BI) are the most commonly used methods for PGMM parameter estimation. The validity of PGMM and their parameter estimation are significantly affected by factors such as sample size, number of time points, and latent class separation. Future studies should focus on comparisons between PGMM and other growth models, and the influences of factors such as data characters and latent class attributes on the performance of parameter estimation methods under the same modeling framework or different modeling frameworks.

Key words: longitudinal data, growth mixture models, piecewise growth mixture models, parameter estimation methods