DOI: 10.3724/SP.J.1042.2017.01696

Advances in Psychological Science (心理科学进展) 2017/25:10 PP.1696-1704

Piecewise growth mixture models and its current researches

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

ReleaseDate:2017-11-17 09:48:02

刘红云. (2007). 如何描述发展趋势的差异:潜变量混合增长模型. 心理科学进展, 15, 539-544.

刘源, 骆方, 刘红云. (2014). 多阶段混合增长模型的影响因素:距离与形态. 心理学报, 46, 1400-1412.

刘红云, 张雷. (2005). 追踪数据分析方法及其应用. 北京:教育科学出版社.

唐文清. (2015). 心理动态变化过程的分析方法——时变效应模型及其在追踪研究的应用(博士学位论文). 华南师范大学, 广州.

张雷. (2003). 多层线性模型应用. 北京:教育科学出版社.

Chou, C. P., Yang, D. Y., Pentz, M. A., & Hser, Y. I. (2004). Piecewise growth curve modeling approach for longitudinal prevention study. Computational Statistics & Data Analysis, 46, 213-225.

Cudeck, R., & Klebe, K. J. (2002). Multiphase mixed-effects models for repeated measures data. Psychological Methods, 7, 41-63.

Cudeck, R., & Harring, J. R. (2010). Developing a random coefficient model for nonlinear repeated measures data. In S. M. Chow, E. Ferrer, & F. Hsieh (Eds.), Statistical methods for modeling human dynamics:An interdisciplinary dialogue (pp. 289-318). New York, NY:Routledge.

Grimm, K. J., Ram, N., & Hamagami, F. (2011). Nonlinear growth curves in developmental research. Child Development, 82, 1357-1371.

Harring, J. R. (2012). Finite mixtures of nonlinear mixed effects models. In J. R. Harring & G. R. Hancock (Eds.), Advances in longitudinal methods in the social and behavioral sciences (pp. 159-192). Charlotte, NC:Information Age Publishing Inc.

Kim, S.-Y. (2012). Sample size requirements in single-and multiphase growth mixture models:A Monte Carlo simulation study. Structural Equation Modeling:A Multidisciplinary Journal, 19, 457-476.

Kim, S.-Y. (2014). Determining the number of latent classes in single-and multiphase growth mixture models. Structural Equation Modeling:A Multidisciplinary Journal, 21, 263-279.

Kim, S.-Y., & Kim, J.-S. (2012). Investigating stage-sequential growth mixture models with multiphase longitudinal data. Structural Equation Modeling:A Multidisciplinary Journal, 19, 293-319.

Kohli, N., Harring, J. R., & Hancock, G. R. (2013). Piecewise linear-linear latent growth mixture models with unknown knots. Educational and Psychological Measurement, 73, 935-955.

Kohli, N., Harring, J. R., & Zopluoglu, C. (2016). A finite mixture of nonlinear random coefficient models for continuous repeated measures data. Psychometrika, 81, 851-880.

Kohli, N., Hughes, J., Wang, C., Zopluoglu, C., & Davison, M. L. (2015). Fitting a linear-linear piecewise growth mixture model with unknown knots:A comparison of two common approaches to inference. Psychological Methods, 20, 259-275.

Li, F. Z., Duncan, T. E., Duncan, S. C., & Hops, H. (2001). Piecewise growth mixture modeling of adolescent alcohol use data. Structural Equation Modeling:A Multidisciplinary Journal, 8, 175-204.

Muthén, B., & Brown, H. C. (2009). Estimating drug effects in the presence of placebo response:Causal inference using growth mixture modeling. Statistics in Medicine, 28, 3363-3385.

Rolfe, M. I., Mengersen, K., Beadle, G., Vearncombe, K., Andrew, B., Johnson, H. L., & Walsh, C. (2010). Latent class piecewise linear trajectory modelling for short-term cognition responses after chemotherapy for breast cancer patients. Journal of Applied Statistics, 37, 725-738.

Serang, S., Zhang, Z. Y., Helm, J., Steele, J. S., & Grimm, K. J. (2015). Evaluation of a Bayesian approach to estimating nonlinear mixed-effects mixture models. Structural Equation Modeling:A Multidisciplinary Journal, 22, 202-215.

Zhao, L., & Banerjee, M. (2012). Bayesian piecewise mixture model for racial disparity in prostate cancer progression. Computational Statistics & Data Analysis, 56, 362-369.

Zopluoglu, C., Harring, J. R., & Kohli, N. (2014). FitPMM:An R routine to fit finite mixture of piecewise mixed-effect models with unknown random knots. Applied Psychological Measurement, 38, 583-584.