MPA 2021

Approaches for Identifying Change Trajectories:

Growth Curves and Latent Class Growth Analyses and Growth Mixture Models, Oh My!

MPA 2021

(last updated: 6:53 P.M., 7/16/21 -- transferred to new site 7:55 A.M., 9/11/21)


Please feel free to send questions or comments to This web page is meant to accompany the statistics workshop held at MPA 2021 on April 22, 2021. However, if there are errors found or things people request after MPA, I'll maintain this site.

Mplus Materials

(all input files may be opened in a text editor such as WordPad or Notepad. All output files have been tested in Google Chrome output; some HTML markup remains, but the essence of the output is readily viewable)

  • Organized by Models

Some References on Different Trajectory Perspectives


    • Maughan, B. (2005). Developmental trajectory modeling: A view from developmental psychopathology. The Annals of the American Academy of Political and Social Science, 602(1):118-130. doi: 10.1177/0002716205281067.

    • Muthén, B., & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55, 463-469. doi: 10.1111/j.0006-341x.1999.00463.x.

    • Nagin, D. S. (2005) Group-based modeling of development. Cambridge, Massachusetts: Harvard University Press.

    • Nagin, D. S., & Tremblay, R. E. (2005a). What has been learned from group-based trajectory modeling? Examples from physical aggression and other problem behavior. The Annals of the American Academy of Political and Social Sciences, 602, (1), 82-117. doi: 10.1177/0002716205280565.

    • Nagin, D. S., & Tremblay, R. E. (2005b). Further reflections on modeling and analyzing developmental trajectories; a response to Maughan and Raudenbush. The Annals of the American Academy of Political and Social Science, 602(1). 145-154. doi: 10.1177/0002716205281232.

    • Raudenbush, S. W. (2005). How Do We Study “What Happens Next”? The Annals of the American Academy of Political and Social Science, 602(1).131-144. doi: 10.1177/0002716205280900.

    • Sampson, R. J., & Laub, J. (2003) Life-course desisters? Trajectories of crime among delinquent boys followed to age 70. Criminology, 41, 555–592 doi: 10.1111/j.1745-9125.2003.tb00997.x.

    • Sampson, R. J., & Laub, J. (2005). Seductions of methods: Rejoinder to Nagin & Tremblay's developmental trajectory groups: fact or fiction? Criminology, 43, 905-914. doi: 10.1111/j.1745-9125.2005.00027.x.

  • Good Overview Article (In Steve Miller's humble opinion)

    • van der Nest, G., Passos, V. L., Candel, M. J. J. M., & van Breuelen, G. J. P. (2020). An overview of mixture modelling for latent evolutions of longitudinal data: Modelling approaches, fit statistics and software. Advances in Life Course Research, 43, 100323. doi: 10.1016/j.alcr.2019.100323.

  • New literature on covariance pattern mixture models (non-comprehensive)

    • Hawrilenko, M., Masyn, K. E., Cerutti, J., & Dunn, E. C. (in press). Individual differences in the stability and change of childhood depression: A growth mixture model with structured residuals. Child Development. 10.1111/cdev.13502.

    • McNeish D., & Harring, J. R. (2020). Covariance pattern mixture models: Eliminating random effects to improve convergence performance. Behavior Research Methods, 52, 947-979. doi: 10.3758/s13428-019-01292-4.

    • McNeish, D.& Harring, J.R. (in press). Improving convergence in growth mixture models without covariance structure constraints. Statistical Methods in Medical Research. doi: 10.1177/0962280220981747.

    • McNeish, D., Harring, J. R., & Bauer, D. (preprint -- 2021. February 22). Nonconvergence, covariance constraints, and class enumeration in growth mixture models. doi: 10.31234/

    • McNeish, D., Peña, A., Vander Wyst, K. B., Ayers, S. L., Olson, M. L., & Shaibi, H. Q. (20