Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2021 Nov;74(3):404-426.
doi: 10.1111/bmsp.12229. Epub 2020 Nov 24.

The impacts of ignoring individual mobility across clusters in estimating a piecewise growth model

Audrey J Leroux  1 , Christopher J Cappelli  1   2 , David R J Fikis  1
Affiliations

The impacts of ignoring individual mobility across clusters in estimating a piecewise growth model

Audrey J Leroux et al. Br J Math Stat Psychol. 2021 Nov.

Abstract

A three-level piecewise growth model (3L-PGM) can be used to break up nonlinear growth into multiple components, providing the opportunity to examine potential sources of variation in individual and contextual growth within different segments of the model. The conventional 3L-PGM assumes that the data are strictly hierarchical in nature, where measurement occasions (level 1) are nested within individuals (level 2) who are members of a single cluster (level 3). However, in longitudinal research, it is sometimes difficult for data structures to remain purely clustered during a study, such as when some students change classrooms or schools over time. One resulting data structure in this situation is known as a multiple membership structure, where some lower-level units are members of more than one higher-level unit. The new multiple membership PGM (MM-PGM) extends the 3L-PGM to handle multiple membership data structures frequently found in the social sciences. This study sought to examine the consequences of ignoring individual mobility across clusters when estimating a 3L-PGM in comparison to estimating a MM-PGM. MM-PGM estimates were less biased (especially in the cluster-level coefficient estimates), although we found substantial bias in cluster-level variance components across some conditions for both models.

Keywords: MCMC estimation; Multilevel modelling; multiple membership; piecewise growth; simulation.

PubMed Disclaimer

References

    1. Aikens, N. L., & Barbarin, O. (2008). Socioeconomic differences in reading trajectories: The contribution of family, neighborhood, and school contexts. Journal of Educational Psychology, 100, 235-251. https://doi.org/10.1037/0022-0663.100.2.235
    1. Bauer, D. J., & Cai, L. (2009). Consequences of unmodeled nonlinear effects in multilevel models. Journal of Educational and Behavioral Statistics, 34, 97-114. https://doi.org/10.3102/1076998607310504
    1. Beretvas, S. N. (2011). Cross-classified and multiple membership models. In J.J. Hox & J.K. Roberts (Eds.), Handbook of advanced multilevel analysis (pp. 313-334). New York: Routledge.
    1. Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31(2), 144-152. https://doi.org/10.1111/j.2044-8317.1978.tb00581.x
    1. Browne, W. J., & Draper, D. (2006). A comparison of Bayesian and likelihood-based methods for fitting multilevel models. Bayesian Analysis, 1, 473-514. https://doi.org/10.1214/06-BA117

LinkOut - more resources