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IES Grant

Title: Addressing Small Sample and Computational Issues in Mixture Models of Repeated Measures Data with Covariance Pattern Mixture Models
Center: NCER Year: 2019
Principal Investigator: McNeish, Daniel Awardee: Arizona State University
Program: Statistical and Research Methodology in Education–Early Career      [Program Details]
Award Period: 2 Years (08/01/19–07/31/21) Award Amount: $209,305
Type: Methodological Innovation Award Number: R305D190011

Purpose: In this project, the research team applied a covariance pattern model approach to growth mixture models so that they can be applied more reliably within contexts in which they are already applied and to lower the data requirements needed to apply the method so that researchers with more modest samples (e.g., hard-to-reach populations) can use the method. The project team developed an alternative way to fit growth mixture models that is less demanding computationally, carried out simulations to assess the performance of the developed model in realistic settings, and developed resources for empirical researchers to use the method without needing to be experts in growth mixture model estimation.

Key Outcomes: The project team applied a covariance pattern model approach to growth mixture models. Covariance pattern models model the marginalcovariance of the repeated measures directly rather than splitting the covariance into between-person and within-person sources with random effects. In non-mixture contexts, this is computationally much simpler and typically preferred if the between-person covariance is not needed to answer the research questions. Similarly, for growth mixture models between-person covariance is rarely needed to address research questions.

  • The project team proposed the hypothesis that random effects make growth mixture model estimation difficult and taking random effects out of growth mixture models should improve estimation and should not adversely affect the ability of a covariance pattern mixture model to answer relevant research questions. They performed a simulation which showed that the covariance pattern version of the model demonstrated much better convergence properties and, as a result, was better at identifying who belonged in which class and what the growth trajectories should be (McNeish & Harring, 2020).
  • The project team addressed the disadvantage of the covariance pattern approach for growth mixture models that specifying a marginal covariance in covariance pattern models is difficult with many repeated measures because there are too many parameters. They showed that large covariance matrices can be represented as a factor analytic covariance matrix to reduce their dimensionality and the number of parameters needed to fill the matrix (McNeish & Bauer 2022).
  • The project team carried out a simulation study to assess the class enumeration properties of covariance pattern mixture models relative to other methods. The simulation generated data from a growth mixture model and examined conditions that are common in empirical studies but that are known to be challenging to estimate with conventional methods. Different types of mixture models were fit to assess how well often each method would extract the correct number of classes in these conditions. The simulation showed that he covariance pattern model performed the best and (a) converged most often, (b) most often extracted the correct number of classes, and (c) best assigned observations to the correct class (McNeish, Harring, & Bauer 2022).
  • The project team carried out a simulation study comparing how well four methods of growth mixture models dealt with missing data and found that the covariance pattern growth mixture model performed best across conditions as its convergence was unaffected by attrition whereas convergence with the other methods declined as a function of the attrition percentage (McNeish & Harring 2021).
  • The project team originally proposed to develop a generalized estimating equation version of a growth mixture model. Between the time the proposal was submitted and the project period, other research groups had largely accomplished this work so the project team redirected its efforts to the use of a factor analytic covariance matrix described above.
  • The project team took part in a series of empirical papers to demonstrate how covariance pattern growth mixture models conceptually work; can be fit, interpreted, and reported with real data; and successfully converge and provide interpretable results even where other approaches have failed because only a modest sample is available for analysis (McNeish et al. 2021; Pena et al. 2020; Perez et al. 2022).


ERIC Citations: Find available citations in ERIC for this award here.

Select Publications:

Journal Articles

McNeish, D. & Bauer, D.J. (2022). Reducing incidence of nonpositive definite covariance matrices in mixed effect models. Multivariate Behavioral Research, 3-8-340.

McNeish, D. & Harring, J.R. (2020). Covariance pattern mixture models: Eliminating random effects to improve convergence and performance. Behavior Research Methods, 52, 947–979.

McNeish, D. & Harring, J.R. (2021). Improving convergence in growth mixture models without covariance structure constraints. Statistical Methods in Medical Research, 30, 994–1012.

McNeish, D., Harring, J.R., & Bauer, D.J. (2022). Nonconvergence, covariance constraints, and class enumeration in growth mixture models. Psychological Methods.

McNeish, D., Peña, A., Vander Wyst, K.B., Ayers, S.L., Olsen, M.L., & Shaibi, G.Q. (2021). Facilitating growth mixture model convergence in preventive interventions. Prevention Science.

Peña, A., McNeish, D., Ayers, S.L., Olson, M.L., Vander Wyst, K.B., Williams, A.N., & Shaibi, G.Q. (2020). Response heterogeneity to lifestyle intervention among Latino adolescents. Pediatric Diabetes, 21, 1430–1436.

Perez, M., Winstone, L.K., Hernández, J.C., Curci, S.G., McNeish, D., & Luecken, L.J (2022). Association of BMI Trajectories with Cardiometabolic Risk at age 7.5 years among Low-income Mexican American children. Journal of Pediatrics.