Nonconvergence, Covariance Constraints, and Class Enumeration in Growth Mixture Models

Growth mixture models (GMMs) are a popular method to identify latent classes of growth trajectories. One shortcoming of GMMs is nonconvergence, which often leads researchers to apply covariance equality constraints to simplify estimation. This approach is criticized because it introduces a dubious homoskedasticity assumption across classes. Alternative methods have been proposed to reduce nonconvergence without imposing covariance equality constraints, and though studies have shown that these methods perform well when the correct number of classes is known, research has not examined whether they can accurately identify the number of classes. Given that selecting the number of classes tends to be the most difficult aspect of GMMs, more information about class enumeration performance is crucial to assess the potential utility of these methods. We conduct an extensive simulation based on model characteristics from studies in the PTSD literature to explore class enumeration and classification accuracy of methods for improving nonconvergence. Despite its popularity, results showed that typical approach of applying covariance equality constraints performs quite poorly and is not recommended. However, we recommended covariance pattern GMMs because they (a) had the highest convergence rates, (b) were most likely to identify the correct number of classes, and (c) had the highest classification accuracy in many conditions, even with modest sample sizes. An analysis of empirical PTSD data is provided to show that the typical 4-Class solution found in many empirical PTSD studies may be an artefact of the covariance equality constraint method that has permeated this literature.

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Covariance Pattern Mixture Models: Eliminating Random Effects to Improve Convergence and Performance

10.31234/osf.io/3796x ◽

2019 ◽

Author(s):

Daniel McNeish ◽

Jeffrey Harring

Keyword(s):

Mixture Models ◽

Random Effects ◽

Convergence Rates ◽

Empirical Studies ◽

Population Heterogeneity ◽

Latent Classes ◽

Growth Mixture Models ◽

Class Enumeration ◽

Growth Mixture ◽

And Performance

Growth mixture models (GMMs) are prevalent for modeling unknown population heterogeneity via distinct latent classes. However, GMMs are riddled with convergence issues, often requiring researchers to atheoretically alter the model with cross-class constraints to obtain convergence. We discuss how within-class random effects in GMMs exacerbate convergence issues even though these random effects rarely help to answer typical research questions. That is, latent classes provide a discretization of continuous random effects, so including additional random effects within latent classes can unnecessarily complicate the model. These random effects are commonly included to properly specify the marginal covariance; however, random effects are inefficient for patterning a covariance matrix, resulting in estimation issues. Such a goal can be achieved more simply covariance pattern models, which we extend to the mixture model context in this paper (covariance pattern mixture models, CPMMs). We provide evidence from theory, simulation, and an empirical example showing that employing CPMMs (even if misspecified) instead of GMMs can circumvent computational difficulties that can plague GMMs without sacrificing the ability to answer the type of questions commonly asked in empirical studies. Results show advantages of CPMMs with respect to improved class enumeration, and less biased class-specific growth trajectories in addition to vastly improved convergence rates. Results also show that constraining covariance parameters across classes to bypass convergence issues with GMMs leads to poor results. An extensive software appendix is included to assist researchers run CPMMs in Mplus.

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Latent Class Trajectory and Growth Mixture Models in the Study of Physical Resilience

Innovation in Aging ◽

10.1093/geroni/igaa057.3030 ◽

2020 ◽

Vol 4 (Supplement_1) ◽

pp. 828-829

Author(s):

Carl Pieper ◽

Jane Pendergast ◽

Megan Neely

Keyword(s):

Mixture Models ◽

Latent Class ◽

Real Life ◽

Individual Characteristics ◽

Model Specification ◽

Growth Mixture Models ◽

Class Enumeration ◽

Growth Mixture ◽

Study Population ◽

Number Of Classes

Abstract After a stressor, individuals may experience different trajectories of function and recovery. One potential explanation for this variation is differing trajectories may be indicators of differing classes or levels of resilience to the stressor. Latent Class Trajectory (LCTA) and Growth Mixture models (GMM) are two similar approaches used to discover the number and types of trajectories in a study population. Class membership may determine the shape and level of recovery, which may be predicted by individual characteristics. In this talk, we present some insights to using these models to successfully identify the number of classes of trajectories, membership of trajectory classes, and the functional form of the trajectory. We will identify methods for deciding class enumeration, indices for assessing fit quality, and, importantly, the importance of proper model specification. Real life and simulated examples will be shown to compare and contrast differences between GMM and LCTA results. Part of a symposium sponsored by Epidemiology of Aging Interest Group.

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Class enumeration false positive in skew-t family of continuous growth mixture models

PLoS ONE ◽

10.1371/journal.pone.0231525 ◽

2020 ◽

Vol 15 (4) ◽

pp. e0231525

Author(s):

Kiero Guerra-Peña ◽

Zoilo Emilio García-Batista ◽

Sarah Depaoli ◽

Luis Eduardo Garrido

Keyword(s):

Mixture Models ◽

False Positive ◽

Continuous Growth ◽

Growth Mixture Models ◽

Class Enumeration ◽

Growth Mixture

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Impact of Misspecifications of the Latent Variance–Covariance and Residual Matrices on the Class Enumeration Accuracy of Growth Mixture Models

Structural Equation Modeling A Multidisciplinary Journal ◽

10.1080/10705511.2016.1169188 ◽

2016 ◽

Vol 23 (4) ◽

pp. 507-531 ◽

Cited By ~ 59

Author(s):

Thierno M. O. Diallo ◽

Alexandre J. S. Morin ◽

HuiZhong Lu

Keyword(s):

Mixture Models ◽

Growth Mixture Models ◽

Class Enumeration ◽

Growth Mixture

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Improving convergence in growth mixture models without covariance structure constraints

Statistical Methods in Medical Research ◽

10.1177/0962280220981747 ◽

2021 ◽

pp. 096228022098174

Author(s):

Daniel McNeish ◽

Jeffrey R. Harring

Keyword(s):

Mixture Models ◽

Random Effect ◽

Covariance Structure ◽

Poor Performance ◽

Covariance Structures ◽

Parameter Estimates ◽

Growth Mixture Models ◽

Class Enumeration ◽

Growth Mixture ◽

Pattern Growth

Growth mixture models are a popular method to uncover heterogeneity in growth trajectories. Harnessing the power of growth mixture models in applications is difficult given the prevalence of nonconvergence when fitting growth mixture models to empirical data. Growth mixture models are rooted in the random effect tradition, and nonconvergence often leads researchers to modify their intended model with constraints in the random effect covariance structure to facilitate estimation. While practical, doing so has been shown to adversely affect parameter estimates, class assignment, and class enumeration. Instead, we advocate specifying the models with a marginal approach to prevent the widespread practice of sacrificing class-specific covariance structures to appease nonconvergence. A simulation is provided to show the importance of modeling class-specific covariance structures and builds off existing literature showing that applying constraints to the covariance leads to poor performance. These results suggest that retaining class-specific covariance structures should be a top priority and that marginal models like covariance pattern growth mixture models that model the covariance structure without random effects are well-suited for such a purpose, particularly with modest sample sizes and attrition commonly found in applications. An application to PTSD data with such characteristics is provided to demonstrate (a) convergence difficulties with random effect models, (b) how covariance structure constraints improve convergence but to the detriment of performance, and (c) how covariance pattern growth mixture models may provide a path forward that improves convergence without forfeiting class-specific covariance structures.

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Residual-Based Algorithm for Growth Mixture Modeling: A Monte Carlo Simulation Study

Frontiers in Psychology ◽

10.3389/fpsyg.2021.618647 ◽

2021 ◽

Vol 12 ◽

Author(s):

Katerina M. Marcoulides ◽

Laura Trinchera

Keyword(s):

Mixture Models ◽

Simulation Study ◽

Growth Mixture Modeling ◽

Individual Case ◽

Mixture Modeling ◽

Monte Carlo Simulation Study ◽

New Approach ◽

Growth Mixture Models ◽

Growth Mixture ◽

Number Of Classes

Growth mixture models are regularly applied in the behavioral and social sciences to identify unknown heterogeneous subpopulations that follow distinct developmental trajectories. Marcoulides and Trinchera (2019) recently proposed a mixture modeling approach that examines the presence of multiple latent classes by algorithmically grouping or clustering individuals who follow the same estimated growth trajectory based on an evaluation of individual case residuals. The purpose of this article was to conduct a simulation study that examines the performance of this new approach for determining the number of classes in growth mixture models. The performance of the approach to correctly identify the number of classes is examined under a variety of longitudinal data design conditions. The findings demonstrated that the new approach was a very dependable indicator of classes across all the design conditions considered.

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