Residual-Based Algorithm for Detecting Mixtures in Latent Growth Models

• In Event: Methodological Advances in Longitudinal Mixture Modeling

Abstract

Growth mixture models combine latent growth curve models and finite mixture models to examine the existence of latent classes that follow distinct patterns of growth. One general concern that has been raised with this modeling technique is that the number of groups is inferred by the researcher rather than determined directly from the data (Nagin, 2005). Marcoulides and Trinchera (2018) 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. While past research has primarily focused on using individual case residuals for evaluating competing models, in this presentation individual case residuals are used to cluster individuals for the purpose of distinguishing between growth mixture models. The groups that are identified are assumed to represent latent longitudinal strata, or classes, in which variability is characterized by differences across individuals in the intercept and slope of their growth trajectories, as well as their corresponding individual case residuals (Haviland, Rosenbaum, Nagin, & Tremblay, 2008; Raykov & Penev, 2001; 2002).
This algorithmic mixture modeling approach is first illustrated using empirical longitudinal data. Then, using Monte Carlo simulation techniques, we examine to what extent the newly proposed approach can successfully select the correct latent class model under a variety of longitudinal data design conditions with varying class characteristics and sample sizes. Parameters that are varied in the simulations include the number of true classes in the population, the sample size, and the shapes of the latent growth trajectories. Parameters that are fixed in the simulations include the number of measurement occasions, the degree of class separation, the mixing ratio, the variance and covariance for the intercept and slope, and the residuals for the repeated measurement occasions. These design elements are selected based on previous simulation studies (Nylund, Asparouhov, & Muthén, 2007; Peugh & Fan, 2012; He & Fan, 2018). Specifically, the number of true classes for the population were stipulated to range from two to four classes, the sample sizes were set at N = 180, N = 540, and N = 1080 observations (to reflect small, medium, and large samples), and the shapes of the latent trajectories are specified to reflect different-intercept-same-slope and different-intercept-different-slope growth trajectory conditions.
To evaluate the accuracy of the approach, a performance rate measure is defined as the percentage of the total replications where the true number of latent classes is correctly identified. High percentage values indicate that the approach was able to correctly identify the true class growth model. Overall, the findings demonstrated that the new approach is a very dependable indicator of classes across all the design conditions considered. The presentation concludes with a discussion of the limitations and benefits of this new approach.

Authors

• Katerina M. Marcoulides, University of Minnesota

• Laura TRINCHERA, NEOMA Business School