A Comparison of Methods for Uncovering Sample Heterogeneity: Structural Equation Model Trees and Finite Mixture Models

Abstract

Although finite mixture models have received considerable attention, particularly in the social and behavioral sciences, an alternative method for creating homogeneous groups, structural equation model trees (Brandmaier, von Oertzen, McArdle, & Lindenberger, 2013), is a recent development that has received much less application and consideration. It is our aim to compare and contrast these methods for uncovering sample heterogeneity. We illustrate the use of these methods with longitudinal reading achievement data collected as part of the Early Childhood Longitudinal Study–Kindergarten Cohort. We present the use of structural equation model trees as an alternative framework that does not assume the classes are latent and uses observed covariates to derive their structure. We consider these methods as complementary and discuss their respective strengths and limitations for creating homogeneous groups.

Reconsidering important outcomes of the nonsuicidal self‐injury disorder diagnostic criterion A

“…The model fit poorly using the entire sample (all participants endorsing past 12‐month NSSI), with a root‐mean‐squared error of approximation (RMSEA) of 0.141 (90% confidence interval [CI] = 0.108, 0.176). Note that some degree of misfit is necessary for the identification of subgroups (see Jacobucci et al () for further detail). See Figure for the resulting SEM tree diagram.…”

“…Structural equation model trees (SEM trees; Brandmaier, von Oertzen, McArdle, & Lindenberger, ; Jacobucci, Grimm, & McArdle, ) are a generalization of DT that build tree structures that separate a data set recursively into subsets that are maximally different with respect to the fit of an SEM. By splitting observations into groups based on their predictor values, SEM trees can be thought of as a form of exploratory multiple group modeling that results in a tree‐like structure indicating final group membership.…”

The performance of latent growth curve model-based structural equation model trees to uncover population heterogeneity in growth trajectories

“…For example, larger values of the number of true nodes C, which is also a newly specified factor in the current simulation, have a negative impact on correct estimation of the number of true classes, because when C = 4, statistical power for correct estimation of classes dramatically decreases compared with the case of C = 2. This point is critically important, since in many applications of tree analyses there is more than one split, extracting more than two classes (e.g., Brandmaier et al 2013;Jacobucci et al 2017). Therefore, the previous investigations might show overly optimistic results regarding the performance of SEM Trees in general.…”

“…During the past decade, researchers have shown growing interest in applying latent growth curve mixture models (LGCMMs; Berlin et al 2014;Leiby et al 2009;Neelon et al 2011;Ram and Grimm 2009), and, more recently, in applying machine learning techniques including SEM Trees (e.g., Hayes et al 2015;Martin 2015;Jacobucci et al 2017). Both LGCMMs and SEM Trees utilize SEM to model changes using latent variables estimated with a smaller number of parameters.…”

“…However, only allowing for two classes, thus only one split without covariate interactions, is a very limited case in general applications of tree analyses. Actually, previous research that applied LGCMM or SEM Trees extracted more than two classes (e.g., see the above examples of Jacobucci et al 2017;Leiby et al 2009;Nagin and Tremblay 1999), and we expect that researchers usually collect multiple covariates that can explain population heterogeneity in practice. Importantly, as the number of true classes and covariates become larger, exact estimation of population heterogeneity should become more difficult, since all covariates and corresponding criterion values must be identified correctly, demanding larger sample sizes in total when estimating trees.…”