Theory-guided exploration with structural equation model forests.

Abstract

Structural equation model (SEM) trees, a combination of SEMs and decision trees, have been proposed as a data-analytic tool for theory-guided exploration of empirical data. With respect to a hypothesized model of multivariate outcomes, such trees recursively find subgroups with similar patterns of observed data. SEM trees allow for the automatic selection of variables that predict differences across individuals in specific theoretical models, for instance, differences in latent factor profiles or developmental trajectories. However, SEM trees are unstable when small variations in the data can result in different trees. As a remedy, SEM forests, which are ensembles of SEM trees based on resamplings of the original dataset, provide increased stability. Because large forests are less suitable for visual inspection and interpretation, aggregate measures provide researchers with hints on how to improve their models: (a) variable importance is based on random permutations of the out-of-bag (OOB) samples of the individual trees and quantifies, for each variable, the average reduction of uncertainty about the model-predicted distribution; and (b) case proximity enables researchers to perform clustering and outlier detection. We provide an overview of SEM forests and illustrate their utility in the context of cross-sectional factor models of intelligence and episodic memory. We discuss benefits and limitations, and provide advice on how and when to use SEM trees and forests in future research.

Neurocognitive reorganization between crystallized intelligence, fluid intelligence and white matter microstructure in two age-heterogeneous developmental cohorts

“…In terms of analytical frameworks, here we implement a relatively new analytical framework, called SEM-trees (Brandmaier et al, 2013) (Zadelaar et al, 2019), Gaussian process structural equation models (e.g. Silva and Gramacy, 2010), latent class and latent profile analysis (Oberski, 2016), general frameworks such as decision trees (McArdle, 2013) and model-based cluster analysis (Fraley and Raftery, 1999), as well as extensions of SEM trees such as SEM forests (Brandmaier et al, 2016). All of these techniques differ in their strengths and weaknesses, ease of implementation, degree of confirmation versus exploration and their flexibility (e.g.…”

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

“…As indicated by the present simulation, this point should be more critical when the true classification structure is complex (i.e., a large number of true classes). In that respect, although the computation burden is still heavy, using SEM Forests (Brandmaier et al 2016) could be a useful alternative to address this problem, and more research is needed into the propensity for SEM Trees and SEM Forests to over-fit. From a technical aspect, additional future investigations should also include the development of more computationally efficient algorithms.…”

“…SEM Trees analyses can be performed using the R package semtree (Brandmaier et al 2013), with SEM models handled by either lavaan (Rosseel 2012) or Open M x (Boker et al 2011). In this package, we can also use a more advanced version of SEM Trees called SEM forests (Brandmaier et al 2016), which are ensembles of SEM Trees based on resamplings of the original dataset that provide increased stability of the estimation results. Currently, SEM forests can only be paired with OpenMx.…”

Developmental cognitive neuroscience using Latent Change Score models: A tutorial and applications

“…boys and girls show differential response dynamics following divorce, Malone et al, 2004). In cases where a large number of covariates are potentially relevant but we have no strong theories to guide us, more exploratory techniques such as SEM trees (Brandmaier, von Oertzen, McArdle, & Lindenberger, 2013) and SEM forests (Brandmaier, Prindle, McArdle, & Lindenberger, 2016) allows researchers to hierarchically split empirical data into homogeneous groups sharing similar data patterns, by recursively selecting optimal predictors of these differences from a potentially large set of candidates. The resulting tree structure reflects set of subgroups with distinct model parameters, where the groups are derived in a data-driven way.…”