Structural equation model trees.

Abstract

In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree structures that separate a data set recursively into subsets with significantly different parameter estimates in a SEM. SEM Trees provide means for finding covariates and covariate interactions that predict differences in structural parameters in observed as well as in latent space and facilitate theory-guided exploration of empirical data. We describe the methodology, discuss theoretical and practical implications, and demonstrate applications to a factor model and a linear growth curve model.

Terminal decline in well-being: The role of multi-indicator constellations of physical health and psychosocial correlates.

“…For example, in clinical decision making, decision trees have been applied to identify constellations of cognitive, biomarker and other variables as effective correlates for outcomes as diverse as treatment success of inpatient psychotherapy (Hannöver & Kordy, 2005), alcohol or smoking behavior (Kitsantas, Kitsantas, & Anagnostopoulou, 2008;Kitsantas, Moore, & Sly, 2007), functional impairment (Lemsky, Smith, Malec, & Ivnik, 1996), depression (Schmitz, Kugler, & Rollnik, 2003), subjective memory impairment (Jessen et al, 2007), suicidal ideation in older people (Handley et al, 2014), and mortality hazards (Gruenewald, Seeman, Ryff, Karlamangla, & Singer, 2006). Increasingly, these methods are also employed to support psychological theorybuilding, for example, to explore contextual features contributing to feelings of stress in later life (Scott, Jackson, & Bergeman, 2011), to predict longitudinal attrition in surveys (McArdle, 2013), to explore differences in cross-sectional factor profiles and developmental latent growth curves of intelligence (Brandmaier et al, 2013), or to explore correlates of differential trajectories of cognitive functioning in old age (Brandmaier et al, 2014).…”

“…The non-parametric approach offered by trees enables us to model nonlinear interactions among the correlates (see Brandmaier et al, 2013), and also avoids making the often too strict assumption that effects are additive (e.g., as done in linear regression). Trees are particularly useful for data sets with a large number of potential correlates and interrelations that are expected to be complex and interactive.…”

“…Structural equation model (SEM) Trees and Forests have recently been introduced into the literature as a methodological tool to structure and understand heterogeneity (Brandmaier et al, in press;Brandmaier et al, 2013;Brandmaier, von Oertzen, McArdle, & Lindenberger, 2014). In brief, SEM Trees and SEM Forests are an instance of model-based recursive partitioning, a non-parametric statistical method that originates from the field of machine learning and data mining but can be traced back to early work on binary segmentation methods from five decades ago (Sonquist & Morgan, 1964).…”

Theory-guided exploration with structural equation model forests.

“…• control -a SEM Tree control object as described in Brandmaier, von Oertzen, McArdle, & Lindenberger (2013b).…”

“…Below, we will present two applications to illustrate the approach, (a) a factor model of intelligence, and (b) a factor model of episodic memory. The first data set may not be seen as particular "big" but was chosen to complement our earlier tree analyses (Brandmaier et al, 2013b) and to highlight the added benefits of forest analyses. The second analysis is included to provide a data set that may be considered closer to a big data type of application.…”