Score-Guided Structural Equation Model Trees

Abstract

Structural equation model (SEM) trees are data-driven tools for finding variables that predict group differences in SEM parameters. SEM trees build upon the decision tree paradigm by growing tree structures that divide a data set recursively into homogeneous subsets. In past research, SEM trees have been estimated predominantly with the R package semtree. The original algorithm in the semtree package selects split variables among covariates by calculating a likelihood ratio for each possible split of each covariate. Obtaining these likelihood ratios is computationally demanding. As a remedy, we propose to guide the construction of SEM trees by a family of score-based tests that have recently been popularized in psychometrics (Merkle and Zeileis, 2013; Merkle et al., 2014). These score-based tests monitor fluctuations in case-wise derivatives of the likelihood function to detect parameter differences between groups. Compared to the likelihood-ratio approach, score-based tests are computationally efficient because they do not require refitting the model for every possible split. In this paper, we introduce score-guided SEM trees, implement them in semtree, and evaluate their performance by means of a Monte Carlo simulation.

Predicting Differences in Model Parameters with Individual Parameter Contribution Regression Using the R Package ipcr

“…These methods divide a data set into homogeneous subgroups by finding covariates that predict parameter differences. For SEMs, model-based recursive partitioning was popularized as SEM trees and gained attention in the past years [43][44][45]. Finally, it is important to note that the performance of IPC regression depends primarily on the available covariates.…”

Science Interest, Utility, Self-Efficacy, Identity, and Science Achievement Among High School Students: An Application of SEMTree

“…Therefore, the score-guided SEM tree comes as a remedy for multiple ML comparisons by proposing an additional five methods. One simulation study found that two score-guided methods, i.e., maxLMO and CvM, outperformed ML methods in terms of statistical power, reducing computational time, and group recovery when examining multiple parameters (Arnold et al, 2021).…”

Science Interest, Utility, Self-Efficacy, Identity, and Science Achievement Among High School Students: An Application of SEM Tree

“…Therefore, the score-guided SEM tree comes as a remedy for multiple ML comparisons by proposing an additional five methods. One simulation study found that two score-guided methods, i.e., maxLMO and CvM, outperformed ML methods in terms of statistical power, reducing computational time, and group recovery when examining multiple parameters (Arnold et al, 2021 ).…”

“…Therefore, an SEM tree package was used to construct the tree. The updated score-guided SEM tree, particularly maxLMO, controlled the tree depth (Arnold et al, 2021 ).…”