Specification search in structural equation modeling with SEM forests

Silva Díaz, John Alexander (2025): Specification search in structural equation modeling with SEM forests. Dissertation, LMU München: Faculty of Psychology and Educational Sciences

Abstract

Model misspecification is a prevalent challenge in applied SEM, often requiring specification search to improve model fit. Traditional approaches, such as modification indices, are limited to variables already included in the model and are therefore ineffective at detecting omitted influential variables and their interaction effects. To address these limitations, the two studies presented in this dissertation introduce SEM forests as a novel and robust technique for specification search in SEM. The first study evaluates the performance of SEM forests to identify unique, mixed, and interaction covariate paths across different factor loading magnitudes, covariate path magnitudes, and sample sizes. The results indicate that SEM forests consistently do not incorrectly identify noninfluential omitted covariate paths under all examined conditions and accurately identify influential omitted covariate paths in multiple condition combinations explored, particularly when covariate-latent variable regression coefficients are strong and sample sizes are large. The second study provides a step-by-step guide for using SEM forests with the semtree R package, covering data preparation, model specification, forest generation, results interpretation, and model respecification. This practical guide equips researchers with the tools to apply SEM forests for specification search in SEM, addressing the limitations of traditional methods regarding omitted variables. Together, these studies demonstrate SEM forests as a robust alternative for specification search, enabling the identification of omitted influential covariates and interactions that traditional methods may overlook, ultimately enhancing the validity and reliability of SEM models.

• Item Type: Theses (Dissertation, LMU Munich)
• Keywords: Model specification search, SEM forests, structural equation modeling, variable importance, omitted variables
• Subjects: 300 Social sciences; 300 Social sciences > 370 Education
• Faculties: Faculty of Psychology and Educational Sciences
• Language: English
• Date of oral examination: 18. July 2025
• 1. Referee: Heene, Moritz
• Signature of the printed copy: 0001/UMC 31632