SEMi-Complete by Design: A Monte Carlo simulation to assess Measurement Invariance in Moderated Nonlinear Factor Analysis and SEM-Trees

Abstract

Ensuring the validity of psychological assessments is crucial, yet differential itemfunctioning (DIF) can threaten measurement invariance (MI) (Bauer, Belzak, and Cole2020). Recent calls for improved DIF detection methods emphasize the need for moreadvanced statistical approaches (Lee, Han, and Choi 2024). Moderated nonlinear factoranalysis (MNLFA) is a recent approach for assessing MI via parameter moderation within asingle-group confirmatory factor analysis framework. MLNFA evaluates MI across multiplecontinuous and categorical covariates, and accounts for heteroskedasticity by modeling factorand residual variances as functions of these covariates. While MNLFA offers continuousmoderation of several parameters of Structural Equation Models (SEMs) (e.g.: factorloadings, covariances etc.), it requires a priori specification of covariates and their functionalrelationships (Bauer 2017; Kolbe et al. 2024). In contrast, Structural Equation Model (SEM)trees and forests are data-driven, non-parametric methods that use recursive partitioning toidentify latent subgroups in which model parameters differ, without assuming specificfunctional forms or predefined covariate effects. These approaches allow for nonlinearmoderation of factor loadings and can reveal complex interaction effects, enabling theexploratory detection of DIF (Brandmaier et al. 2016, 2013). In this study, we conduct aMonte Carlo simulation to compare the performance of MNLFA and SEM trees as well asforests in detecting DIF and assessing MI under varying conditions. Specifically, we evaluatetheir effectiveness in identifying non-invariance and detecting relevant covariates.