Regularized multigroup exploratory approximate factor analysis with orthogonal factors

Exploring similarities and differences in measurement models across groups is a central task in the behavioral and social sciences. Multigroup exploratory factor analysis is often used for this purpose, yet existing approaches face challenges when the number of variables is large relative to the sample size. Such high-dimensional settings are increasingly common as a result of digitalization and technological advances in measurement. In this article, we propose a multigroup regularized exploratory approximate factor analysis method that addresses these challenges. The method combines a zero-inducing constraint with a fusion penalty to obtain solutions that exhibit simple structure and similarity of factor loadings across groups when supported by the data. The method is applicable in settings where traditional approaches become unstable or computationally demanding. An important limitation is that the method is currently restricted to orthogonal factors and focuses on the comparison of correlation patterns between groups. In a simulation study based on commonly used multigroup factor analysis designs and including conditions with small sample sizes relative to the number of variables, the proposed method shows substantially improved recovery of both factor loading structure and (non)invariance of factor loadings compared with existing rotation-based and penalized approaches. Applications to empirical data, including a truly high-dimensional setting with tens of thousands of variables, illustrate that the method scales to large data and can reveal both shared and group-specific aspects of measurement models. (PsycInfo Database Record (c) 2026 APA, all rights reserved).