modsem: An R package for estimating latent interactions and quadratic effects

The estimation of interaction and quadratic effects in Structural Equation Models (SEMs) is acomplex task in psychometrics. Latent product term (LPT) models, initially developed forinteraction effects between latent variables, are also used to model quadratic effects. Despite over30 years of research, no consensus has emerged on the best method for modeling interactions inSEMs, partly due to efforts to simplify existing approaches for broader accessibility. LPT modelsare categorized into Product Indicator (PI) and Distribution Analytic (DA) approaches. PImethods are conceptually simple but often sacrifice accuracy due to necessary simplifications,making them error-prone and difficult to implement manually. In contrast, DA methods, such asLatent Moderated Structural Equations (LMS) and Quasi Maximum Likelihood (QML), providemore accurate estimates in simulations but are computationally intensive and less accessible dueto limited implementations. We introduce modsem, an R package that simplifies the estimation ofinteraction and quadratic effects in SEMs. modsem supports various methods, including PI, LMS,and QML, and extends them to models with multiple endogenous variables. It integratesseamlessly with the popular lavaan syntax, enhancing accessibility for researchers. Wedemonstrate modsem’s utility with applications to the Theory of Planned Behaviour and PISA2006 data, highlighting its effectiveness in estimating complex models. Future work will focus onvalidating and refining LMS and QML approaches, and exploring alternative methods likeBayesian and Structural After Measurement (SAM) approaches.