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

The estimation of interaction and quadratic effects in Structural Equation Models (SEMs) is a complex task in psychometrics. Latent product term (LPT) models, initially developed for interaction effects between latent variables, are also used to model quadratic effects. Despite over 30 years of research, no consensus has emerged on the best method for modeling interactions in SEMs, partly due to efforts to simplify existing approaches for broader accessibility. LPT models are categorized into Product Indicator (PI) and Distribution Analytic (DA) approaches. PI methods 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 as Latent Moderated Structural Equations (LMS) and Quasi Maximum Likelihood (QML), provide more accurate estimates in simulations but are computationally intensive and less accessible due to limited implementations. We introduce modsem, an R package that simplifies the estimation of interaction and quadratic effects in SEMs. modsem supports various methods, including PI, LMS, and QML, and extends them to models with multiple endogenous variables. It integrates seamlessly with the popular lavaan syntax, enhancing accessibility for researchers. We demonstrate modsem’s utility with applications to the Theory of Planned Behaviour and PISA 2006 data, highlighting its effectiveness in estimating complex models. Future work will focus on validating and refining LMS and QML approaches, and exploring alternative methods like Bayesian and Structural After Measurement (SAM) approaches.