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Estimating interaction and quadratic effects in structural equation models (SEMs) is complex. Latent product term (LPT) models, designed for interaction effects, also accommodate quadratic effects. After 30 years of research, no consensus has emerged on the best modeling methods in SEMs, partly due to efforts to simplify approaches for accessibility. LPT models include product indicator (PI) and distribution analytic (DA) approaches. While PI methods are simpler, they sacrifice accuracy and can be error prone. DA methods, like latent moderated structural equations (LMS) and Quasi maximum likelihood (QML), are more accurate but computationally intensive. We introduce modsem, an R package that simplifies these estimations and enhances accessibility.
Slupphaug et al. (Wed,) studied this question.