Specification issues in nonlinear SEM: The moderation that wasn't

Analysis of interaction or moderation effects between latent variables is a common requirement in the social sciences. However, when predictors are correlated, interaction and quadratic effects become more alike, making them difficult to distinguish. As a result, when data are drawn from a quadratic population model and the analysis model specifies interactions only, misleading results may be obtained.

This article addresses the consequences of different types of specification error in nonlinear structural equation models using a Monte Carlo study.

Results show that fitting a model with interactions when quadratic effects are present in the population will almost certainly lead to erroneous detection of moderation effects, and that the same is true in the opposite scenario. Simultaneous estimation of interactions and quadratic effects yields correct results.

Simultaneous estimation of interaction and quadratic effects prevents detection of spurious or misleading nonlinear effects. Results are discussed and recommendations are offered to applied researchers.