Modelling nonlinear moderation effects with local structural equation modelling (LSEM): A non-technical introduction

Understanding the differential strength of effects in the presence of a third variable, known as a moderation effect, is a common research goal in many psychological and behavioural science fields. If structural equation modelling is applied to test effects of interest, the investigation of differential strength of effects will typically ask how parameters of a latent variable model are influenced by categorical or continuous moderators, such as age, socio-economic status, personality traits, etc. Traditional approaches to continuous moderators in SEMs predominantly address linear moderation effects, risking the oversight of nonlinear effects. Moreover, some approaches have methodological limitations, for example, the need to categorise moderators or to pre-specify parametric forms of moderation. This tutorial introduces local structural equation modelling (LSEM) in a non-technical way. LSEM is a nonparametric approach that allows the analysis of nonlinear moderation effects without the above-mentioned limitations. Using an empirical dataset, we demonstrate the implementation of LSEM through the R-sirt package, emphasising its versatility in both exploratory analysis of nonlinear moderation without prior knowledge and confirmatory testing of hypothesised moderation functions. The tutorial also addresses common modelling issues and extends the discussion to different application scenarios, demonstrating its flexibility.