Evaluating local structural-after-measurement and traditional approaches for the estimation of complex nonlinear effects among latent variables.

Various methods exist to include interaction or quadratic terms involving latent variables in structural equation models. Most use system-wide estimation, where all parameters are estimated simultaneously and have been investigated in models with few nonlinear effects. Recently, structural-after-measurement approaches have been proposed, where estimation proceeds in two stages: the measurement model first, then the structural model. Rosseel et al. (2025) extended local structural after measurement (LSAM) to handle second-order nonlinear effects among latent variables, although analytical standard errors for this extension had not been derived. In this article, we provide such a two-step standard error formula for LSAM and evaluate its performance, alongside that of LSAM more broadly, in two simulation studies. These varied latent exogenous predictor distributions (normal, right-skewed, and uniform), reliabilities (0.4, 0.6, and 0.8), sample sizes (400 and 1,000), and measurement error and structural disturbance distributions (normal and right-skewed). The first study examined a model with three nonlinear effects. LSAM produced largely unbiased estimates with stable coverage, standard errors, and Type I error rates, although some metrics were less stable under low reliability and with uniform latent exogenous distributions-issues that were mitigated by larger sample sizes. Traditional methods (latent moderated structural equations, quasimaximum likelihood, and unconstrained product indicator) showed results consistent with prior literature. The second study, excluding latent moderated structural equations, tested a more complex model with eight nonlinear effects. LSAM maintained adequate performance despite greater complexity, although similar limitations emerged. Traditional methods yielded more variable results, with generally poorer performance overall. Right-skewed measurement errors affected results more than right-skewed structural disturbances, particularly under low and medium reliability. (PsycInfo Database Record (c) 2026 APA, all rights reserved).