Evaluating the standard error estimation of the Local Structural-After-Measurement (LSAM) approach in structural equation modeling [Author Accepted Manuscript]

Accurate estimation of standard errors (SEs) is essential in SEM as they quantify the uncertainty of parameter estimates, are fundamental to computing test statistics, and ensure robust population inferences. This study evaluated SEs within the Local Structural-After-Measurement (LSAM) framework, a two-step approach to SEM. Two simulation studies examined analytic and resampling-based SE methods under varying conditions, including normal and nonnormal data, different sample sizes, and both correct and misspecified models. The nonparametric bootstrap yielded near-unbiased SEs under nonnormality, even when models were misspecified, while the parametric bootstrap performed well under normal conditions with correct model specification. The analytic two-step method performed well under normal conditions but showed increased bias with nonnormal data and smaller samples. The robust two-step method reduced this bias in larger samples, though some underestimation remained in small-sample and misspecified conditions. To complement SE bias results, 90% coverage rates were assessed. Findings confirm LSAM’s capability for accurate SE estimation in challenging research contexts.