Resampling Based Bias Correction for Small Sample SEM

Structural Equation Models (SEMs) are typically estimated via Maximum Likelihood. Grounded in large sample theory, estimates are prone to finite sample bias. Although Restricted Maximum Likelihood (REML) can alleviate this bias, its applicability is constrained to SEMs that are mathematically equivalent to mixed effect models. Via Monte Carlo simulations, we explored whether resampling based corrections could serve as viable, more broadly applicable alternatives. Results indicate that Bootstrap and Jackknife corrections effectively attenuate small sample bias, at the expected expense of an increase in variability. Similar conclusions are drawn with respect to a more recently proposed analytic approach by Ozenne et al., which was included for comparison. For all corrective methods, caution is advised when dealing with non-normal data and/or low reliability.

Automated summary

This article investigates the estimation methods for Structural Equation Models (SEMs) and finds that the traditional Maximum Likelihood estimation suffers from finite sample bias, while Restricted Maximum Likelihood (REML) is only applicable to SEMs that are mathematically equivalent to mixed effect models. Through Monte Carlo simulations, it is discovered that resampling-based corrections such as Bootstrap and Jackknife effectively reduce small sample bias but increase variability. Similar conclusions are drawn for a proposed analytic approach by Ozenne et al., which is included for comparison.