A Faster Procedure for Estimating SEMs Applying Minimum Distance Estimators With a Fixed Weight Matrix

Abstract

This study presents a separable nonlinear least squares (SNLLS) implementation of the minimum distance (MD) estimator employing a fixed-weight matrix for estimating structural equation models (SEMs). In contrast to the standard implementation of the MD estimator, in which the complete set of parameters is estimated using nonlinear optimization, the SNLLS implementation allows a subset of parameters to be estimated using (linear) least squares (LS). The SNLLS implementation possesses a number of benefits, such as faster convergence, better performance in ill-conditioned estimation problems, and fewer required starting values. The present work demonstrates that SNLLS, when applied to SEM estimation problems, significantly reduces the estimation time. Reduced estimation time makes SNLLS particularly useful in applications involving some form of resampling, such as simulation and bootstrapping.