Title: Model-Robust Estimation of Multiple-Group Structural Equation Models

Author: Alexander Robitzsch

Abstract:
Structural equation models (SEM) are widely used in the social sciences. They
model the relationships between latent variables in structural models while
defining the latent variables by observed variables in measurement models.
Frequently, it is of interest to compare particular parameters in an SEM as a
function of a discrete grouping variable. Multiple-group SEM is employed to
compare structural relationships between groups. In this article, estimation
approaches for the multiple-group are reviewed. We focus on comparing
different estimation strategies in the presence of local model
misspecifications (i.e., model errors). In detail, maximum likelihood and
weighted least-squares estimation approaches are compared with a newly
proposed robust $L_p$ loss function and regularized maximum likelihood
estimation. The latter methods are referred to as model-robust estimators
because they show some resistance to model errors. In particular, we focus on
the performance of the different estimators in the presence of unmodelled
residual error correlations and measurement noninvariance (i.e.,
group-specific item intercepts). The performance of the different estimators
is compared in two simulation studies and an empirical example. It turned out
that the robust loss function approach is computationally much less demanding
than regularized maximum likelihood estimation but resulted in similar
statistical performance.