RGLS and RLS in Covariance Structure Analysis

This paper assesses the performance of regularized generalized least squares (RGLS) and reweighted least squares (RLS) methodologies in a confirmatory factor analysis model. Normal theory maximum likelihood (ML) and GLS statistics are based on large sample statistical theory. However, violation of asymptotic sample size is ubiquitous in real applications of structural equation modeling (SEM), and ML and GLS goodness-of-fit tests in SEM often make incorrect decisions on the true model. The novel methods RGLS and RLS aim to correct the over-rejection by ML and under-rejection by GLS. Proposed by Arruda and Bentler (2017), RGLS replaces a GLS weight matrix with a regularized one. Rediscovered by Hayakawa (2019), RLS replaces this weight matrix with one that derives from an ML function. Both of these methods outperform ML and GLS when samples are small, yet no studies have compared their relative performance. A confirmatory factor analysis Monte Carlo simulation study with normal and non-normal data was carried out to examine the statistical performance of these two methods at different sample sizes. Based on empirical rejection frequencies and empirical distributions of test statistics, we find that RLS and RGLS have equivalent performance when N≥70; whereas when N<70, RLS outperforms RGLS. Both methods clearly outperform ML and GLS with N≤400. Nonetheless, adopting mean and variance adjusted test proposed by Hayakawa (2019) for non-normal data, our results show that RGLS slightly outperforms RLS.