RGLS and RLS in Covariance Structure Analysis

Abstract

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 generalized least squares (GLS) statistics are based on large sample statistical theory. However, ML and GLS goodness-of-fit tests often make incorrect decisions on the true model, when sample size is small. The novel methods RGLS and RLS aim to correct the over-rejection by ML and under-rejection by GLS. Both methods outperform ML and GLS when samples are small, yet no studies have compared their relative performance. A Monte Carlo simulation study was carried out to examine the statistical performance of these two methods. We find that RLS and RGLS have equivalent performance when N $\ge$70; whereas when N $<$70, RLS outperforms RGLS. Both methods clearly outperform ML and GLS with N $\le$400. Nonetheless, adopting mean and variance adjusted test for non-normal data, RGLS slightly outperforms RLS. Power analyses found that RLS generally showed small loss in power compared to ML and performed better than RGLS.

Keywords:

• Covariance structure
• eigenvalue
• estimation method
• goodness of fit
• weight matrix

Acknowledgements

We want to thank Han Du for her suggestions in the nonnormal data distribution programming.