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RGLS and RLS in Covariance Structure Analysis

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  • Zheng, Bang Quan

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 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.

Suggested Citation

  • Zheng, Bang Quan, 2021. "RGLS and RLS in Covariance Structure Analysis," SocArXiv aejgf, Center for Open Science.
  • Handle: RePEc:osf:socarx:aejgf
    DOI: 10.31219/osf.io/aejgf
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    References listed on IDEAS

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    1. Muni S. Srivastava & Hirokazu Yanagihara & Tatsuya Kubokawa, 2014. "Tests for Covariance Matrices in High Dimension with Less Sample Size," CIRJE F-Series CIRJE-F-933, CIRJE, Faculty of Economics, University of Tokyo.
    2. Yuan, Ke-Hai & Bentler, Peter M., 1999. "On asymptotic distributions of normal theory MLE in covariance structure analysis under some nonnormal distributions," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 107-113, April.
    3. Chi, Eric C. & Lange, Kenneth, 2014. "Stable estimation of a covariance matrix guided by nuclear norm penalties," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 117-128.
    4. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    5. Jianhua Z. Huang & Naiping Liu & Mohsen Pourahmadi & Linxu Liu, 2006. "Covariance matrix selection and estimation via penalised normal likelihood," Biometrika, Biometrika Trust, vol. 93(1), pages 85-98, March.
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