IDEAS home Printed from https://ideas.repec.org/p/osf/socarx/aejgf.html
   My bibliography  Save this paper

RGLS and RLS in Covariance Structure Analysis

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://osf.io/download/615c9a2cfd5b23004598419b/
    Download Restriction: no

    File URL: https://libkey.io/10.31219/osf.io/aejgf?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sonia Nawrocka & Hans De Witte & Margherita Pasini & Margherita Brondino, 2023. "A Person-Centered Approach to Job Insecurity: Is There a Reciprocal Relationship between the Quantitative and Qualitative Dimensions of Job Insecurity?," IJERPH, MDPI, vol. 20(7), pages 1-27, March.
    2. Md. Mominur Rahman & Bilkis Akhter, 2021. "The impact of investment in human capital on bank performance: evidence from Bangladesh," Future Business Journal, Springer, vol. 7(1), pages 1-13, December.
    3. Masashi Soga & Kevin J. Gaston & Yuichi Yamaura & Kiyo Kurisu & Keisuke Hanaki, 2016. "Both Direct and Vicarious Experiences of Nature Affect Children’s Willingness to Conserve Biodiversity," IJERPH, MDPI, vol. 13(6), pages 1-12, May.
    4. César Merino-Soto & Gina Chávez-Ventura & Verónica López-Fernández & Guillermo M. Chans & Filiberto Toledano-Toledano, 2022. "Learning Self-Regulation Questionnaire (SRQ-L): Psychometric and Measurement Invariance Evidence in Peruvian Undergraduate Students," Sustainability, MDPI, vol. 14(18), pages 1-17, September.
    5. Li, Yang & Wang, Zhaojun & Zou, Changliang, 2016. "A simpler spatial-sign-based two-sample test for high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 192-198.
    6. Nathaniel Oliver Iotti & Damiano Menin & Tomas Jungert, 2022. "Early Adolescents’ Motivations to Defend Victims of Cyberbullying," IJERPH, MDPI, vol. 19(14), pages 1-9, July.
    7. AJ Golio, 2024. "Whose Neighborhood Now? Gentrification and Community Life in Low-Income Urban Neighborhoods," Working Papers 24-29, Center for Economic Studies, U.S. Census Bureau.
    8. Peter Tavel & Bibiana Jozefiakova & Peter Telicak & Jana Furstova & Michal Puza & Natalia Kascakova, 2022. "Psychometric Analysis of the Shortened Version of the Spiritual Well-Being Scale on the Slovak Population (SWBS-Sk)," IJERPH, MDPI, vol. 19(1), pages 1-12, January.
    9. Allen, Jaime & Eboli, Laura & Forciniti, Carmen & Mazzulla, Gabriella & Ortúzar, Juan de Dios, 2019. "The role of critical incidents and involvement in transit satisfaction and loyalty," Transport Policy, Elsevier, vol. 75(C), pages 57-69.
    10. Christoph Dworschak, 2024. "Bias mitigation in empirical peace and conflict studies: A short primer on posttreatment variables," Journal of Peace Research, Peace Research Institute Oslo, vol. 61(3), pages 462-476, May.
    11. Andreea-Ionela Puiu & Anca Monica Ardeleanu & Camelia Cojocaru & Anca Bratu, 2021. "Exploring the Effect of Status Quo, Innovativeness, and Involvement Tendencies on Luxury Fashion Innovations: The Mediation Role of Status Consumption," Mathematics, MDPI, vol. 9(9), pages 1-18, May.
    12. Slupphaug, KJell & Mehmetoglu, Mehmet & Mittner, Matthias, 2024. "modsem: An R package for estimating latent interactions and quadratic effects," OSF Preprints h3rpw, Center for Open Science.
    13. Andres Trujillo-Barrera & Joost M. E. Pennings & Dianne Hofenk, 2016. "Understanding producers' motives for adopting sustainable practices: the role of expected rewards, risk perception and risk tolerance," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 43(3), pages 359-382.
    14. Daria J. Kuss & Lydia Harkin & Eiman Kanjo & Joel Billieux, 2018. "Problematic Smartphone Use: Investigating Contemporary Experiences Using a Convergent Design," IJERPH, MDPI, vol. 15(1), pages 1-16, January.
    15. Allen, Jaime & Muñoz, Juan Carlos & Ortúzar, Juan de Dios, 2019. "On evasion behaviour in public transport: Dissatisfaction or contagion?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 130(C), pages 626-651.
    16. Cloarec, Julien, 2022. "Privacy controls as an information source to reduce data poisoning in artificial intelligence-powered personalization," Journal of Business Research, Elsevier, vol. 152(C), pages 144-153.
    17. Merkle, Edgar C. & Steyvers, Mark & Mellers, Barbara & Tetlock, Philip E., 2017. "A neglected dimension of good forecasting judgment: The questions we choose also matter," International Journal of Forecasting, Elsevier, vol. 33(4), pages 817-832.
    18. Lam, Clifford, 2008. "Estimation of large precision matrices through block penalization," LSE Research Online Documents on Economics 31543, London School of Economics and Political Science, LSE Library.
    19. Sai-fu Fung & Esther Oi-wah Chow & Chau-kiu Cheung, 2020. "Development and Evaluation of the Psychometric Properties of a Brief Wisdom Development Scale," IJERPH, MDPI, vol. 17(8), pages 1-14, April.
    20. Giraud Christophe & Huet Sylvie & Verzelen Nicolas, 2012. "Graph Selection with GGMselect," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(3), pages 1-52, February.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:osf:socarx:aejgf. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: OSF (email available below). General contact details of provider: https://arabixiv.org .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.