IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v5y2022i3p39-672d869466.html

Comparing the Robustness of the Structural after Measurement (SAM) Approach to Structural Equation Modeling (SEM) against Local Model Misspecifications with Alternative Estimation Approaches

Author

Listed:
  • Alexander Robitzsch

    (IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstraße 62, 24118 Kiel, Germany
    Centre for International Student Assessment (ZIB), Olshausenstraße 62, 24118 Kiel, Germany)

Abstract

Structural equation models (SEM), or confirmatory factor analysis as a special case, contain model parameters at the measurement part and the structural part. In most social-science SEM applications, all parameters are simultaneously estimated in a one-step approach (e.g., with maximum likelihood estimation). In a recent article, Rosseel and Loh (2022, Psychol. Methods ) proposed a two-step structural after measurement (SAM) approach to SEM that estimates the parameters of the measurement model in the first step and the parameters of the structural model in the second step. Rosseel and Loh claimed that SAM is more robust to local model misspecifications (i.e., cross loadings and residual correlations) than one-step maximum likelihood estimation. In this article, it is demonstrated with analytical derivations and simulation studies that SAM is generally not more robust to misspecifications than one-step estimation approaches. Alternative estimation methods are proposed that provide more robustness to misspecifications. SAM suffers from finite-sample bias that depends on the size of factor reliability and factor correlations. A bootstrap-bias-corrected LSAM estimate provides less biased estimates in finite samples. Nevertheless, we argue in the discussion section that applied researchers should nevertheless adopt SAM because robustness to local misspecifications is an irrelevant property when applying SAM. Parameter estimates in a structural model are of interest because intentionally misspecified SEMs frequently offer clearly interpretable factors. In contrast, SEMs with some empirically driven model modifications will result in biased estimates of the structural parameters because the meaning of factors is unintentionally changed.

Suggested Citation

  • Alexander Robitzsch, 2022. "Comparing the Robustness of the Structural after Measurement (SAM) Approach to Structural Equation Modeling (SEM) against Local Model Misspecifications with Alternative Estimation Approaches," Stats, MDPI, vol. 5(3), pages 1-42, July.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:3:p:39-672:d:869466
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/5/3/39/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/5/3/39/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Po-Hsien Huang & Hung Chen & Li-Jen Weng, 2017. "A Penalized Likelihood Method for Structural Equation Modeling," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 329-354, June.
    2. Alexander Robitzsch, 2020. "L p Loss Functions in Invariance Alignment and Haberman Linking with Few or Many Groups," Stats, MDPI, vol. 3(3), pages 1-38, August.
    3. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    4. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    5. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    6. Bai, Jushan & Liao, Yuan, 2016. "Efficient estimation of approximate factor models via penalized maximum likelihood," Journal of Econometrics, Elsevier, vol. 191(1), pages 1-18.
    7. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
    8. Lee Cronbach, 1951. "Coefficient alpha and the internal structure of tests," Psychometrika, Springer;The Psychometric Society, vol. 16(3), pages 297-334, September.
    9. Jules L. Ellis, 2021. "A Test Can Have Multiple Reliabilities," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 869-876, December.
    10. She, Yiyuan & Owen, Art B., 2011. "Outlier Detection Using Nonconvex Penalized Regression," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 626-639.
    11. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    12. Gerhard Arminger & Ronald Schoenberg, 1989. "Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 409-425, September.
    13. Steffen Zitzmann & Julian F. Lohmann & Georg Krammer & Christoph Helm & Burak Aydin & Martin Hecht, 2022. "A Bayesian EAP-Based Nonlinear Extension of Croon and Van Veldhoven’s Model for Analyzing Data from Micro–Macro Multilevel Designs," Mathematics, MDPI, vol. 10(5), pages 1-15, March.
    14. Ledyard Tucker & Raymond Koopman & Robert Linn, 1969. "Evaluation of factor analytic research procedures by means of simulated correlation matrices," Psychometrika, Springer;The Psychometric Society, vol. 34(4), pages 421-459, December.
    15. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    16. Elvezio Ronchetti, 2021. "The main contributions of robust statistics to statistical science and a new challenge," METRON, Springer;Sapienza Università di Roma, vol. 79(2), pages 127-135, August.
    17. Jong-Wuu Wu, 1996. "The quasi-likelihood estimation in regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(2), pages 283-294, June.
    18. Robert Jennrich, 2006. "Rotation to Simple Loadings Using Component Loss Functions: The Oblique Case," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 173-191, March.
    19. Ke-Hai Yuan & Peter Bentler & Wai Chan, 2004. "Structural equation modeling with heavy tailed distributions," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 421-436, September.
    20. White, Halbert, 1983. "Corrigendum [Maximum Likelihood Estimation of Misspecified Models]," Econometrica, Econometric Society, vol. 51(2), pages 513-513, March.
    21. Hao Wu & Michael Browne, 2015. "Quantifying Adventitious Error in a Covariance Structure as a Random Effect," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 571-600, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Md. Abu Issa Gazi & Abdullah Al Masud & Mohammad Bin Amin & MD. Shakhawat Hossain & Refat Ferdous & Md. Al-Amin & Abdul Rahman S Senathirajah, 2026. "Unveiling the nexus: exploring the relationship of e-satisfaction, e-trust, and online repurchase intentions among students in a developing country," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 13(1), pages 1-16, December.
    2. Alexander Robitzsch, 2023. "Modeling Model Misspecification in Structural Equation Models," Stats, MDPI, vol. 6(2), pages 1-17, June.

    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. Keke Lai, 2019. "Creating Misspecified Models in Moment Structure Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 781-801, September.
    2. Alexander Robitzsch, 2023. "Modeling Model Misspecification in Structural Equation Models," Stats, MDPI, vol. 6(2), pages 1-17, June.
    3. Shaoxin Wang & Hu Yang & Chaoli Yao, 2019. "On the penalized maximum likelihood estimation of high-dimensional approximate factor model," Computational Statistics, Springer, vol. 34(2), pages 819-846, June.
    4. Elena Geminiani & Giampiero Marra & Irini Moustaki, 2021. "Single- and Multiple-Group Penalized Factor Analysis: A Trust-Region Algorithm Approach with Integrated Automatic Multiple Tuning Parameter Selection," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 65-95, March.
    5. Geminiani, Elena & Marra, Giampiero & Moustaki, Irini, 2021. "Single and multiple-group penalized factor analysis: a trust-region algorithm approach with integrated automatic multiple tuning parameter selection," LSE Research Online Documents on Economics 108873, London School of Economics and Political Science, LSE Library.
    6. Wang, Xin & Kong, Lingchen & Wang, Liqun, 2024. "Estimation of sparse covariance matrix via non-convex regularization," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    7. Yang, Yihe & Zhou, Jie & Pan, Jianxin, 2021. "Estimation and optimal structure selection of high-dimensional Toeplitz covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    8. Alessandra Cretarola & Gianna Fig`a-Talamanca & Marco Patacca, 2017. "A sentiment-based model for the BitCoin: theory, estimation and option pricing," Papers 1709.08621, arXiv.org.
    9. Wooldridge, Jeffrey M., 2014. "Quasi-maximum likelihood estimation and testing for nonlinear models with endogenous explanatory variables," Journal of Econometrics, Elsevier, vol. 182(1), pages 226-234.
    10. Jin-Chuan Duan & Weimin Miao, 2016. "Default Correlations and Large-Portfolio Credit Analysis," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 536-546, October.
    11. John Mullahy, 2010. "Multivariate Fractional Regression Estimation of Econometric Share Models," NBER Working Papers 16354, National Bureau of Economic Research, Inc.
    12. Chen, Willa W. & Deo, Rohit S., 2006. "Estimation of mis-specified long memory models," Journal of Econometrics, Elsevier, vol. 134(1), pages 257-281, September.
    13. Vasiliki Christou & Konstantinos Fokianos, 2014. "Quasi-Likelihood Inference For Negative Binomial Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 55-78, January.
    14. repec:gnv:wpaper:unige:76321 is not listed on IDEAS
    15. Dietmar Harhoff, 1999. "Firm Formation And Regional Spillovers - Evidence From Germany," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 8(1-2), pages 27-55.
    16. Vijverberg, Wim P. & Hasebe, Takuya, 2015. "GTL Regression: A Linear Model with Skewed and Thick-Tailed Disturbances," IZA Discussion Papers 8898, IZA Network @ LISER.
    17. Tang, Niansheng & Wang, Wenjun, 2019. "Robust estimation of generalized estimating equations with finite mixture correlation matrices and missing covariates at random for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 640-655.
    18. Francisco Blasques & Christian Francq & Sébastien Laurent, 2020. "A New Class of Robust Observation-Driven Models," Tinbergen Institute Discussion Papers 20-073/III, Tinbergen Institute.
    19. Gabriele Fiorentini & Enrique Sentana, 2021. "Specification tests for non‐Gaussian maximum likelihood estimators," Quantitative Economics, Econometric Society, vol. 12(3), pages 683-742, July.
    20. Wooldridge, Jeffrey M., 2020. "On the consistency of the logistic quasi-MLE under conditional symmetry," Economics Letters, Elsevier, vol. 194(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:gam:jstats:v:5:y:2022:i:3:p:39-672:d:869466. 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: MDPI Indexing Manager The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (email available below). General contact details of provider: https://www.mdpi.com .

    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.