IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v80y2015i3p571-600.html
   My bibliography  Save this article

Quantifying Adventitious Error in a Covariance Structure as a Random Effect

Author

Listed:
  • Hao Wu
  • Michael Browne

Abstract

We present an approach to quantifying errors in covariance structures in which adventitious error, identified as the process underlying the discrepancy between the population and the structured model, is explicitly modeled as a random effect with a distribution, and the dispersion parameter of this distribution to be estimated gives a measure of misspecification. Analytical properties of the resultant procedure are investigated and the measure of misspecification is found to be related to the root mean square error of approximation. An algorithm is developed for numerical implementation of the procedure. The consistency and asymptotic sampling distributions of the estimators are established under a new asymptotic paradigm and an assumption weaker than the standard Pitman drift assumption. Simulations validate the asymptotic sampling distributions and demonstrate the importance of accounting for the variations in the parameter estimates due to adventitious error. Two examples are also given as illustrations. Copyright The Psychometric Society 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:3:p:571-600
    DOI: 10.1007/s11336-015-9451-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-015-9451-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-015-9451-3?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    2. A. Swain, 1975. "A class of factor analysis estimation procedures with common asymptotic sampling properties," Psychometrika, Springer;The Psychometric Society, vol. 40(3), pages 315-335, September.
    3. White, Halbert, 1980. "Nonlinear Regression on Cross-Section Data," Econometrica, Econometric Society, vol. 48(3), pages 721-746, April.
    4. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    5. Chun, So Yeon & Alexander, Shapiro, 2009. "Normal versus Noncentral Chi-square Asymptotics of Misspecified Models," MPRA Paper 17310, University Library of Munich, Germany.
    6. Ledyard Tucker & Charles Lewis, 1973. "A reliability coefficient for maximum likelihood factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 38(1), pages 1-10, March.
    7. Ledyard Tucker, 1958. "An inter-battery method of factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(2), pages 111-136, June.
    8. 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.
    9. Yuan, Ke-Hai & Hayashi, Kentaro & Bentler, Peter M., 2007. "Normal theory likelihood ratio statistic for mean and covariance structure analysis under alternative hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1262-1282, July.
    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. Hao Wu & Michael Browne, 2015. "Random Model Discrepancy: Interpretations and Technicalities (A Rejoinder)," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 619-624, September.
    2. 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.
    3. Alexander Robitzsch, 2023. "Modeling Model Misspecification in Structural Equation Models," Stats, MDPI, vol. 6(2), pages 1-17, June.
    4. Alberto Maydeu-Olivares, 2017. "Assessing the Size of Model Misfit in Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 533-558, September.
    5. Robert MacCallum & Anthony O’Hagan, 2015. "Advances in Modeling Model Discrepancy: Comment on Wu and Browne (2015)," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 601-607, September.
    6. Keke Lai, 2019. "Creating Misspecified Models in Moment Structure Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 781-801, September.
    7. So Yeon Chun & Michael W. Browne & Alexander Shapiro, 2018. "Modified Distribution-Free Goodness-of-Fit Test Statistic," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 48-66, March.

    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. Hao Wu & Michael Browne, 2015. "Random Model Discrepancy: Interpretations and Technicalities (A Rejoinder)," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 619-624, September.
    2. Yuan, Ke-Hai & Chan, Wai, 2008. "Structural equation modeling with near singular covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4842-4858, June.
    3. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
    4. Foss, Tron & Jöreskog, Karl G. & Olsson, Ulf H., 2011. "Testing structural equation models: The effect of kurtosis," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2263-2275, July.
    5. Jeffrey M. Woodridge, 1988. "A Unified Approach to Robust, Regression-Based Specification Tests," Working papers 480, Massachusetts Institute of Technology (MIT), Department of Economics.
    6. 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.
    7. Yuan, Jun & Nian, Victor & He, Junliang & Yan, Wei, 2019. "Cost-effectiveness analysis of energy efficiency measures for maritime shipping using a metamodel based approach with different data sources," Energy, Elsevier, vol. 189(C).
    8. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, vol. 6(1), pages 17-43, March.
    9. Bart Spiessens & Emmanuel Lesaffre & Geert Verbeke & KyungMann Kim, 2002. "Group Sequential Methods for an Ordinal Logistic Random-Effects Model Under Misspecification," Biometrics, The International Biometric Society, vol. 58(3), pages 569-575, September.
    10. Bierens, H.J., 1987. "Nonlinear parametric regression analysis," Serie Research Memoranda 0021, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    11. Stanislav Kolenikov & Kenneth A. Bollen, 2012. "Testing Negative Error Variances," Sociological Methods & Research, , vol. 41(1), pages 124-167, February.
    12. Robert MacCallum & Anthony O’Hagan, 2015. "Advances in Modeling Model Discrepancy: Comment on Wu and Browne (2015)," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 601-607, September.
    13. Keke Lai, 2019. "Creating Misspecified Models in Moment Structure Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 781-801, September.
    14. So Yeon Chun & Michael W. Browne & Alexander Shapiro, 2018. "Modified Distribution-Free Goodness-of-Fit Test Statistic," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 48-66, March.
    15. Vanslette, Kevin & Tohme, Tony & Youcef-Toumi, Kamal, 2020. "A general model validation and testing tool," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    16. Das, Debojyoti & Bhatia, Vaneet & Kumar, Surya Bhushan & Basu, Sankarshan, 2022. "Do precious metals hedge crude oil volatility jumps?," International Review of Financial Analysis, Elsevier, vol. 83(C).
    17. P.A.V.B. Swamy & I-Lok Chang & Jatinder S. Mehta & William H. Greene & Stephen G. Hall & George S. Tavlas, 2016. "Removing Specification Errors from the Usual Formulation of Binary Choice Models," Econometrics, MDPI, vol. 4(2), pages 1-21, June.
    18. Carlo Altavilla & Raffaella Giacomini & Giuseppe Ragusa, 2017. "Anchoring the yield curve using survey expectations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1055-1068, September.
    19. Fernando Rios-Avila & Gustavo Canavire-Bacarreza, 2018. "Standard-error correction in two-stage optimization models: A quasi–maximum likelihood estimation approach," Stata Journal, StataCorp LP, vol. 18(1), pages 206-222, March.
    20. Sandy Fréret & Denis Maguain, 2017. "The effects of agglomeration on tax competition: evidence from a two-regime spatial panel model on French data," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(6), pages 1100-1140, December.

    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:spr:psycho:v:80:y:2015:i:3:p:571-600. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.