IDEAS home Printed from https://ideas.repec.org/a/sae/somere/v41y2012i1p124-167.html
   My bibliography  Save this article

Testing Negative Error Variances

Author

Listed:
  • Stanislav Kolenikov
  • Kenneth A. Bollen

Abstract

Heywood cases, or negative variance estimates, are a common occurrence in factor analysis and latent variable structural equation models. Though they have several potential causes, structural misspecification is among the most important. This article explains how structural misspecification can lead to a Heywood case in the population, and provides several ways to test whether a negative error variance is a symptom of structural misspecification. The authors consider z -tests based on a variety of standard errors, confidence intervals, bootstrap resampling, and likelihood-ratio-type tests. In their discussion of z -tests, the authors demonstrate which of the standard errors are consistent under different kinds of misspecification. They also introduce new tests based on the scaled chi-square difference: the test on the boundary and the signed root of the scaled chi-square difference. A simulation study assesses the performance of these tests. The authors find that signed root tests and z -tests based on the empirical sandwich and the empirical bootstrap standard errors perform best in detecting negative error variances. They outperform z -tests based on the information matrix or distribution-robust standard errors.

Suggested Citation

  • Stanislav Kolenikov & Kenneth A. Bollen, 2012. "Testing Negative Error Variances," Sociological Methods & Research, , vol. 41(1), pages 124-167, February.
    • Handle: RePEc:sae:somere:v:41:y:2012:i:1:p:124-167
    DOI: 10.1177/0049124112442138
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0049124112442138
    Download Restriction: no
    File URL: https://libkey.io/10.1177/0049124112442138?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. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, January.
    2. Albert Satorra, 1990. "Robustness issues in structural equation modeling: a review of recent developments," Quality & Quantity: International Journal of Methodology, Springer, vol. 24(4), pages 367-386, November.
    3. Morgan, B.J.T. & Palmer, K.J. & Ridout, M.S., 2007. "Negative Score Test Statistic," The American Statistician, American Statistical Association, vol. 61, pages 285-288, November.
    4. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    5. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    6. 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.
    7. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    8. Albert Satorra & Peter Bentler, 2001. "A scaled difference chi-square test statistic for moment structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 507-514, December.
    9. Chun, So Yeon & Alexander, Shapiro, 2009. "Normal versus Noncentral Chi-square Asymptotics of Misspecified Models," MPRA Paper 17310, University Library of Munich, Germany.
    10. Robert Jennrich, 2008. "Nonparametric Estimation of Standard Errors in Covariance Analysis Using the Infinitesimal Jackknife," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 579-594, December.
    11. Lafontaine, Francine & White, Kenneth J., 1986. "Obtaining any Wald statistic you want," Economics Letters, Elsevier, vol. 21(1), pages 35-40.
    12. Neudecker, Heinz & Satorra, Albert, 1991. "Linear structural relations: Gradient and Hessian of the fitting function," Statistics & Probability Letters, Elsevier, vol. 11(1), pages 57-61, January.
    13. Albert Satorra & Willem Saris, 1985. "Power of the likelihood ratio test in covariance structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 83-90, March.
    14. Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-1083, September.
    15. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    16. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    17. Albert Satorra, 1989. "Alternative test criteria in covariance structure analysis: A unified approach," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 131-151, March.
    18. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2004. "Generalized multilevel structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 167-190, June.
    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. Clarysse, Bart & Andries, Petra & Boone, Sarah & Roelandt, Jolien, 2023. "Institutional logics and founders' identity orientation: Why academic entrepreneurs aspire lower venture growth," Research Policy, Elsevier, vol. 52(3).
    2. Hugo Horta & João M. Santos, 2016. "An instrument to measure individuals’ research agenda setting: the multi-dimensional research agendas inventory," Scientometrics, Springer;Akadémiai Kiadó, vol. 108(3), pages 1243-1265, September.
    3. See Kwong Goh & Nan Jiang & Muhamad Faiz Abdul Hak & Pei Leng Tee, 2016. "Determinants of Smartphone Repeat Purchase Intention among Malaysians: A Moderation Role of Social Influence and a Mediating Effect of Consumer Satisfaction," International Review of Management and Marketing, Econjournals, vol. 6(4), pages 993-1004.
    4. Kenneth Bollen & Stanislav Kolenikov & Shawn Bauldry, 2014. "Model-Implied Instrumental Variable—Generalized Method of Moments (MIIV-GMM) Estimators for Latent Variable Models," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 20-50, January.
    5. Ann Stes & Sven De Maeyer & Peter Van Petegem, 2013. "Examining the Cross-Cultural Sensitivity of the Revised Two-Factor Study Process Questionnaire (R-SPQ-2F) and Validation of a Dutch Version," PLOS ONE, Public Library of Science, vol. 8(1), pages 1-7, January.
    6. Wong Ming Wong & Shian-Yang Tzeng, 2021. "Mediating Role of Organic Labeling Awareness and Food Safety Attitudes in the Correlation Between Green Product Awareness and Purchase Intentions," SAGE Open, , vol. 11(4), pages 21582440211, November.
    7. Oscar Tapera & Greta Dreyer & Babill Stray-Pedersen & Stephen James Heinrich Hendricks, 2019. "Design and Validation of Questionnaires Investigating Access and Utilization of Cervical Cancer Treatment and Palliative Care," Global Journal of Health Science, Canadian Center of Science and Education, vol. 11(1), pages 113-113, January.
    8. Brownlees, Christian & Mesters, Geert, 2021. "Detecting granular time series in large panels," Journal of Econometrics, Elsevier, vol. 220(2), pages 544-561.
    9. See Kwong Goh & Nan Jiang & Muhamad Faiz Abdul Hak & Pei Leng Tee, 2016. "Determinants of Smartphone Repeat Purchase Intention among Malaysians: A Moderation Role of Social Influence and a Mediating Effect of Consumer Satisfaction," International Review of Management and Marketing, Econjournals, vol. 6(4), pages 993-1004.
    10. Yeojin Chung & Andrew Gelman & Sophia Rabe-Hesketh & Jingchen Liu & Vincent Dorie, 2015. "Weakly Informative Prior for Point Estimation of Covariance Matrices in Hierarchical Models," Journal of Educational and Behavioral Statistics, , vol. 40(2), pages 136-157, April.
    11. Loes M. Derikx & Dea van Lierop, 2021. "Intentions to Participate in Carsharing: The Role of Self- and Social Identity," Sustainability, MDPI, vol. 13(5), pages 1-31, February.

    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. Albert Satorra, 1991. "Asymptotic robust inferences in the analysis of mean and covariance structures," Economics Working Papers 3, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Jean-Marie Dufour & Alain Trognon & Purevdorj Tuvaandorj, 2017. "Invariant tests based on M -estimators, estimating functions, and the generalized method of moments," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 182-204, March.
    3. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2019. "Parametric Inference on the Mean of Functional Data Applied to Lifetime Income Curves," Working papers 2019rwp-153, Yonsei University, Yonsei Economics Research Institute.
    4. Cho, Jin Seo & White, Halbert, 2010. "Testing for unobserved heterogeneity in exponential and Weibull duration models," Journal of Econometrics, Elsevier, vol. 157(2), pages 458-480, August.
    5. Naorayex K Dastoor, 2008. "A simple explanation for the non-invariance of a Wald statistic to a reformulation of a null hypothesis," Economics Bulletin, AccessEcon, vol. 3(62), pages 1-10.
    6. Dastoor, Naorayex, 2009. "The perceived framework of a classical statistic: Is the non-invariance of a Wald statistic much ado about null thing?," Working Papers 2009-25, University of Alberta, Department of Economics.
    7. Piotr Tarka, 2018. "An overview of structural equation modeling: its beginnings, historical development, usefulness and controversies in the social sciences," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(1), pages 313-354, January.
    8. repec:ebl:ecbull:v:3:y:2008:i:62:p:1-10 is not listed on IDEAS
    9. Goh, Kim-Leng & King, Maxwell L., 1996. "Modified Wald tests for non-linear restrictions: A cautionary tale," Economics Letters, Elsevier, vol. 53(2), pages 133-138, November.
    10. Gabriele Fiorentini & Enrique Sentana, 2021. "Specification tests for non‐Gaussian maximum likelihood estimators," Quantitative Economics, Econometric Society, vol. 12(3), pages 683-742, July.
    11. Kemp, Gordon C. R., 2001. "Invariance and the Wald test," Journal of Econometrics, Elsevier, vol. 104(2), pages 209-217, September.
    12. Pedersen, Rasmus Søndergaard, 2017. "Inference and testing on the boundary in extended constant conditional correlation GARCH models," Journal of Econometrics, Elsevier, vol. 196(1), pages 23-36.
    13. Kenneth A. Bollen & James B. Kirby & Patrick J. Curran & Pamela M. Paxton & Feinian Chen, 2007. "Latent Variable Models Under Misspecification: Two-Stage Least Squares (2SLS) and Maximum Likelihood (ML) Estimators," Sociological Methods & Research, , vol. 36(1), pages 48-86, August.
    14. Brown, Kenneth & Cribari-Neto, Francisco, 1992. "On Hypothesis Testing: A Selective Look at the Lagrange Multiplier, Likelihood Ratio and Wald Tests," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 12(2), November.
    15. Hong, H. & Scaillet, O., 2006. "A fast subsampling method for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 133(2), pages 557-578, August.
    16. Lung-fei Lee & Jihai Yu, 2012. "The C(α)-type gradient test for spatial dependence in spatial autoregressive models," Letters in Spatial and Resource Sciences, Springer, vol. 5(3), pages 119-135, October.
    17. Helen Popper, 1995. "Term premia comovement in German, Japanese, and U.S. domestic markets," Open Economies Review, Springer, vol. 6(1), pages 49-62, January.
    18. Po-Hsien Huang, 2017. "Asymptotics of AIC, BIC, and RMSEA for Model Selection in Structural Equation Modeling," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 407-426, June.
    19. Granziera, Eleonora & Hubrich, Kirstin & Moon, Hyungsik Roger, 2014. "A predictability test for a small number of nested models," Journal of Econometrics, Elsevier, vol. 182(1), pages 174-185.
    20. Bera Anil K. & Bilias Yannis & Yoon Mann J. & Taşpınar Süleyman & Doğan Osman, 2020. "Adjustments of Rao’s Score Test for Distributional and Local Parametric Misspecifications," Journal of Econometric Methods, De Gruyter, vol. 9(1), pages 1-29, January.
    21. Albert Satorra, 2015. "A Comment on a Paper by H. Wu and M. W. Browne (2014)," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 613-618, September.

    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:sae:somere:v:41:y:2012:i:1:p:124-167. 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: SAGE Publications (email available below). General contact details of provider: .

    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.