IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v78y2013i3p545-552.html
   My bibliography  Save this article

Continuous Orthogonal Complement Functions and Distribution-Free Goodness of Fit Tests in Moment Structure Analysis

Author

Listed:
  • Robert Jennrich
  • Albert Satorra

Abstract

It is shown that for any full column rank matrix X 0 with more rows than columns there is a neighborhood $\mathcal{N}$ of X 0 and a continuous function f on $\mathcal{N}$ such that f(X) is an orthogonal complement of X for all X in $\mathcal{N}$ . This is used to derive a distribution free goodness of fit test for covariance structure analysis. This test was proposed some time ago and is extensively used. Unfortunately, there is an error in the proof that the proposed test statistic has an asymptotic χ 2 distribution. This is a potentially serious problem, without a proof the test statistic may not, in fact, be asymptoticly χ 2 . The proof, however, is easily fixed using a continuous orthogonal complement function. Similar problems arise in other applications where orthogonal complements are used. These can also be resolved by using continuous orthogonal complement functions. Copyright The Psychometric Society 2013

Suggested Citation

  • Robert Jennrich & Albert Satorra, 2013. "Continuous Orthogonal Complement Functions and Distribution-Free Goodness of Fit Tests in Moment Structure Analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 545-552, July.
    • Handle: RePEc:spr:psycho:v:78:y:2013:i:3:p:545-552
    DOI: 10.1007/s11336-013-9320-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-013-9320-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-013-9320-x?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. 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.
    2. Kenneth Bollen & Albert Maydeu-Olivares, 2007. "A Polychoric Instrumental Variable (PIV) Estimator for Structural Equation Models with Categorical Variables," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 309-326, 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. Robert Jennrich & Albert Satorra, 2016. "The Infinitesimal Jackknife and Moment Structure Analysis Using Higher Order Moments," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 90-101, March.
    2. Albert Satorra & Heinz Neudecker, 2015. "A Theorem on the Rank of a Product of Matrices with Illustration of Its Use in Goodness of Fit Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 938-948, December.
    3. Lifang Deng & Ke-Hai Yuan, 2016. "Comparing Latent Means Without Mean Structure Models: A Projection-Based Approach," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 802-829, September.
    4. Michael Browne & Alexander Shapiro, 2015. "Comment on the Asymptotics of a Distribution-Free Goodness of Fit Test Statistic," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 196-199, 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. Ruth Hancock & Marcello Morciano & Stephen Pudney & Francesca Zantomio, 2015. "Do household surveys give a coherent view of disability benefit targeting?: a multisurvey latent variable analysis for the older population in Great Britain," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(4), pages 815-836, October.
    2. Dara M Wald & Susan K Jacobson, 2014. "A Multivariate Model of Stakeholder Preference for Lethal Cat Management," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-9, April.
    3. 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.
    4. Sohn, Stefanie, 2017. "A contextual perspective on consumers' perceived usefulness: The case of mobile online shopping," Journal of Retailing and Consumer Services, Elsevier, vol. 38(C), pages 22-33.
    5. Laura Castro-Schilo & Barbara L. Fredrickson & Dan Mungas, 2019. "Association of Positive Affect with Cognitive Health and Decline for Elder Mexican Americans," Journal of Happiness Studies, Springer, vol. 20(8), pages 2385-2400, December.
    6. Zi Jia Ng & Eugene Scott Huebner & Alberto Maydeu-Olivares & Kimberly Joy Hills, 2018. "Confirmatory Factor Analytic Structure and Measurement Invariance of the Brief Multidimensional Students’ Life Satisfaction Scale (BMSLSS) in a Longitudinal Sample of Adolescents," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 11(4), pages 1237-1247, August.
    7. Junjiao Feng & Liang Zhang & Chunhui Chen & Jintao Sheng & Zhifang Ye & Kanyin Feng & Jing Liu & Ying Cai & Bi Zhu & Zhaoxia Yu & Chuansheng Chen & Qi Dong & Gui Xue, 2022. "A cognitive neurogenetic approach to uncovering the structure of executive functions," Nature Communications, Nature, vol. 13(1), pages 1-19, December.
    8. Michael Sheppard, 2020. "The relationship between discretionary slack and growth in small firms," International Entrepreneurship and Management Journal, Springer, vol. 16(1), pages 195-219, March.
    9. Jorge Sinval & M. Joseph Sirgy & Dong-Jin Lee & João Marôco, 2020. "The Quality of Work Life Scale: Validity Evidence from Brazil and Portugal," Applied Research in Quality of Life, Springer;International Society for Quality-of-Life Studies, vol. 15(5), pages 1323-1351, November.
    10. Ana Villar & César Camisón & Montserrat Boronat, 2007. "Technical Strategic Alliances And Performance: The Mediating Effect Of Knowledge ¿Based Competencies," Working Papers. Serie EC 2007-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    11. Garrido-Moreno, Aurora & Padilla-Meléndez, Antonio, 2011. "Analyzing the impact of knowledge management on CRM success: The mediating effects of organizational factors," International Journal of Information Management, Elsevier, vol. 31(5), pages 437-444.
    12. Lars Petersen & Jacob Hörisch & Kathleen Jacobs, 2021. "Worse is worse and better doesn't matter?: The effects of favorable and unfavorable environmental information on consumers’ willingness to pay," Journal of Industrial Ecology, Yale University, vol. 25(5), pages 1338-1356, October.
    13. P. Couper, Mick & Cernat, Alexandru & Beth Ofstedal, Mary, 2015. "Estimation of mode effects in the Health and Retirement Study using measurement models," ISER Working Paper Series 2015-19, Institute for Social and Economic Research.
    14. Nizar Allouch & Arkadi Predtetchinski, 2008. "On the non-emptiness of the fuzzy core," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 203-210, June.
    15. Juliana Toro-Arias & Pablo Ruiz-Palomino & María Pilar Rodríguez-Córdoba, 2022. "Measuring Ethical Organizational Culture: Validation of the Spanish Version of the Shortened Corporate Ethical Virtues Model," Journal of Business Ethics, Springer, vol. 176(3), pages 551-574, March.
    16. Ali Mashuri & Esti Zaduqisti & Miftahul Ula, 2017. "A Majority Group’s Perspective-taking Towards a Minority Group," Psychology and Developing Societies, , vol. 29(1), pages 44-73, March.
    17. Monica Pedrazza & Elena Trifiletti & Sabrina Berlanda & Gian Antonio Di Bernardo, 2013. "Self-Efficacy in Social Work: Development and Initial Validation of the Self-Efficacy Scale for Social Workers," Social Sciences, MDPI, vol. 2(3), pages 1-17, September.
    18. Halkias, Georgios & Diamantopoulos, Adamantios, 2020. "Universal dimensions of individuals' perception: Revisiting the operationalization of warmth and competence with a mixed-method approach," International Journal of Research in Marketing, Elsevier, vol. 37(4), pages 714-736.
    19. Antonio J. Rodríguez-Hidalgo & Anabel Alcívar & Mauricio Herrera-López, 2019. "Traditional Bullying and Discriminatory Bullying Around Special Educational Needs: Psychometric Properties of Two Instruments to Measure It," IJERPH, MDPI, vol. 16(1), pages 1-15, January.
    20. Barbara Loera & Daniela Converso & Sara Viotti, 2014. "Evaluating the Psychometric Properties of the Maslach Burnout Inventory-Human Services Survey (MBI-HSS) among Italian Nurses: How Many Factors Must a Researcher Consider?," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-18, 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:78:y:2013:i:3:p:545-552. 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.