IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v83y2018i2d10.1007_s11336-018-9607-z.html
   My bibliography  Save this article

Unidimensional factor models imply weaker partial correlations than zero-order correlations

Author

Listed:
  • Riet Bork

    (University of Amsterdam)

  • Raoul P. P. P. Grasman

    (University of Amsterdam)

  • Lourens J. Waldorp

    (University of Amsterdam)

Abstract

In this paper we present a new implication of the unidimensional factor model. We prove that the partial correlation between two observed variables that load on one factor given any subset of other observed variables that load on this factor lies between zero and the zero-order correlation between these two observed variables. We implement this result in an empirical bootstrap test that rejects the unidimensional factor model when partial correlations are identified that are either stronger than the zero-order correlation or have a different sign than the zero-order correlation. We demonstrate the use of the test in an empirical data example with data consisting of fourteen items that measure extraversion.

Suggested Citation

  • Riet Bork & Raoul P. P. P. Grasman & Lourens J. Waldorp, 2018. "Unidimensional factor models imply weaker partial correlations than zero-order correlations," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 443-452, June.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:2:d:10.1007_s11336-018-9607-z
    DOI: 10.1007/s11336-018-9607-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-018-9607-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11336-018-9607-z?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. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, January.
    2. Louis Guttman, 1940. "Multiple rectilinear prediction and the resolution into components," Psychometrika, Springer;The Psychometric Society, vol. 5(2), pages 75-99, June.
    3. Louis Guttman, 1953. "Image theory for the structure of quantitative variates," Psychometrika, Springer;The Psychometric Society, vol. 18(4), pages 277-296, December.
    4. Maria Salgueiro & Peter Smith & John McDonald, 2008. "The Manifest Association Structure of the Single-Factor Model: Insights from Partial Correlations," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 665-670, December.
    5. Jules Ellis, 2014. "An Inequality for Correlations in Unidimensional Monotone Latent Variable Models for Binary Variables," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 303-316, April.
    6. Michael W. Browne & Robert Cudeck, 1992. "Alternative Ways of Assessing Model Fit," Sociological Methods & Research, , vol. 21(2), pages 230-258, November.
    7. Langford E. & Schwertman N. & Owens M., 2001. "Is the Property of Being Positively Correlated Transitive?," The American Statistician, American Statistical Association, vol. 55, pages 322-325, November.
    8. Paul Rosenbaum, 1984. "Testing the conditional independence and monotonicity assumptions of item response theory," Psychometrika, Springer;The Psychometric Society, vol. 49(3), pages 425-435, September.
    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. Roderick McDonald, 1986. "Describing the elephant: Structure and function in multivariate data," Psychometrika, Springer;The Psychometric Society, vol. 51(4), pages 513-534, December.
    2. Jules L. Ellis & Klaas Sijtsma, 2023. "A Test to Distinguish Monotone Homogeneity from Monotone Multifactor Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 387-412, June.
    3. Louis Guttman, 1957. "Simple proofs of relations between the communality problem and multiple correlation," Psychometrika, Springer;The Psychometric Society, vol. 22(2), pages 147-157, June.
    4. Rudy Ligtvoet, 2022. "Incomplete Tests of Conditional Association for the Assessment of Model Assumptions," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1214-1237, December.
    5. Rubén Trigueros & José M. Aguilar-Parra & Adolfo J. Cangas & Joaquín F. Álvarez, 2019. "Validation of the Scale of Emotional States in the Physical Education Context," Sustainability, MDPI, vol. 11(18), pages 1-13, September.
    6. Skallerud, Kåre & Korneliussen, Tor & Olsen, Svein Ottar, 2009. "An examination of consumers’ cross-shopping behaviour," Journal of Retailing and Consumer Services, Elsevier, vol. 16(3), pages 181-189.
    7. Morosan, Cristian, 2016. "An empirical examination of U.S. travelers’ intentions to use biometric e-gates in airports," Journal of Air Transport Management, Elsevier, vol. 55(C), pages 120-128.
    8. Kitagawa, Toru & Muris, Chris, 2016. "Model averaging in semiparametric estimation of treatment effects," Journal of Econometrics, Elsevier, vol. 193(1), pages 271-289.
    9. Jeffrey S. Racine & Qi Li & Dalei Yu & Li Zheng, 2023. "Optimal Model Averaging of Mixed-Data Kernel-Weighted Spline Regressions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1251-1261, October.
    10. Jun Hong Park & Sang Ho Kook & Hyeonu Im & Soomin Eum & Chulung Lee, 2018. "Fabless Semiconductor Firms’ Financial Performance Determinant Factors: Product Platform Efficiency and Technological Capability," Sustainability, MDPI, vol. 10(10), pages 1-22, September.
    11. chatterjee, susmita, 2017. "Empowerment translated to transition," MPRA Paper 80067, University Library of Munich, Germany.
    12. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
    13. Davide Fiaschi & Andrea Mario Lavezzi & Angela Parenti, 2020. "Deep and Proximate Determinants of the World Income Distribution," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 66(3), pages 677-710, September.
    14. Hsu, Chia-Lin & Chang, Chi-Ya & Yansritakul, Chutinart, 2017. "Exploring purchase intention of green skincare products using the theory of planned behavior: Testing the moderating effects of country of origin and price sensitivity," Journal of Retailing and Consumer Services, Elsevier, vol. 34(C), pages 145-152.
    15. A. Béguin & C. Glas, 2001. "MCMC estimation and some model-fit analysis of multidimensional IRT models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 541-561, December.
    16. Fabio Canova & Christian Matthes, 2021. "Dealing with misspecification in structural macroeconometric models," Quantitative Economics, Econometric Society, vol. 12(2), pages 313-350, May.
    17. Yu, Jun & Meng, Xiran & Wang, Yaping, 2023. "Optimal designs for semi-parametric dose-response models under random contamination," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    18. Lau, Patricia Yin Yin & Tong, Jane L.Y. Terpstra & Lien, Bella Ya-Hui & Hsu, Yen-Chen & Chong, Chooi Ling, 2017. "Ethical work climate, employee commitment and proactive customer service performance: Test of the mediating effects of organizational politics," Journal of Retailing and Consumer Services, Elsevier, vol. 35(C), pages 20-26.
    19. Zhongqi Liang & Qihua Wang & Yuting Wei, 2022. "Robust model selection with covariables missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 539-557, June.
    20. 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.

    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:83:y:2018:i:2:d:10.1007_s11336-018-9607-z. 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.