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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
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    References listed on IDEAS

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    1. 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.
    2. Michael W. Browne & Robert Cudeck, 1992. "Alternative Ways of Assessing Model Fit," Sociological Methods & Research, , vol. 21(2), pages 230-258, November.
    3. 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.
    4. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258.
    5. Louis Guttman, 1940. "Multiple rectilinear prediction and the resolution into components," Psychometrika, Springer;The Psychometric Society, vol. 5(2), pages 75-99, June.
    6. Louis Guttman, 1953. "Image theory for the structure of quantitative variates," Psychometrika, Springer;The Psychometric Society, vol. 18(4), pages 277-296, December.
    7. 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.
    8. 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.
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