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Extending multivariate distance matrix regression with an effect size measure and the asymptotic null distribution of the test statistic

Author

Listed:
  • Daniel B. McArtor

    (University of Notre Dame)

  • Gitta H. Lubke

    (University of Notre Dame
    VU University Amsterdam)

  • C. S. Bergeman

    (University of Notre Dame)

Abstract

Person-centered methods are useful for studying individual differences in terms of (dis)similarities between response profiles on multivariate outcomes. Multivariate distance matrix regression (MDMR) tests the significance of associations of response profile (dis)similarities and a set of predictors using permutation tests. This paper extends MDMR by deriving and empirically validating the asymptotic null distribution of its test statistic, and by proposing an effect size for individual outcome variables, which is shown to recover true associations. These extensions alleviate the computational burden of permutation tests currently used in MDMR and render more informative results, thus making MDMR accessible to new research domains.

Suggested Citation

  • Daniel B. McArtor & Gitta H. Lubke & C. S. Bergeman, 2017. "Extending multivariate distance matrix regression with an effect size measure and the asymptotic null distribution of the test statistic," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1052-1077, December.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:4:d:10.1007_s11336-016-9527-8
    DOI: 10.1007/s11336-016-9527-8
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    References listed on IDEAS

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    1. Duchesne, Pierre & Lafaye De Micheaux, Pierre, 2010. "Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 858-862, April.
    2. Stephen Johnson, 1967. "Hierarchical clustering schemes," Psychometrika, Springer;The Psychometric Society, vol. 32(3), pages 241-254, September.
    3. Warren Torgerson, 1952. "Multidimensional scaling: I. Theory and method," Psychometrika, Springer;The Psychometric Society, vol. 17(4), pages 401-419, December.
    4. Henk Kiers & Donatella Vicari & Maurizio Vichi, 2005. "Simultaneous classification and multidimensional scaling with external information," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 433-460, September.
    5. Jacqueline Meulman, 1992. "The integration of multidimensional scaling and multivariate analysis with optimal transformations," Psychometrika, Springer;The Psychometric Society, vol. 57(4), pages 539-565, December.
    6. J. Kruskal, 1964. "Nonmetric multidimensional scaling: A numerical method," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 115-129, June.
    7. J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 29(1), pages 1-27, March.
    8. Jamshid Etezadi-Amoli & Roderick McDonald, 1983. "A second generation nonlinear factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 315-342, September.
    9. Roderick McDonald, 1962. "A general approach to nonlinear factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 27(4), pages 397-415, December.
    10. Jerome H. Friedman & Jacqueline J. Meulman, 2004. "Clustering objects on subsets of attributes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 815-849, November.
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