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

Psychometrika volume 82, pages1052–1077(2017)Cite this article

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.

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References

  1. Anderson, M. J. (2001). A new method for non-parametric multivariate analysis of variance. Austral Ecology, 26, 32–46.

    Google Scholar 

  2. Anderson, M. J., & Walsh, D. C. I. (2013). PERMANOVA, ANOSIM, and the Mantel test in the face of heterogeneous dispersions: What null hypothesis are you testing? Ecological Monographs, 83, 557–574.

    Article  Google Scholar 

  3. Bauer, D. J., & Shanahan, M. J. (2007). Modeling complex interactions: Person-centered and variable-centered approaches. In T. D. Little, J. A. Bovaird, & N. A. Card (Eds.), Modeling contextual effects in longitudinal studies (pp. 255–283). London: Rouledge.

    Google Scholar 

  4. Belloc, N. B., Breslow, L., & Hochstim, J. R. (1971). Measurement of physical health in a general population survey. American Journal of Epidemiology, 93, 328–336.

    Article  PubMed  Google Scholar 

  5. Bergeman, C. S., & Deboeck, P. R. (2014). Trait stress resistance and dynamic stress dissipation on health and well-being: The reservoir model. Research in Human Development, 11, 108–125.

    Article  Google Scholar 

  6. Bergman, L. R., & Magnusson, D. (1997). A person-oriented approach in research on developmental psychopathology. Development and psychopathology, 9, 291–319.

    Article  PubMed  Google Scholar 

  7. Bernstein, A., Stickle, T. R., Zvolensky, M. J., Taylor, S., Abramowitz, J., & Stewart, S. (2010). Dimensional, categorical, or dimensional-categories: Testing the latent structure of anxiety sensitivity among adults using factor-mixture modeling. Behavior Therapy, 41, 515–529.

    Article  PubMed  Google Scholar 

  8. Braeckman, U., Van Colen, C., Soetaert, K., Vincx, M., & Vanaverbeke, J. (2011). Contrasting macrobenthic activities differentially affect nematode density and diversity in a shallow subtidal marine sediment. Marine Ecology Progress Series, 422, 179–191.

    Article  Google Scholar 

  9. Bray, J. H., & Maxwell, S. E. (1985). Multivariate analysis of variance. Sage University Paper Series on Quantitative Research Methods, 54, 1–79.

    Google Scholar 

  10. Breslau, N., Reboussin, B. A., Anthony, J. C., & Storr, C. L. (2005). The structure of posttraumatic stress disorder. Archives of General Psychiatry, 62, 1343–1351.

    Article  PubMed  Google Scholar 

  11. Buhrmester, M., Kwang, T., & Gosling, S. D. (2011). Amazon’s mechanical turk: A new source of inexpensive, yet high-quality, data? Perspectives on Psychological Science, 6, 3–5.

    Article  PubMed  Google Scholar 

  12. Carmody, R. N., Gerber, G. K., Luevano, J. M., Gatti, D. M., Somes, L., Svenson, K. L., et al. (2015). Diet dominates host genotype in shaping the murine gut microbiota. Cell Host & Microbe, 17, 72–84.

    Article  Google Scholar 

  13. Cassady, J. C., & Finch, W. H. (2015). Using factor mixture modeling to identify dimensions of cognitive test anxiety. Learning and Individual Differences, 41, 14–20.

    Article  Google Scholar 

  14. Clopper, C. J., & Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26, 404–413.

    Article  Google Scholar 

  15. Costa, P. T., & McCrae, R. R. (1992). Professional manual: Revised NEO personality inventory (NEO-PI-R) and NEO five-factor inventory (NEO-FFI). Odessa FL Psychological Assessment Resources, 3, 101.

    Google Scholar 

  16. Davies, R. B. (1980). The distribution of a linear combination of chi-square random variables. Journal of the Royal Statistical Society, 29, 323–333.

    Google Scholar 

  17. Duchesne, P., & de Micheaux, P. L. (2010). Computing the distribution of quadratic forms: Further comparisons between the Liu–Tang–Zhang approximation and exact methods. Computational Statistics and Data Analysis, 54, 858–862.

    Article  Google Scholar 

  18. Efron, B., & Tibshirani, R. J. (1994). An introduction to the bootstrap. Boca Raton: CRC Press.

    Google Scholar 

  19. Etezadi-Amoli, J., & McDonald, R. P. (1983). A second generation nonlinear factor analysis. Psychometrika, 48, 315–342.

    Article  Google Scholar 

  20. Friedman, J. H., & Meulman, J. J. (2004). Clustering objects on subsets of attributes. Journal of the Royal Statistical Society, 66, 815–839.

    Article  Google Scholar 

  21. Gower, J. C. (1966). Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53, 325–338.

    Article  Google Scholar 

  22. Johnson, S. C. (1967). Hierarchical clustering schemes. Psychometrika, 32, 241–254.

    Article  PubMed  Google Scholar 

  23. Kelly, B. J., Gross, R., Bittinger, K., Sherrill-Mix, S., Lewis, J. D., Collman, R. G., et al. (2015). Power and sample-size estimation for microbiome studies using pairwise distances and PERMANOVA. Bioinformatics, 31, 2461–2468.

    Article  PubMed  PubMed Central  Google Scholar 

  24. Kiers, H. A. L., Vicari, D., & Vichi, M. (2005). Simultaneous classification and multidimensional scaling with external information. Psychometrika, 70, 433–460.

    Article  Google Scholar 

  25. Kruskal, J. B. (1964a). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1–27.

    Article  Google Scholar 

  26. Kruskal, J. B. (1964b). Nonmetric multidimensional scalling: A numerical method. Psychometrika, 29, 115–129.

    Article  Google Scholar 

  27. Kubarych, T. S., Aggen, S. H., Kendler, K. S., Torgersen, S., Reichborn-Kjennerud, T., & Neale, M. C. (2010). Measurement non-invariance of DSM-IV narcissistic personality disorder criteria across age and sex in a population-based sample of Norwegian twins. International Journal of Methods in Psychiatric Research, 19, 156–166.

    Article  PubMed  PubMed Central  Google Scholar 

  28. Lubke, G. H., & McArtor, D. B. (2014). Multivariate genetic analyses in heterogeneous populations. Behavior Genetics, 44, 232–239.

    Article  PubMed  Google Scholar 

  29. Lubke, G. H., & Muthén, B. (2005). Investigating population heterogeneity with factor mixture models. Psychological methods, 10, 21–39.

    Article  PubMed  Google Scholar 

  30. McArdle, B. H., & Anderson, M. J. (2001). Fitting multivariate models to community data: A comment on distance-based redundancy analysis. Ecology, 82, 290–297.

    Article  Google Scholar 

  31. McDonald, R. P. (1962). A general approach to nonlinear factor analysis. Psychometrika, 27, 397–415.

    Article  Google Scholar 

  32. Meulman, J. J. (1992). The integration of multidimensional scaling and multivariate analysis with optimal transformations. Psychometrika, 57, 539–565.

    Article  Google Scholar 

  33. Muthén, B., & Muthén, L. K. (2000). Integrating person-centered and variable-centered analyses: Growth mixture modeling with latent trajectory classes. Alcoholism, Clinical and Experimental Research, 24, 882–891.

    Article  PubMed  Google Scholar 

  34. Osborne, D., & Weiner, B. (2015). A latent profile analysis of attributions for poverty: Identifying response patterns underlying people’s willingness to help the poor. Personality and Individual Differences, 85, 149–154.

    Article  Google Scholar 

  35. R Core Team. (2015). R: A language and environment for statistical computing. Vienna: R Core Team.

    Google Scholar 

  36. Salem, R. M., O’Connor, D. T., & Schork, N. J. (2010). Curve-based multivariate distance matrix regression analysis: Application to genetic association analyses involving repeated measures. Physiological Genomics, 42, 236–247.

    Article  PubMed  PubMed Central  Google Scholar 

  37. Satterthwaite, T. D., Vandekar, S. N., Wolf, D. H., Bassett, D. S., Ruparel, K., Shehzad, Z., et al. (2015). Connectome-wide network analysis of youth with psychosis-spectrum symptoms. Molecular Psychiatry, 20, 1–8.

    Article  Google Scholar 

  38. Shehzad, Z., Kelly, C., Reiss, P. T., Cameron Craddock, R., Emerson, J. W., McMahon, K., et al. (2014). A multivariate distance-based analytic framework for connectome-wide association studies. NeuroImage, 93, 74–94.

    Article  PubMed  PubMed Central  Google Scholar 

  39. Torgerson, W. S. (1952). Multidimensional scaling: I Theory and method. Psychometrika, 17, 401–419.

    Article  Google Scholar 

  40. Yalcin, I., & Amemiya, Y. (2001). Nonlinear factor analysis as a statistical method. Statistical Science, 16, 275–294.

    Article  Google Scholar 

  41. Zapala, M. A., & Schork, N. J. (2012). Statistical properties of multivariate distance matrix regression for high-dimensional data analysis. Frontiers in Genetics, 3, 1–10.

    Article  Google Scholar 

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Author information

Affiliations

  1. University of Notre Dame, 118 Haggar Hall, Notre Dame, IN, 46556 , USA

    Daniel B. McArtor, Gitta H. Lubke & C. S. Bergeman

  2. VU University Amsterdam, Amsterdam, Netherlands

    Gitta H. Lubke

Authors
  1. Daniel B. McArtor
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  2. Gitta H. Lubke
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  3. C. S. Bergeman
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Correspondence to Daniel B. McArtor.

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McArtor, D.B., Lubke, G.H. & Bergeman, C.S. Extending multivariate distance matrix regression with an effect size measure and the asymptotic null distribution of the test statistic. Psychometrika 82, 1052–1077 (2017). https://doi.org/10.1007/s11336-016-9527-8

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Keywords

  • effect size
  • distances
  • MDMR
  • MDS
  • multivariate outcome
  • null distribution
  • person-centered
  • permutation