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Extending Multivariate Distance Matrix Regression with an Effect Size Measure and the Asymptotic Null Distribution of the Test Statistic

Published online by Cambridge University Press:  01 January 2025

Daniel B. McArtor ,
Gitta H. Lubke  and
C. S. Bergeman
Daniel B. McArtor*
Affiliation:
University of Notre Dame
Gitta H. Lubke
Affiliation:
University of Notre Dame VU University Amsterdam
C. S. Bergeman
Affiliation:
University of Notre Dame
*
Correspondence should be made to Daniel B. McArtor, University of Notre Dame, 118 Haggar Hall, Notre Dame, IN 46556, USA. Email: dmcartor@nd.edu
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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.

Keywords

effect sizedistancesMDMRMDSmultivariate outcomenull distributionperson-centeredpermutation
Type
Original Paper
Information
Psychometrika , Volume 82 , Issue 4 , December 2017 , pp. 1052 - 1077
Copyright
Copyright © 2016 The Psychometric Society

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References

Anderson, M. J. (2001). A new method for non-parametric multivariate analysis of variance. Austral Ecology 26, 32–46Google Scholar
Anderson, M. J. & Walsh, DCI (2013). PERMANOVA, ANOSIM, and the Mantel test in the face of heterogeneous dispersions: What null hypothesis are you testing?. Ecological Monographs 83, 557–574CrossRefGoogle Scholar
Bauer, D. J. Shanahan, M. J. Little, T. D. Bovaird, J. A. & Card, N. A. (2007). Modeling complex interactions: Person-centered and variable-centered approaches. Modeling contextual effects in longitudinal studies London: Rouledge 255–283Google Scholar
Belloc, N. B. Breslow, L. & Hochstim, J. R. (1971). Measurement of physical health in a general population survey. American Journal of Epidemiology 93, 328–336CrossRefGoogle Scholar
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, 108–125CrossRefGoogle ScholarPubMed
Bergman, L. R. & Magnusson, D. (1997). A person-oriented approach in research on developmental psychopathology. Development and psychopathology 9, 291–319CrossRefGoogle ScholarPubMed
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, 515–529CrossRefGoogle ScholarPubMed
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, 179–191CrossRefGoogle Scholar
Bray, J. H. & Maxwell, S. E. (1985). Multivariate analysis of variance. Sage University Paper Series on Quantitative Research Methods 54, 1–79Google Scholar
Breslau, N. Reboussin, B. A. Anthony, J. C. & Storr, C. L. (2005). The structure of posttraumatic stress disorder. Archives of General Psychiatry 62, 1343–1351CrossRefGoogle ScholarPubMed
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, 3–5CrossRefGoogle Scholar
Carmody, R. N. Gerber, G. K. Luevano, J. M. Gatti, D. M. Somes, L. & Svenson, K. L. (2015). et al. Diet dominates host genotype in shaping the murine gut microbiota. Cell Host & Microbe 17, 72–84CrossRefGoogle ScholarPubMed
Cassady, J. C. & Finch, W. H. (2015). Using factor mixture modeling to identify dimensions of cognitive test anxiety. Learning and Individual Differences 41, 14–20CrossRefGoogle Scholar
Clopper, C. J. & Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26, 404–413CrossRefGoogle Scholar
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, 101Google Scholar
Davies, R. B. (1980). The distribution of a linear combination of chi-square random variables. Journal of the Royal Statistical Society 29, 323–333Google Scholar
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, 858–862CrossRefGoogle Scholar
Efron, B. & Tibshirani, R. J. (1994). An introduction to the bootstrap Boca Raton: CRC PressCrossRefGoogle Scholar
Etezadi-Amoli, J. & McDonald, R. P. (1983). A second generation nonlinear factor analysis. Psychometrika 48, 315–342CrossRefGoogle Scholar
Friedman, J. H. & Meulman, J. J. (2004). Clustering objects on subsets of attributes. Journal of the Royal Statistical Society 66, 815–839CrossRefGoogle Scholar
Gower, J. C. (1966). Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53, 325–338CrossRefGoogle Scholar
Johnson, S. C. (1967). Hierarchical clustering schemes. Psychometrika 32, 241–254CrossRefGoogle ScholarPubMed
Kelly, B. J. Gross, R. Bittinger, K. Sherrill-Mix, S. Lewis, J. D. & Collman, R. G. (2015). et al. Power and sample-size estimation for microbiome studies using pairwise distances and PERMANOVA. Bioinformatics 31, 2461–2468CrossRefGoogle ScholarPubMed
Kiers, HAL Vicari, D. & Vichi, M. (2005). Simultaneous classification and multidimensional scaling with external information. Psychometrika 70, 433–460CrossRefGoogle Scholar
Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29, 1–27CrossRefGoogle Scholar
Kruskal, J. B. (1964). Nonmetric multidimensional scalling: A numerical method. Psychometrika 29, 115–129CrossRefGoogle Scholar
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, 156–166CrossRefGoogle Scholar
Lubke, G. H. & McArtor, D. B. (2014). Multivariate genetic analyses in heterogeneous populations. Behavior Genetics 44, 232–239CrossRefGoogle ScholarPubMed
Lubke, G. H. & Muthén, B. (2005). Investigating population heterogeneity with factor mixture models. Psychological methods 10, 21–39CrossRefGoogle ScholarPubMed
McArdle, B. H. & Anderson, M. J. (2001). Fitting multivariate models to community data: A comment on distance-based redundancy analysis. Ecology 82, 290–297CrossRefGoogle Scholar
McDonald, R. P. (1962). A general approach to nonlinear factor analysis. Psychometrika 27, 397–415CrossRefGoogle Scholar
Meulman, J. J. (1992). The integration of multidimensional scaling and multivariate analysis with optimal transformations. Psychometrika 57, 539–565CrossRefGoogle Scholar
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, 882–891CrossRefGoogle ScholarPubMed
Osborne, D. & Weiner, B. (2015). (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, 149–154CrossRefGoogle Scholar
R Core Team R: A language and environment for statistical computing Vienna: R Core TeamGoogle Scholar
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, 236–247CrossRefGoogle ScholarPubMed
Satterthwaite, T. D. Vandekar, S. N. Wolf, D. H. Bassett, D. S. Ruparel, K. & Shehzad, Z. (2015). et al. Connectome-wide network analysis of youth with psychosis-spectrum symptoms. Molecular Psychiatry 20, 1–8CrossRefGoogle ScholarPubMed
Shehzad, Z. Kelly, C. Reiss, P. T. Cameron Craddock, R. Emerson, J. W. & McMahon, K. (2014). et al. A multivariate distance-based analytic framework for connectome-wide association studies. NeuroImage 93, 74–94CrossRefGoogle ScholarPubMed
Torgerson, W. S. (1952). Multidimensional scaling: I Theory and method. Psychometrika 17, 401–419CrossRefGoogle Scholar
Yalcin, I. & Amemiya, Y. (2001). Nonlinear factor analysis as a statistical method. Statistical Science 16, 275–294Google Scholar
Zapala, M. A. & Schork, N. J. (2012). Statistical properties of multivariate distance matrix regression for high-dimensional data analysis. Frontiers in Genetics 3, 1–10CrossRefGoogle ScholarPubMed