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Dirichlet component regression and its applications to psychiatric data

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  • Gueorguieva, Ralitza
  • Rosenheck, Robert
  • Zelterman, Daniel

Abstract

We describe a Dirichlet multivariable regression method useful for modeling data representing components as a percentage of a total. This model is motivated by the unmet need in psychiatry and other areas to simultaneously assess the effects of covariates on the relative contributions of different components of a measure. The model is illustrated using the Positive and Negative Syndrome Scale (PANSS) for assessment of schizophrenia symptoms which, like many other metrics in psychiatry, is composed of a sum of scores on several components, each in turn, made up of sums of evaluations on several questions. We simultaneously examine the effects of baseline socio-demographic and co-morbid correlates on all of the components of the total PANSS score of patients from a schizophrenia clinical trial and identify variables associated with increasing or decreasing relative contributions of each component. Several definitions of residuals are provided. Diagnostics include measures of overdispersion, Cook's distance, and a local jackknife influence metric.

Suggested Citation

  • Gueorguieva, Ralitza & Rosenheck, Robert & Zelterman, Daniel, 2008. "Dirichlet component regression and its applications to psychiatric data," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5344-5355, August.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5344-5355
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    References listed on IDEAS

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    1. Patricia Espinheira & Silvia Ferrari & Francisco Cribari-Neto, 2008. "On beta regression residuals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(4), pages 407-419.
    2. Espinheira, Patri­cia L. & Ferrari, Silvia L.P. & Cribari-Neto, Francisco, 2008. "Influence diagnostics in beta regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4417-4431, May.
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    Cited by:

    1. Melo, Tatiane F.N. & Vasconcellos, Klaus L.P. & Lemonte, Artur J., 2009. "Some restriction tests in a new class of regression models for proportions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3972-3979, October.
    2. Tsagris, Michail, 2015. "Regression analysis with compositional data containing zero values," MPRA Paper 67868, University Library of Munich, Germany.
    3. J. Veldwijk & I. P. Smith & S. Oliveri & S. Petrocchi & M. Y. Smith & L. Lanzoni & R. Janssens & I. Huys & G. A. de Wit & C. G. M Groothuis-Oudshoorn, 2024. "Comparing Discrete Choice Experiment with Swing Weighting to Estimate Attribute Relative Importance: A Case Study in Lung Cancer Patient Preferences," Medical Decision Making, , vol. 44(2), pages 203-216, February.
    4. Tsagris, Michail, 2015. "A novel, divergence based, regression for compositional data," MPRA Paper 72769, University Library of Munich, Germany.
    5. Angelo Moretti, 2023. "Estimation of small area proportions under a bivariate logistic mixed model," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(4), pages 3663-3684, August.
    6. Graziani, Rebecca & NIGRI, ANDREA, 2023. "An Age–Period–Cohort Model in a Dirichlet Framework: A Coherent Causes of Death Estimation," SocArXiv 856yw, Center for Open Science.
    7. Tsagris, Michail & Preston, Simon & T.A. Wood, Andrew, 2016. "Improved classi cation for compositional data using the $\alpha$-transformation," MPRA Paper 67657, University Library of Munich, Germany.
    8. Michail Tsagris & Simon Preston & Andrew T. A. Wood, 2016. "Improved Classification for Compositional Data Using the α-transformation," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 243-261, July.
    9. Jiajia Chen & Xiaoqin Zhang & Shengjia Li, 2017. "Multiple linear regression with compositional response and covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2270-2285, September.
    10. Monique Graf, 2020. "Regression for compositions based on a generalization of the Dirichlet distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 913-936, December.
    11. Jamali, Mehdi & Nejat, Ali & Ghosh, Souparno & Jin, Fang & Cao, Guofeng, 2019. "Social media data and post-disaster recovery," International Journal of Information Management, Elsevier, vol. 44(C), pages 25-37.

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