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Bivariate Continuous Negatively Correlated Proportional Models with Applications in Schizophrenia Research

Author

Listed:
  • Yuan Sun

    (Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
    These authors contributed equally to this work.)

  • Guoliang Tian

    (Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen 518055, China
    These authors contributed equally to this work.)

  • Shuixia Guo

    (MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
    Key Laboratory of Applied Statistics and Data Science, Hunan Normal University, Changsha 410081, China)

  • Lianjie Shu

    (Faculty of Business, University of Macau, Macau, China)

  • Chi Zhang

    (College of Economics, Shenzhen University, Shenzhen 518055, China)

Abstract

Bivariate continuous negatively correlated proportional data defined in the unit square ( 0 , 1 ) 2 often appear in many different disciplines, such as medical studies, clinical trials and so on. To model this type of data, the paper proposes two new bivariate continuous distributions (i.e., negatively correlated proportional inverse Gaussian (NPIG) and negatively correlated proportional gamma (NPGA) distributions) for the first time and provides corresponding distributional properties. Two mean regression models are further developed for data with covariates. The normalized expectation–maximization (N-EM) algorithm and the gradient descent algorithm are combined to obtain the maximum likelihood estimates of parameters of interest. Simulations studies are conducted, and a data set of cortical thickness for schizophrenia is used to illustrate the proposed methods. According to our analysis between patients and controls of cortical thickness in typical mutual inhibitory brain regions, we verified the compensatory of cortical thickness in patients with schizophrenia and found its negative correlation with age.

Suggested Citation

  • Yuan Sun & Guoliang Tian & Shuixia Guo & Lianjie Shu & Chi Zhang, 2022. "Bivariate Continuous Negatively Correlated Proportional Models with Applications in Schizophrenia Research," Mathematics, MDPI, vol. 10(3), pages 1-22, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:353-:d:732212
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    References listed on IDEAS

    as
    1. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    2. Lijoi, Antonio & Mena, Ramses H. & Prunster, Igor, 2005. "Hierarchical Mixture Modeling With Normalized Inverse-Gaussian Priors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1278-1291, December.
    3. Simas, Alexandre B. & Barreto-Souza, Wagner & Rocha, Andréa V., 2010. "Improved estimators for a general class of beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 348-366, February.
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