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Bivariate Continuous Negatively Correlated Proportional Models with Applications in Schizophrenia Research
Sun, Yuan1; Tian, Guoliang2; Guo, Shuixia3,4; Shu, Lianjie5; Zhang, Chi6
2022-01-24
Source PublicationMathematics
ISSN2227-7390
Volume10Issue:3Pages:353
Abstract

Bivariate continuous negatively correlated proportional data defined in the unit square (0, 1) 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.

KeywordBivariate Npga Models Bivariate Npig Models Cortical Thickness N-em Algorithm Proportional Data
DOI10.3390/math10030353
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000755261000001
PublisherMDPIST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND
Scopus ID2-s2.0-85123550419
Fulltext Access
Citation statistics
Document TypeJournal article
CollectionFaculty of Business Administration
Corresponding AuthorZhang, Chi
Affiliation1.Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China
2.Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen, 518055, China
3.MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, China
4.Key Laboratory of Applied Statistics and Data Science, Hunan Normal University, Changsha, 410081, China
5.Faculty of Business, University of Macau, Macau, China
6.College of Economics, Shenzhen University, Shenzhen, 518055, China
Recommended Citation
GB/T 7714
Sun, Yuan,Tian, Guoliang,Guo, Shuixia,et al. Bivariate Continuous Negatively Correlated Proportional Models with Applications in Schizophrenia Research[J]. Mathematics, 2022, 10(3), 353.
APA Sun, Yuan., Tian, Guoliang., Guo, Shuixia., Shu, Lianjie., & Zhang, Chi (2022). Bivariate Continuous Negatively Correlated Proportional Models with Applications in Schizophrenia Research. Mathematics, 10(3), 353.
MLA Sun, Yuan,et al."Bivariate Continuous Negatively Correlated Proportional Models with Applications in Schizophrenia Research".Mathematics 10.3(2022):353.
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