Compositional inverse Gaussian models with applications in compositional data analysis with possible zero observations

Liu，Pengyi1; Tian，Guo Liang2; Yuen，Kam Chuen3; Sun，Yuan2; Zhang，Chi4

2023

10.1080/00949655.2023.2242550

Journal of Statistical Computation and Simulation   Impact Factor & Quartile

0094-9655

1563-5163

Compositional data (CoDa) often appear in various fields such as biology, medicine, geology, chemistry, economics, ecology and sociology. Although existing Dirichlet and related models are frequently employed in CoDa analysis, sometimes they may provide unsatisfactory performances in modelling CoDa as shown in our first real data example. First, this paper develops a multivariate compositional inverse Gaussian (CIG) model as a new tool for analysing CoDa. By incorporating the stochastic representation (SR), the expectation–maximization (EM) algorithm (aided by a one-step gradient descent algorithm) can be established to solve the parameter estimation for the proposed distribution (model). Next, zero observations may be often encountered in the real CoDa analysis. Therefore, the second aim of this paper is to propose a new model (called as ZCIG model) through a novel mixture SR based on both the CIG random vector and a so-called zero-truncated product Bernoulli random vector to model CoDa with zeros. Corresponding statistical inference methods are also developed for both cases without/with covariates. Two real data sets are analysed to illustrate the proposed statistical methods by comparing the proposed CIG and ZCIG models with existing Dirichlet and logistic-normal models.

Compositional inverse Gaussian distribution EM algorithm inverse Gaussian distribution zero-truncated product Bernoulli distribution

SCI

English

Others

National Natural Science Foundation of China[11801380] ; Fundamental Research Funds of Yunnan, China[202301AU070085] ; Research Grants Council of the Hong Kong Special Administrative Region, China[HKU17306220]

Computer Science ; Mathematics

Computer Science, Interdisciplinary Applications ; Statistics & Probability

WOS:001038085600001

TAYLOR & FRANCIS LTD

MATHEMATICS

2-s2.0-85166679086

Scopus

1.Department of Statistics,Yunnan University of Finance and Economics,Kunming,China
2.Department of Statistics and Data Science,Southern University of Science and Technology,Shenzhen,China
3.Department of Statistics and Actuarial Science,The University of Hong Kong,Hong Kong
4.College of Economics,Shenzhen University,Shenzhen,China

Liu，Pengyi,Tian，Guo Liang,Yuen，Kam Chuen,et al. Compositional inverse Gaussian models with applications in compositional data analysis with possible zero observations[J]. Journal of Statistical Computation and Simulation,2023.

Liu，Pengyi,Tian，Guo Liang,Yuen，Kam Chuen,Sun，Yuan,&Zhang，Chi.(2023).Compositional inverse Gaussian models with applications in compositional data analysis with possible zero observations.Journal of Statistical Computation and Simulation.

Liu，Pengyi,et al."Compositional inverse Gaussian models with applications in compositional data analysis with possible zero observations".Journal of Statistical Computation and Simulation (2023).