Statistics and Its Interface

Volume 13 (2020)

Number 2

Zero-one-inflated simplex regression models for the analysis of continuous proportion data

Pages: 193 – 208

DOI: https://dx.doi.org/10.4310/SII.2020.v13.n2.a5

Authors

Pengyi Liu (Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong)

Kam Chuen Yuen (Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong)

Liu-Cang Wu (Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan, China)

Guo-Liang Tian (Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen, Guangdong, China)

Tao Li (Department of Mathematics, Southern University of Science and Technology, Shenzhen, Guangdong, China)

Abstract

Continuous data restricted in the closed unit interval [0,1] often appear in various fields. Neither the beta distribution nor the simplex distribution provides a satisfactory fitting for such data, since the densities of the two distributions are defined only in the open interval (0,1). To model continuous proportional data with excessive zeros and excessive ones, it is the first time that we propose a zero-one-inflated simplex (ZOIS) distribution, which can be viewed as a mixture of the Bernoulli distribution and the simplex distribution. Besides, we introduce a new minorization–maximization (MM) algorithm to calculate the maximum likelihood estimates (MLEs) of parameters in the simplex distribution without covariates. Likelihood-based inference methods for the ZOIS regression model are also provided. Some simulation studies are performed and the hospital stay data of Barcelona in 1988 and 1990 are analyzed to illustrate the proposed methods. The comparison between the ZOIS model and the zero-one-inflated beta (ZOIB) model is also presented.

Keywords

continuous proportion data, MM algorithm, simplex distribution, zero-one-inflated beta model, zero-one-inflated simplex model

G.L. Tian’s research was supported by a grant from the National Natural Science Foundation of China (No. 11771199). K.C. Yuen’s research was supported by a Seed Fund for Basic Research of the University of Hong Kong (Project Code: 201711159190). L.C. Wu’s research was supported by a grant from the National Natural Science Foundation of China (No. 11861041).

Received 9 May 2018

Received revised 15 October 2019

Accepted 14 October 2019