基于单纯形分布的比例数据的回归分析

很多应用领域中的实验结果都表达成连续比例型数据,这类数据通常度量成为百分比、比率或比例,并取值于单位区间.为了采用弥散模型中的单纯形分布来模拟此类实验结果,本文首先研究单纯形分布的部分重要性质,在回归分析中参数估计和统计推断需要运用这些性质.模拟研究表明,当所研究情形不满足分布假设时,单纯形回归模型比Beta回归和分对数-正态回归模型更为稳健.通过对体外造血干细胞移植技术的真实数据分析,本文阐释这种方法和它针对异常值的稳健性.在R软件中,单纯形回归可以由程序包"simplexreg"实现,读者可以自行下载这个程序包,地址为http://my.zju.edu.cn/share/2466293(验证码:7919).

Regression analysis of proportional data using simplex distribution

Outcomes of continuous proportions arise in many applied areas. Such data are typically measured as percentages, rates or proportions confined in the unitary interval. In this paper, we propose to use a dispersion model of the simplex distribution to model such proportional outcomes. We study some key properties of the simplex distribution, which will be applied to establish estimation and inference in the regression analysis. Simulation studies show better robustness of the proposed simplex regression model against violation in some dis- tributional assumptions than the beta distribution based regression model and the logit-normal linear regression model. We illustrate the proposed methodology by a real data analysis on peripheral blood stem cell transplants and robustness against outliers. The proposed framework is implemented on the R platform in a package named ＂simplexreg＂, which can be downloaded from http：//my.zju.edu.cn/share/2466293 （verification code： 7919）.