Modelling Compositional Data Using Dirichlet Regression Models
Modelling Compositional Data Using Dirichlet Regression Models
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发表时间：
2007
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通讯作者：
Raflq H. Hijazi;R. Jernigan
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作者：
Raflq H. Hijazi;R. Jernigan
成分数据是具有单位和的非负比例。每当我们将对象分类为不相交的类别并记录它们产生的相对频率，或者将整个测量划分为其各个部分的百分比贡献时，就会出现这些类型的数据。在单位和约束下，协方差和相关性的基本概念具有误导性。因此，很少用通常的多元统计方法来分析成分数据。 Aitchison (1986) 引入对数比分析来模拟成分数据。 Campbell 和 Mosimann (1987a) 建议将狄利克雷协变量模型作为此类数据的零模型。在本文中，我们研究了狄利克雷协变量模型并将其与对数分析进行比较。开发了最大似然估计方法并研究了这些估计的抽样分布。提出了总变异性和 flt 优度的测量，以评估建议模型在分析成分数据时的充分性。
Compositional data are non-negative proportions with unit-sum. These types of data arise whenever we classify objects into disjoint categories and record their resulting relative frequencies, or partition a whole measurement into percentage contributions from its various parts. Under the unit-sum constraint, the elementary concepts of covariance and correlation are misleading. Therefore, compositional data are rarely analyzed with the usual multivariate statistical methods. Aitchison (1986) introduced the logratio analysis to model compositional data. Campbell and Mosimann (1987a) suggested the Dirichlet Covariate Model as a null model for such data. In this paper we investigate the Dirichlet Covariate Model and compare it to the logratio analysis. Maximum likelihood estimation methods are developed and the sampling distributions of these estimates are investigated. Measures of total variability and goodness of flt are proposed to assess the adequacy of the suggested models in analyzing compositional data.