成分数据的空间自回归模型

doi:10.13700/j.bh.1001-5965.2018.0253

北京航空航天大学学报 ›› 2019, Vol. 45 ›› Issue (1): 93-98.doi: 10.13700/j.bh.1001-5965.2018.0253

成分数据的空间自回归模型

黄婷婷^1,2, 王惠文^1,3, SAPORTA Gilbert⁴

1. 北京航空航天大学经济与管理学院, 北京 100083;
2. 城市运行应急保障模拟技术北京市重点实验室, 北京 10008;
3. 北京航空航天大学大数据科学与脑机智能高精尖创新中心, 北京 100083;
4. 法国国立工艺学院计算机和通信研究中心, 巴黎 75003

收稿日期:2018-05-03 修回日期:2018-07-28 出版日期:2019-01-20 发布日期:2019-01-28
通讯作者: 王惠文 E-mail:wanghw@vip.sina.com
作者简介:黄婷婷,女,博士研究生。主要研究方向:复杂数据的回归模型建模方法;王惠文,女,博士,教授,博士生导师。主要研究方向:经济管理中复杂数据统计分析的理论、方法与应用。
基金资助:
国家自然科学基金（71420107025）

Spatial autoregressive model for compositional data

HUANG Tingting^1,2, WANG Huiwen^1,3, SAPORTA Gilbert⁴

1. School of Economics and Management, Beihang University, Beijing 100083, China;
2. Beijing Key Laboratory of Emergency Support Simulation Technologies for City Operations, Beijing 10008;
3. Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing 100083, China;
4. Centre d'études et de Recherche en Informatique et Communications, Conservatoire National des Arts et Métiers, Paris 75003, France

Received:2018-05-03 Revised:2018-07-28 Online:2019-01-20 Published:2019-01-28
Supported by:
National Natural Science Foundation of China (71420107025)

摘要/Abstract

摘要： 针对已有成分数据线性回归模型对研究对象相互独立的严格要求，提出了含有成分数据和普通数据的空间自回归模型，在此基础上提出了成分数据空间自回归模型的估计方法。新模型结合了空间自回归模型处理因变量之间相互依赖的优势，可同时处理成分数据和普通数据。通过利用等距对数比（ilr）变换将成分数据解约束，得到了新模型的参数估计量。蒙特卡罗模拟实验验证了所提估计方法的有效性。

关键词: 成分数据, 等距对数比(ilr)变换, 极大似然估计, 空间依赖, 空间自回归模型

Abstract: The existing compositional linear models assume that samples are independent, which is often violated in practice. To solve this problem, we put forward a spatial autoregressive model for compositional data, which contains both compositional covariates and scalar predictors. Furthermore, a new estimation method is proposed. The new model has advantages of coping with mixed compositional and numerical data and expressing dependence between the responses. And the parameter estimators are obtained through isometric logratio (ilr) transformation, which transforms dependent compositional data into independent real vector. A Monte-Carlo simulation experiment verifies the effectiveness of the proposed estimation method.

Key words: compositional data, isometric logratio (ilr) transformation, maximum likelihood estimation, spatial dependence, spatial autoregressive model

中图分类号:

F222

黄婷婷, 王惠文, SAPORTA Gilbert. 成分数据的空间自回归模型[J]. 北京航空航天大学学报, 2019, 45(1): 93-98.

HUANG Tingting, WANG Huiwen, SAPORTA Gilbert. Spatial autoregressive model for compositional data[J]. JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2019, 45(1): 93-98.

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成分数据的空间自回归模型

Spatial autoregressive model for compositional data

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