成分数据的空间自回归模型

黄婷婷; 王惠文; SAPORTAGilbert

doi:10.13700/j.bh.1001-5965.2018.0253

成分数据的空间自回归模型

doi: 10.13700/j.bh.1001-5965.2018.0253

黄婷婷^{1, 2},
王惠文^{1, 3, ,},
SAPORTAGilbert⁴

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

基金项目:

国家自然科学基金 71420107025

详细信息

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

通讯作者:
王惠文, E-mail: wanghw@vip.sina.com

中图分类号: F222
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- 被引次数: 0
出版历程
- 收稿日期: 2018-05-03
- 录用日期: 2018-07-28
- 网络出版日期: 2019-01-20

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

Funds:

National Natural Science Foundation of China 71420107025

More Information

Corresponding author: WANG Huiwen, E-mail: wanghw@vip.sina.com

摘要

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。
- 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.
- compositional data /
- isometric logratio (ilr) transformation /
- maximum likelihood estimation /
- spatial dependence /
- spatial autoregressive model

HTML全文

图 1 和的样本偏差

Figure 1. Sample deviation of and

下载: 全尺寸图片幻灯片

图 2 、的标准差及的总方差

Figure 2. Standard deviation of , and total variance of

下载: 全尺寸图片幻灯片

图 3 n和ρ取不同值时，偏差箱线图

Figure 3. Boxplots of deviation of when n and ρ change

下载: 全尺寸图片幻灯片

参考文献(27)

[1]	RAMSAY J O, SILVERMAN B W.Functional data analysis[M].Berlin:Springer, 1997.
[2]	RAMSAY J O, SILVERMAN B W.Applied functional data analysis:Methods and case studies[M].Berlin:Springer, 2002.
[3]	VIEU P, FERRATY F.Nonparametric functional data analysis[M].Berlin:Springer, 2006.
[4]	PAWLOWSKY-GLAHN V, BUCCIANTI A.Compositional data analysis:Theory and applications[M].Chichester:Wiley-Blackwell, 2011.
[5]	BILLARD L, DIDAY E.Symbolic regression analysis[M]//JAJUGA K, SOKOLOWSKI A, BOCK H.Classification, clustering, and data analysis.Berlin: Springer, 2002: 281-288.
[6]	BILLARD L, DIDAY E.Regression analysis for interval-valued data[M].Berlin:Springer, 2000:369-374.
[7]	FRY J M, FRY T R L, MCLAREN K R.Compositional data analysis and zeros in micro data[J].Applied Economics, 2000, 32(8):953-959. doi: 10.1080/000368400322002
[8]	PAWLOWSKY-GLAHN V, EGOZCUE J J.Exploring compositional data with the CoDa-dendrogram[J].Austrian Journal of Statistics, 2011, 40(1 & 2):103-113.
[9]	PAWLOWSKY-GLAHN V, EGOZCUE J J, TOLOSANA-DELGADO R.Modelling and analysis of compositional data[J].Hoboken:John Wiley & Sons, Ltd., 2015:152-154.
[10]	AITCHISON J.The statistical analysis of compositional data[M].Berlin:Springer, 1986.
[11]	AITCHISON J.The statistical analysis of compositional data[J].Journal of the Royal Statistical Society Series B, 1982, 44(2):139-177.
[12]	HRON K, FILZMOSER P, THOMPSON K.Linear regression with compositional explanatory variables[J].Journal of Applied Statistics, 2012, 39(5):1115-1128. doi: 10.1080/02664763.2011.644268
[13]	ATCHISON J, SHEN S M.Logistic-normal distributions:Some properties and uses[J].Biometrika, 1980, 67(2):261-272.
[14]	WANG H, SHANGGUAN L, WU J, et al.Multiple linear regression modeling for compositional data[J].Neurocomputing, 2013, 122:490-500. doi: 10.1016/j.neucom.2013.05.025
[15]	TOLOSANA-DELGADO R, EYNATTEN H V.Simplifying compositional multiple regression:Application to grain size controls on sediment geochemistry[J].Computers & Geosciences, 2010, 36(5):577-589.
[16]	ANSELIN L.Spatial econometrics:Methods and models[M].Berlin:Springer, 1988.
[17]	林光平, 龙志和, 吴梅.中国地区经济σ-收敛的空间计量实证分析[J].数量经济技术经济研究, 2006, 23(4):14-21. doi: 10.3969/j.issn.1000-3894.2006.04.002 LIN G P, LONG Z H, WU M.A spatial investigation of σ-convergence in China[J].The Journal of Quantitative & Technical Economics, 2006, 23(4):14-21(in Chinese). doi: 10.3969/j.issn.1000-3894.2006.04.002
[18]	郭金龙, 王宏伟.中国区域间资本流动与区域经济差距研究[J].管理世界, 2003(7):45-58. GUO J L, WANG H W.Study on the regional capital flows and regional economic differences in China[J].Management World, 2003(7):45-58(in Chinese).
[19]	TOPA G.Social interactions, local spillovers and unemployment[J].Review of Economic Studies, 2010, 68(2):261-295.
[20]	BAICKER K.The spillover effects of state spending[J].Journal of Public Economics, 2005, 89(2-3):529-544. doi: 10.1016/j.jpubeco.2003.11.003
[21]	ORD H.Estimation methods for models of spatial interaction[J].Publications of the American Statistical Association, 1975, 70(349):120-126. doi: 10.1080/01621459.1975.10480272
[22]	LEE L F.Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models[J].Econometrica, 2004, 72(6):1899-1925. doi: 10.1111/ecta.2004.72.issue-6
[23]	KELEJIAN H, PRUCHA I R.A generalized moments estimator for the autoregressive parameter in a spatial model[J].International Economic Review, 1999, 40(2):509-533. doi: 10.1111/iere.1999.40.issue-2
[24]	LEE L F.GMM and 2SLS estimation of mixed regressive, spatial autoregressive models[J].Journal of Econometrics, 2007, 137(2):489-514. doi: 10.1016/j.jeconom.2005.10.004
[25]	LESAGE J P, PACE R K.Introduction to spatial econometrics[M].New York:CRC Press, 2009:513-514.
[26]	EGOZCUE J J, PAWLOWSKYGLAHN V, MATEUFIGUERAS G, et al.Isometric logratio transformations for compositional data analysis[J].Mathematical Geology, 2003, 35(3):279-300. doi: 10.1023/A:1023818214614
[27]	QU X, LEE L F.Estimating a spatial autoregressive model with an endogenous spatial weight matrix[J].Journal of Econometrics, 2015, 184(2):209-232. doi: 10.1016/j.jeconom.2014.08.008