成分数据路径分析模型
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摘要
路径分析是一种探索和验证系统内部各个因素之间因果关系的多元统计方法.本文针对现实中大量存在的成分数据变量,提出成分数据路径分析模型,给出模型的方程表达形式和图形表达形式.在成分数据多元线性回归的基础上,提出模型的参数估计方法,并利用Bootstrap分析技术,给出路径系数显著性检验办法.在某公司官方网站的用户满意度与推荐意愿影响因素应用研究中,成分数据路径分析建模结果表明,满意度主要受到易用性的影响,而推荐意愿主要受到有用性的影响.这一结论为网站原型设计与营销推广提供了新的启示.
Path analysis is a multivariate statistical method for exploring and verifying the causal relationship among the various factors in a system.In this paper,for the existence of large amount of compositional data variables in reality,a path model for compositional data is proposed,and the expression forms of the equation and graphics of the model are given.Based on the multivariate linear regression of compositional data,the parameter estimation method of the model is proposed,and Bootstrap technique is used to test the significance of the model parameters.In the research on user satisfaction and recommendation intention of the official website of one mobile company,application results using path model for compositional data show that user satisfaction is mainly determined by ease of use while recommendation intention is strongly influenced by usefulness.This conclusion provides new references for the prototyping and marketing promotion of a website.
Path analysis is a multivariate statistical method for exploring and verifying the causal relationship among the various factors in a system.In this paper,for the existence of large amount of compositional data variables in reality,a path model for compositional data is proposed,and the expression forms of the equation and graphics of the model are given.Based on the multivariate linear regression of compositional data,the parameter estimation method of the model is proposed,and Bootstrap technique is used to test the significance of the model parameters.In the research on user satisfaction and recommendation intention of the official website of one mobile company,application results using path model for compositional data show that user satisfaction is mainly determined by ease of use while recommendation intention is strongly influenced by usefulness.This conclusion provides new references for the prototyping and marketing promotion of a website.
引文
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[4]Anderson E W,Fornell C,Lehmann D R.Customer satisfaction,market share,and profitability:findings from sweden[J].Journal of Marketing,1994,58(3):53-66.
[5]Henseler J,Ringle C M,Sinkovics R R.The use of partial least squares path modeling in internar tional marketing[J].Social Science Electronic Publishing,2009,20(4):277-319.
[6]Tenenhaus M,Vinzi V E,Chatelin Y M,et al.PLS path modelling[J].Computational Statistics and Data Analysis,2005,48(1):159-205.
[7]Wang H,Shangguan L,Guan R,et al.Principal component analysis for compositional data vectors[J].Computational Statistics,2015,30(4):1079-1096.
[8]Palarea-Albaladejo J,Xed M,Xe N,et al.Dealing with distances and transformations for fuzzy c-means clustering of compositional data[J].Journal of Classification,2012,29(2):144-169.
[9]Filzmoser P,Hr on K,Templ M.Discriminant analysis for compositional data and robust parameter estimation[J].Computational Statistics,2012,27(4):585-604.
[10]Chen J,Zhang X,Li S.Multiple linear regression with compositional response and covariates[Jl.Journal of Applied Statistics,2017,44(12):2270-2285.
[11]Pawlowsky-Glahn V,Egozcue J J.BLU estimators and compositional data[J].Mathematical Geology,2002,34(3):259-274.
[12]Aitchison J.The Statistical Analysis of Compositional Data[M].New York:Chapman and Hal,London,1986.
[13]Egozcue J J,Barcelo-Vidal C,Jarauta-Bragulat E,et al.Elements of Simplicial Linear Algebra and Geometry[M].Compositional Data Analysis:Theory and Applications.John Wiley&Sons,Ltd,2011.
[14]Berry W.D.Nonrecursive Causal Models[M].Beverly Hills Calif,1984.
[15]Heise D R.Causal Analysis[M].Qxford England:John Wiley&sons,1975.
[16]Wang H,Shangguan L,Wu J,et al.Multiple Linear Regression Modeling for Compositional Data[J].Neurocomputing,2013,122(122):490-500.
[17]Efron B.Bootstrap methods:another look at the jackknife[J].Annals of Statistics,1979,7(1):1-26.
[1]Wold H.Estimation of principal components and related models by iterative least squares[J].Journal of Multivariate Analysis,1966,1:391-420.
[3]Chin W.The Partial Least squares approach for structural equation modeling[J].Modern methods for business research,1998,295:295-336.
[4]Anderson E W,Fornell C,Lehmann D R.Customer satisfaction,market share,and profitability:findings from sweden[J].Journal of Marketing,1994,58(3):53-66.
[5]Henseler J,Ringle C M,Sinkovics R R.The use of partial least squares path modeling in internar tional marketing[J].Social Science Electronic Publishing,2009,20(4):277-319.
[6]Tenenhaus M,Vinzi V E,Chatelin Y M,et al.PLS path modelling[J].Computational Statistics and Data Analysis,2005,48(1):159-205.
[7]Wang H,Shangguan L,Guan R,et al.Principal component analysis for compositional data vectors[J].Computational Statistics,2015,30(4):1079-1096.
[8]Palarea-Albaladejo J,Xed M,Xe N,et al.Dealing with distances and transformations for fuzzy c-means clustering of compositional data[J].Journal of Classification,2012,29(2):144-169.
[9]Filzmoser P,Hr on K,Templ M.Discriminant analysis for compositional data and robust parameter estimation[J].Computational Statistics,2012,27(4):585-604.
[10]Chen J,Zhang X,Li S.Multiple linear regression with compositional response and covariates[Jl.Journal of Applied Statistics,2017,44(12):2270-2285.
[11]Pawlowsky-Glahn V,Egozcue J J.BLU estimators and compositional data[J].Mathematical Geology,2002,34(3):259-274.
[12]Aitchison J.The Statistical Analysis of Compositional Data[M].New York:Chapman and Hal,London,1986.
[13]Egozcue J J,Barcelo-Vidal C,Jarauta-Bragulat E,et al.Elements of Simplicial Linear Algebra and Geometry[M].Compositional Data Analysis:Theory and Applications.John Wiley&Sons,Ltd,2011.
[14]Berry W.D.Nonrecursive Causal Models[M].Beverly Hills Calif,1984.
[15]Heise D R.Causal Analysis[M].Qxford England:John Wiley&sons,1975.
[16]Wang H,Shangguan L,Wu J,et al.Multiple Linear Regression Modeling for Compositional Data[J].Neurocomputing,2013,122(122):490-500.
[17]Efron B.Bootstrap methods:another look at the jackknife[J].Annals of Statistics,1979,7(1):1-26.