路径模型和PLS.ppt

,单击以编辑母片标题样式,*,单击以编辑母片,第二层,第三层,第四层,第五层,路径模型和,PLS,吴喜之,基于回归的传统方法的假定,(e.g.,multiple,regression analysis,discriminant analysis,logistic,regression,analysis of variance),简单模型结构,:The,postulation of a simple model structure(at least in the case,of regression-based,approaches);,变量是可观测的,:The,assumption that all variables can be,considered as,observable;,所有变量可精确测量,:The,conjecture that all variables are measured,without error,which may limit their applicability in some research situations.,为克服第一代基于回归的模型的弱点,Structural,equation modeling(SEM),SEM,仅同时分析自变量和因变量之间的链接中的一层,.SEM,允许多个自变量和因变量结构中的关系的同时建模,.,因此不再区别因变量和自变量,但是区别外生和内生隐变量变量,(the,exogenous and endogenous latent,variables),前者不被设定的模型所解释,(,总是因变量,),后者为被解释变量,.,SEM,能够构造由指标变量,(indicators,items,manifest variables,or observed measures,),以及可观测变量的度量误差来度量的不可观测变量,两种模型,基于协方差,(,或最大似然,),的方法,:,Covariance-based SEM(,软件工具,:,EQS,AMOS,SEPATH,and COSAN,the LISREL),基于方差,(,成分,),的方法,:,Variance-based SEM(Component-based SEM),and to present partial least squares(PLS),内生和外生隐变量的关系,内生隐变量及其指标及测量误差的关系,外,生隐变量及其指标及测量误差的关系,名词,(eta)=latent endogenous variable,;,(xi)=latent,exogenous,(i.e,.,independent)variable;,(,zeta)=random disturbance term;,“errors in equations”,(,gamma)=path coefficient;,(phi)noncausal relationship between two latent exogenous variables;,yi,=indicators,of,endogenous,variables;,i,(epsilon)=measurement errors for indicators of endogenous variable;,yi(lambda y)=loadings of indicators of endogenous variable;,xi,=indicators of,endogenous,variable,;,i(delta)=measurment errors for indicators of exogenous variable;,xi=(lambda,x),loadings,of indicators of exogenous variable.,内生和外生隐变量的关系,:,theoretical,equations:representing nonobservational,hypotheses and theoretical,definitions,(,structural model,),内生隐变量及其指标及测量误差的关系,(,measurement,equations),(,measurement model,),外,生隐变量及其指标及测量误差的关系,(,measurement,equations),(,measurement model,),矩阵记号,结构模型,度量模型,三种不同类型的不可观测变量,原则上不可观测变量,:variables,that are unobservable in principle(e.g.,theoretical terms,);,原则上不可观测,但暗含经验概念或能够从观测值导出,:variables,that are unobservable in principle but either imply empirical,concepts or,can be inferred from observations(e.g.,attitudes,which might be reflected,in evaluations,);,用可观测变量定义的不可观测变量,:unobservable,variables that are defined in terms,of observables,.,两类指标变量,:,a)reflective indicators that depend on the construct;b)formative ones(also known as cause measures)that cause the formation of or changes in an unobservable variable,二者的区别,Reflective,indicators should have,a high correlation,(as they are all,dependent on,the same unobservable variable),formative,indicators of the same,construct can,have,positive,negative,or zero correlation with one another,(Hulland,1999,),which,means that a change in one indicator does not necessarily imply a similar,directional change,in others(Chin,1998a).,基于协方差,(SEM-ML),和基于方差,(SEM-PLS),的两种建模,基于协方差方法,试图减少样本协方差和理论预测的协方差的区别,因此参数估计过程试图重新产生观测到协方差矩阵,(,先计算模型参数,然后用回归得到个体估计值,),基于方差的方法,:,使得被自变量解释的因变量方差最大,而不是再生经验协方差矩阵,.,除了结构模型和测量模型之外,PLS,有第三部分,:,用来估计隐变量的个体值的加权关系,(weight relations),(,先计算个体值,不可观测变量值用他们的指标变量的线性组合表示,所用权重使得最终的个体值反映了因变量的大多数方差,再估计不可观测变量的估计值,.,最后确定结构模型的参数,.),PLS,估计步骤,:,两步确定权重,(,w,i,):,第一步,:,外部近似,(,类似于主成份分析,for reflective,回归,for formative indicators),第二步,:,内部近似,(,三种方法,:centroid,factor,and,path weighting scheme),得到更新的,重复这两步直到收敛,PLS,优点,:,没有总体假定或度量标度的假定,因此也没有分布假定,.,然而需要某些假定,如线性回归的系统部分等于因变量的条件期望,.,根据,Monte Carlo,模拟,PLS,非常稳健,而且隐变量的得分总是和真值吻合,.,由于隐变量的个体值为显变量的整合,由于后者的度量误差,该值为不相合的,(,但渐近相合,).,由于样本及每个隐变量的指标的有限性,PLS,有低估隐变量之间的相关及高估载荷,(,测量变量的系数,),的倾向,.,在基于协方差和基于方差的,SEM,之间的选择,在每个隐变量的指标变量数目太大时,基于协方差的,SEM,就没有办法了,.,而实际上,如果没有足够的指标变量,(,有时达到,500,个,),不能做任何严肃的路径模型研究,.,由于有充分多的指标变量,选择权重不会对路径系数有任何影响,相合性问题就不是问题了,.,Therefore,the researcher would be well,advised to,use PLS instead of covariance-based SEM in such situations.,Recapitulating these,arguments by using the words of S.Wold(1993),H.Wolds son,one can,say that,“,the natural domain for LV latent variable models such as PLSis,where the,number of significant LVs is small,much smaller than the number of,measured variables,and than the number of observations.,”(p.137).,其它,PLS,占优势的情况,Constructs,are,measured primarily by,formative,indicators,.,那时基于协方差的方法,(LISREL),会有严重的识别困难,LISREL,至少要,100,甚至,200,个观测值,但,PLS,只需,50(,甚至在两个隐变量,27,个显变量时只有,10,个观测值的情况,).,Sohn&Park(2001),3,的蒙特卡罗模拟比较表明：（,1,）以均方误差和对因子载荷的方差为标准，在数据量小，而且表现出稍微非正态时，,ML,性能最差；当数据是正态或近似正态时，在,ML,和,PLS,之间没有显著差别，（,2,）以因子载荷的偏差为标准，无论数据量大小，,ML,随着非正态增加而性能变差，（,3,）以回归系数的均方误差为标准，,PLS,比,ML,要好。,顾客满意度模型,瑞典顾客满意度指数模型,感知表现,顾客预期质量,顾客满意度,顾客抱怨,顾客忠诚,SCSB,感知表现,顾客预期质量,顾客满意度,顾客抱怨,顾客忠诚,五个隐含变量中，顾客预期质量为外生隐变量,(exogenous latent variable),，其余为内生隐变量,(endogenous latent variable),。,感知质量软件,预期质量,顾客满意度,顾客忠诚,感知价值,感知质量硬件,形象,ECSI,欧洲顾客满意度指数模型,感知质量软件,感知质量硬件,感知价值,预期质量,形象,顾客满意度,顾客忠诚,感知质量,（可分为产品和服务两部分）,预期质量,顾客满意度,(ACSI),顾客抱怨,顾客忠诚度,感知价值,ACSI,美国顾客满意度指数模型,感知质量,感知价值,预期质量,顾客满意度,顾客抱怨,顾客忠诚度,感知质量,（可分为产品和服务两部分）,预期质量,顾客满意度,(ACSI),顾客抱怨,顾客忠诚度,感知价值,ACSI,满足顾客需求程度,整体印象,满足顾客需求程度,可靠性,可靠性,整体印象,质量价格比,未确认期望值,与理想之距离,总体满意度,向经理抱怨,向雇员抱怨,再购可能性,价格承受度,价格质量比,美国顾客满意度指数模型,感知质量,h,2,预期质量,h,1,顾客满意度,h,4,顾客忠诚度,h,5,感知价值,h,3,品牌形象,h,6,中国耐用消费品满意度指数框图,总体感知质量,x,5,自定义感知质量,x,6,可靠性感知质量,x,7,服务感知质量,x,8,可靠性预期质量,x,3,品牌总体印象,x,17,品牌特征显著度,x,18,价格质量比,x,9,再购可能性,x,15,与理想之距离,x,14,总体满意度,x,11,与其他品牌距离,x,13,与期望之距离,x,12,质量价格比,x,10,价格承受度,x,16,总体预期质量,x,1,自定义预期质量,x,2,服务预期,x,4,中国耐用消费品顾客满意度指数模型,感知质量,顾客满意度,顾客忠诚,感知价值,品牌形象,中国非耐用消费品顾客满意度指数框图,总体感知质量,感知质量指标,1,感知质量指标,2,感知质量指标,n,品牌总体印象,品牌特征显著度,价格质量比,再购可能性,与理想之距离,总体满意度,与其他品牌距离,质量价格比,价格承受度,中国非耐用消费品顾客满意度指数模型,感知质量,预期质量,顾客满意度,顾客忠诚,感知价值,品牌形象,中国服务行业顾客满意度指数框图,总体感知质量,响应性感知质量,可靠性感知质量,保证性感知质量,移情性感知质量,有形性感知质量,总体预期质量,品牌总体印象,品牌特征显著度,价格质量比,回头可能性,与理想之距离,总体满意度,与其他品牌距离,与期望之距离,质量价格比,价格承受度,中国服务行业顾客满意度指数模型,感知质量,h,2,预期质量,h,1,顾客满意度,h,4,顾客忠诚度,h,5,感知价值,h,3,品牌形象,h,6,中国耐用消费品满意度指数框图,总体感知质量,x,5,自定义感知质量,x,6,可靠性感知质量,x,7,服务感知质量,x,8,可靠性期质量,x,3,品牌总体印象,x,17,品牌特征显著度,x,18,价格质量比,x,9,(Price given quality),再购可能性,x,15,与理想之距离,x,14,总体满意度,x,11,与其他品牌距离,x,13,与期望之距离,x,12,质量价格比,x,10,(Quality given price),价格承受度,x,16,总体预期质量,x,1,自定义预期质量,x,2,服务预期,x,4,中国耐用消费品顾客满意度指数模型,这里，包含有,b,的,B,矩阵、,h,及,z,是未知的。而,B,矩阵的形式完全被图模型所确定。,这里，包含有,l,的,L,矩阵、,h,是未知的，而,x,是可观测的。而,L,矩阵的形式完全被图模型所确定。,偏最小二,乘,(PLS),法,解,路径模型,(Path Model),吴喜之,(,plspm,),例子（先不看数字）,其中：,reflective indicators,“,loadings,”,其中：,reflective indicators,“,weights,”,library(plspm),#typical example of PLS-PM in customer satisfaction analysis,#model with six LVs and,reflective indicators,data(satisfaction),IMAG-c(0,0,0,0,0,0),EXPE-c(1,0,0,0,0,0),QUAL-c(0,1,0,0,0,0),VAL -c(0,1,1,0,0,0),SAT -c(1,1,1,1,0,0),LOY -c(1,0,0,0,1,0),sat.mat-rbind(IMAG,EXPE,QUAL,VAL,SAT,LOY),sat.sets-list(1:5,6:10,11:15,16:19,20:23,24:27),sat.mod-rep(,A,6)#,reflective indicators,res2-plspm(satisfaction,sat.mat,sat.sets,sat.mod,scheme=centroid,scaled=FALSE),#plot diagram of the inner model,plot(res2),#plot diagrams of both the inner model and outer model(loadings and weights),plot(res2,what=weights),plot(res2,what=loadings),plot(res2,what=all),#End(Not run),程序,plspm(x,inner.mat,sets,modes=NULL,scheme=centroid,scaled=TRUE,boot.val=FALSE,br=NULL,plsr=FALSE),x,A numeric matrix or data frame containing the manifest variables.,inner.mat,A square(lower triangular)boolean matrix indicating the path relationships betwenn latent variables.,sets,List of vectors with column indices from x indicating which manifest variables correspond to the latent variables.,modes,A character vector indicating the type of measurement for each latent variable.A for reflective measurement or B for formative measurement(NULL by default).,scheme,A string of characters indicating the type of inner weighting scheme.Possible values are centroid or factor.,scaled,A logical value indicating whether scaling data is performed(TRUE by default).,boot.val,A logical value indicating whether bootstrap validation is performed(FALSE by default).,br,An integer indicating the number bootstrap resamples.Used only when boot.val=TRUE.,plsr,A logical value indicating whether pls regression is applied(FALSE by default).,输出,outer.mod,Results of the outer(measurement)model.Includes:outer weights,standardized loadings,communalities,and redundancies.,inner.mod,Results of the inner(structural)model.Includes:path coefficients and R-squared for each endogenous latent variable.,latents,Matrix of standardized latent variables(variance=1 calculated divided by N)obtained from centered data(mean=0).,scores,Matrix of latent variables used to estimate the inner model.If scaled=FALSE then scores are latent variables calculated with the original data(non-stardardized).If scaled=TRUE then scores and latents have the same values.,out.weights,Vector of outer weights.,loadings,Vector of standardized loadings(i.e.correlations with LVs.),path.coefs,Matrix of path coefficients(this matrix has a similar form as inner.mat).,r.sqr,Vector of R-squared coefficients.,An object of class,plspm,.When the function,plspm.fit,is called,it returns a list with basic results:,输出,outer.cor,Correlations between the latent variables and the manifest variables(also called crossloadings).,inner.sum,Summarized results by latent variable of the inner model.Includes:type of LV,type of measurement,number of indicators,R-squared,average communality,average redundancy,and average variance extracted,effects,Path effects of the structural relationships.Includes:direct,indirect,and total effects.,unidim,Results for checking the unidimensionality of blocks(These results are only meaningful for reflective blocks).,gof,Table with indexes of Goodness-of-Fit.Includes:absolute GoF,relative GoF,outer model GoF,and inner model GoF.,data,Data matrix containing the manifest variables used in the model.,boot,List of bootstrapping results;only available when argument boot.val=TRUE.,If the function,plspm,is called,the previous list of results also contains the following elements:,#typical example of PLS-PM in customer satisfaction analysis,#model with six LVs and reflective indicators,data(satisfaction),IMAG-c(0,0,0,0,0,0),EXPE-c(1,0,0,0,0,0),QUAL-c(0,1,0,0,0,0),VAL -c(0,1,1,0,0,0),SAT -c(1,1,1,1,0,0),LOY -c(1,0,0,0,1,0),sat.mat-rbind(IMAG,EXPE,QUAL,VAL,SAT,LOY),sat.sets-list(1:5,6:10,11:15,16:19,20:23,24:27),sat.mod-rep(A,6)#reflective indicators,res2-plspm(satisfaction,sat.mat,sat.sets,sat.mod,scaled=FALSE),summary(res2),plot(res2),res2$unidim,res2$outer.mod,res2$out.weights,输出第,1,列,res2$loadings,输出第,2,列,res2$inner.mod,res2$path.coefs,res2$r.sqr,res2$inner.sum,res2$gof,res2$latents,：输出所有观测值的,latent,值,res2$scores,：输出所有观测值的,latent scores,值,res2$effects#,即路径系数,path.coef,例,data(arizona),ari.inner-matrix(c(0,0,0,0,0,0,1,1,0),3,3,byrow=TRUE),dimnames(ari.inner)-list(c(ENV,SOIL,DIV),c(ENV,SOIL,DIV),ari.outer-list(c(1,2),c(3,4,5),c(6,7,8),ari.mod-c(B,B,B)#formative indicators,res1-plspm(arizona,inner=ari.inner,outer=ari.outer,modes=ari.mod,scheme=factor,scaled=TRUE,plsr=TRUE),res1,summary(res1),plot(res1,what=all),例,#example of PLS-PM in multi-block data analysis,#estimate a path model for the wine data set,#requires package FactoMineR,library(FactoMineR),data(wine),SMELL-c(0,0,0,0),VIEW-c(1,0,0,0),SHAKE-c(1,1,0,0),TASTE-c(1,1,1,0),wine.mat-rbind(SMELL,VIEW,SHAKE,TASTE),wine.sets-list(3:7,8:10,11:20,21:29),wine.mods-rep(A,4),#using function plspm.fit(basic pls algorithm),res4-plspm.fit(wine,wine.mat,wine.sets,wine.mods,scheme=centroid),plot(res4,what=all,arr.pos=.4,box.prop=.4,cex.txt=.8),#End(Not run),#Not run:,#example with customer satisfaction analysis,#group comparison based on the segmentation variable gender,data(satisfaction),IMAG-c(0,0,0,0,0,0),EXPE-c(1,0,0,0,0,0),QUAL-c(0,1,0,0,0,0),VAL -c(0,1,1,0,0,0),SAT -c(1,1,1,1,0,0),LOY -c(1,0,0,0,1,0),sat.inner-rbind(IMAG,EXPE,QUAL,VAL,SAT,LOY),sat.outer-list(1:5,6:10,11:15,16:19,20:23,24:27),sat.mod-rep(A,6)#reflective indicators,pls-plspm(satisfaction,sat.inner,sat.outer,sat.mod,scheme=factor,scaled=FALSE),#permutation test with 100 permutations,res.group-plspm.groups(pls,satisfaction$gender,method=permutation,reps=100),res.group,plot(res.group),#End(Not run),plspm.groups plspm:Group Comparison in PLS-PM,nipals plspm:Non-linear Iterative Partial Least Squares(,主成份分析,),Principal Component Analysis with NIPALS algorithm,library(plspm),data(wines),nip1-nipals(wines,-1,nc=5),plot(nip1),#USArrests data vary,nip2-nipals(USArrests),plot(nip2),plsca plspm:PLS-CA:Partial Least Squares Canonical Analysis(,典型相关分析,),#example of PLSCA with the vehicles dataset,data(vehicles);head(vehicles),names(vehicles),1 diesel turbo two.doors hatchback wheel.base,6 length width height curb.weight eng.size,11 horsepower peak.rpm price symbol city.mpg,16 highway.mpg,can-plsca(vehicles,1:12,vehicles,13:16),can,plot(can),semPLS,library(semPLS),#,下面是如何构建一个模型,(,以,ECSI,为例,),#getting the path to the.csv file representing the inner Model,ptf_Struc-system.file(ECSIstrucmod.csv,package=semPLS),#getting the path to the.csv file representing the outer Models,ptf_Meas-system.file(ECSImeasuremod.csv,package=semPLS),sm-as.matrix(read.csv(ptf_Struc),(w=read.csv(ptf_Struc),mm-as.matrix(read.csv(ptf_Meas),构建一个模型,(,以,ECSI,为例,),Expectation,Quality,Value,Image,Satisfaction,Complaints,Loyalty,ECSI,ECSI,data(mobi),class(mobi);dim(mobi);head(mobi)#data.frame“1 250 24,ECSI-plsm(data=,mobi,strucmod=,sm,measuremod=,mm,),ECSI,exogen(ECSI),endogen(ECSI),reflective(ECSI),formative(ECSI),indicators(ECSI,Image),predecessors(ECSI),#sempls,data(ECSImobi);class(ECSImobi);summary(ECSImobi);names(ECSImobi)#,就是前面的,ECSI,ecsi names(ecsi),#,计算结果的名称,1 coefficients path_coefficients outer_loadings cross_loadings total_effects,6 inner_weights outer_weights blocks factor_scores data,11 scaled model weighting_scheme sum1 pairwise,16 method iterations convCrit tolerance maxit,21 N incomplete,ecsi$coe#,隐变量,-,显变量,ecsi$path_coe#,隐变量,-,隐变量,ecsi$outer_loadings#,和,coefficient,一样,但为矩阵形式,is.matrix(ecsi$outer_loadings),ecsi$cross_loadings#,上面有的这里一样,但上面为,0,的这里也有值,ecsi$total_effects#,隐变量,-,隐变量,和,path_coe,不同,#Total effects=direct effects+indirect effects,ecsi$inner_weights#,隐变量,-,隐变量,和前面不同,.,这是权重,和下面的路径系数不同,(,红线部分,),ecsi$outer_weights#,隐变量,-,显变量,和,coefficient,不同,(,权重相加为,1),ecsi$factor_scores#,隐变量的个体值,(,矩阵,)dim(ecsi$factor_scores)=250 7,ecsi$data#,观测值,class(ecsi$data),数据矩阵,SEM,with R?,(,四页,ppt),