路径模型和PLS课件

路径模型和PLS吴喜之路径模型和PLS吴喜之1基于回归的传统方法的假定

(e.g.,multipleregressionanalysis,discriminantanalysis,logisticregression,analysisofvariance)简单模型结构:Thepostulationofasimplemodelstructure(atleastinthecaseofregression-basedapproaches);变量是可观测的:Theassumptionthatallvariablescanbeconsideredasobservable;所有变量可精确测量:Theconjecturethatallvariablesaremeasuredwithouterror,whichmaylimittheirapplicabilityinsomeresearchsituations.基于回归的传统方法的假定

(e.g.,multipler2为克服第一代基于回归的模型的弱点

Structuralequationmodeling(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(theexogenousandendogenouslatentvariables),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,manifestvariables,orobservedmeasures)以及可观测变量的度量误差来度量的不可观测变量为克服第一代基于回归的模型的弱点

Structurale3两种模型基于协方差(或最大似然)的方法:Covariance-basedSEM(软件工具:EQS,AMOS,SEPATH,andCOSAN,theLISREL)基于方差(成分)的方法:Variance-basedSEM(Component-basedSEM),andtopresentpartialleastsquares(PLS)两种模型基于协方差(或最大似然)的方法:Covarianc4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5名词η(eta)=latentendogenousvariable;ξ(xi)=latentexogenous(i.e.,independent)variable;ζ(zeta)=randomdisturbanceterm;“errorsinequations”γ(gamma)=pathcoefficient;φ(phi)noncausalrelationshipbetweentwolatentexogenousvariables;yi=indicatorsofendogenousvariables;εi(epsilon)=measurementerrorsforindicatorsofendogenousvariable;λyi(lambday)=loadingsofindicatorsofendogenousvariable;xi=indicatorsofendogenousvariable;δi(delta)=measurmenterrorsforindicatorsofexogenousvariable;λxi=(lambdax)loadingsofindicatorsofexogenousvariable.名词η(eta)=latentendogenous6内生和外生隐变量的关系:theoreticalequations:representingnonobservationalhypothesesandtheoreticaldefinitions(structuralmodel)内生隐变量及其指标及测量误差的关系(measurementequations)(measurementmodel)外生隐变量及其指标及测量误差的关系(measurementequations)(measurementmodel)矩阵记号结构模型度量模型内生和外生隐变量的关系:theoreticalequat7三种不同类型的不可观测变量原则上不可观测变量:variablesthatareunobservableinprinciple(e.g.,theoreticalterms);

原则上不可观测,但暗含经验概念或能够从观测值导出:variablesthatareunobservableinprinciplebuteitherimplyempiricalconceptsorcanbeinferredfromobservations(e.g.,attitudes,whichmightbereflectedinevaluations);用可观测变量定义的不可观测变量:unobservablevariablesthataredefinedintermsofobservables.三种不同类型的不可观测变量原则上不可观测变量:variab8两类指标变量:a)reflectiveindicatorsthatdependontheconstruct;b)formativeones(alsoknownascausemeasures)thatcausetheformationoforchangesinanunobservablevariable两类指标变量:a)reflectiveindicato9二者的区别Reflectiveindicatorsshouldhaveahighcorrelation(astheyarealldependentonthesameunobservablevariable),formativeindicatorsofthesameconstructcanhavepositive,negative,orzerocorrelationwithoneanother(Hulland,1999),whichmeansthatachangeinoneindicatordoesnotnecessarilyimplyasimilardirectionalchangeinothers(Chin,1998a).二者的区别Reflectiveindicatorssho10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(weightrelations)(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.)基于协方差(SEM-ML)和基于方差(SEM-PLS)的两种11PLS估计步骤:两步确定权重(wi):第一步:外部近似(类似于主成份分析forreflective,回归forformativeindicators)

第二步:内部近似(三种方法:centroid,factor,andpathweightingscheme)

得到更新的重复这两步直到收敛PLS估计步骤:两步确定权重(wi):得到更新的重复这两步12 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MonteCarlo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. PLS优点:没有总体假定或度量标度的假定,因此也没有13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,theresearcherwouldbewelladvisedtousePLSinsteadofcovariance-basedSEMinsuchsituations.RecapitulatingtheseargumentsbyusingthewordsofS.Wold(1993),H.Wold’sson,onecansaythat“thenaturaldomainforLV[latentvariable]modelssuchasPLS…iswherethenumberof‘significant’LV’sissmall,muchsmallerthanthenumberofmeasuredvariables…andthanthenumberofobservations.”(p.137).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14其它PLS占优势的情况Constructsaremeasuredprimarilybyformativeindicators.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).其它PLS占优势的情况Constructsaremeas15Sohn&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。

Sohn&Park(2001)[3]的蒙特卡罗模拟比较表16顾客满意度模型顾客满意度模型17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(exogenouslatentvariable)，其余为内生隐变量(endogenouslatentvariable)。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18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19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预期质量顾客满意度(ACSI)顾客抱怨顾客忠诚度感知20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预期质量顾客满意度(ACSI)顾客抱怨顾客忠诚度感知21感知质量h2预期质量h1顾客满意度h4顾客忠诚度h5感知价值h3品牌形象h6中国耐用消费品满意度指数框图总体感知质量x5自定义感知质量x6可靠性感知质量x7服务感知质量x8可靠性预期质量x3品牌总体印象x17品牌特征显著度x18价格质量比x9再购可能性x15与理想之距离x14总体满意度x11与其他品牌距离x13与期望之距离x12质量价格比x10价格承受度x16总体预期质量x1自定义预期质量x2服务预期x4中国耐用消费品顾客满意度指数模型感知质量h2预期质量h1顾客满意度h4顾客忠诚度h5感知价值22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23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24感知质量h2预期质量h1顾客满意度h4顾客忠诚度h5感知价值h3品牌形象h6中国耐用消费品满意度指数框图总体感知质量x5自定义感知质量x6可靠性感知质量x7服务感知质量x8可靠性期质量x3品牌总体印象x17品牌特征显著度x18价格质量比x9(Pricegivenquality)再购可能性x15与理想之距离x14总体满意度x11与其他品牌距离x13与期望之距离x12质量价格比x10(Qualitygivenprice)价格承受度x16总体预期质量x1自定义预期质量x2服务预期x4中国耐用消费品顾客满意度指数模型感知质量h2预期质量h1顾客满意度h4顾客忠诚度h5感知价值25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b的B矩阵、h及z是未知的。而B矩阵的形式完全被26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。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27偏最小二乘(PLS)法

解

路径模型(PathModel)吴喜之(plspm)偏最小二乘(PLS)法

解

路径模型(PathModel)28例子（先不看数字）例子（先不看数字）29其中：reflectiveindicators

“loadings”其中：reflectiveindicators

“load30其中：reflectiveindicators

“weights”其中：reflectiveindicators

“weig31library(plspm)##typicalexampleofPLS-PMincustomersatisfactionanalysis##modelwithsixLVsandreflectiveindicatorsdata(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)##reflectiveindicatorsres2<-plspm(satisfaction,sat.mat,sat.sets,sat.mod,scheme="centroid",scaled=FALSE)##plotdiagramoftheinnermodelplot(res2)##plotdiagramsofboththeinnermodelandoutermodel(loadingsandweights)plot(res2,what="weights")plot(res2,what="loadings")plot(res2,what="all")##End(Notrun)library(plspm)32程序plspm(x,inner.mat,sets,modes=NULL,scheme="centroid",scaled=TRUE,boot.val=FALSE,br=NULL,plsr=FALSE)xAnumericmatrixordataframecontainingthemanifestvariables.inner.matAsquare(lowertriangular)booleanmatrixindicatingthepathrelationshipsbetwennlatentvariables.setsListofvectorswithcolumnindicesfromxindicatingwhichmanifestvariablescorrespondtothelatentvariables.modesAcharactervectorindicatingthetypeofmeasurementforeachlatentvariable."A"forreflectivemeasurementor"B"forformativemeasurement(NULLbydefault).schemeAstringofcharactersindicatingthetypeofinnerweightingscheme.Possiblevaluesare"centroid"or"factor".scaledAlogicalvalueindicatingwhetherscalingdataisperformed(TRUEbydefault).boot.valAlogicalvalueindicatingwhetherbootstrapvalidationisperformed(FALSEbydefault).brAnintegerindicatingthenumberbootstrapresamples.Usedonlywhenboot.val=TRUE.plsrAlogicalvalueindicatingwhetherplsregressionisapplied(FALSEbydefault).程序plspm(x,inner.mat,sets,mo33输出outer.modResultsoftheouter(measurement)model.Includes:outerweights,standardizedloadings,communalities,andredundancies.inner.modResultsoftheinner(structural)model.Includes:pathcoefficientsandR-squaredforeachendogenouslatentvariable.latentsMatrixofstandardizedlatentvariables(variance=1calculateddividedbyN)obtainedfromcentereddata(mean=0).scoresMatrixoflatentvariablesusedtoestimatetheinnermodel.Ifscaled=FALSEthenscoresarelatentvariablescalculatedwiththeoriginaldata(non-stardardized).Ifscaled=TRUEthenscoresandlatentshavethesamevalues.out.weightsVectorofouterweights.loadingsVectorofstandardizedloadings(i.e.correlationswithLVs.)path.coefsMatrixofpathcoefficients(thismatrixhasasimilarformasinner.mat).r.sqrVectorofR-squaredcoefficients.Anobjectofclass"plspm".Whenthefunctionplspm.fitiscalled,itreturnsalistwithbasicresults:输出outer.modResultsoftheoute34输出outer.corCorrelationsbetweenthelatentvariablesandthemanifestvariables(alsocalledcrossloadings).inner.sumSummarizedresultsbylatentvariableoftheinnermodel.Includes:typeofLV,typeofmeasurement,numberofindicators,R-squared,averagecommunality,averageredundancy,andaveragevarianceextractedeffectsPatheffectsofthestructuralrelationships.Includes:direct,indirect,andtotaleffects.unidimResultsforcheckingtheunidimensionalityofblocks(Theseresultsareonlymeaningfulforreflectiveblocks).gofTablewithindexesofGoodness-of-Fit.Includes:absoluteGoF,relativeGoF,outermodelGoF,andinnermodelGoF.dataDatamatrixcontainingthemanifestvariablesusedinthemodel.bootListofbootstrappingresults;onlyavailablewhenargumentboot.val=TRUE.Ifthefunctionplspmiscalled,thepreviouslistofresultsalsocontainsthefollowingelements:输出outer.corCorrelationsbetwee35##typicalexampleofPLS-PMincustomersatisfactionanalysis##modelwithsixLVsandreflectiveindicatorsdata(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)##reflectiveindicatorsres2<-plspm(satisfaction,sat.mat,sat.sets,sat.mod,scaled=FALSE)summary(res2)plot(res2)##typicalexampleofPLS-PM36路径模型和PLSppt课件37res2$unidimres2$unidim38res2$outer.modres2$out.weights输出第1列res2$loadings输出第2列res2$outer.modres2$out.weights39路径模型和PLSppt课件40res2$inner.modres2$path.coefsres2$r.sqrres2$inner.modres2$path.coefsr41res2$inner.sumres2$gofres2$inner.sumres2$gof42res2$latents：输出所有观测值的latent值res2$scores：输出所有观测值的latentscores值res2$latents：输出所有观测值的latent值43res2$effects#即路径系数path.coefres2$effects#即路径系数path.coef44路径模型和PLSppt课件45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")##formativeindicatorsres1<-plspm(arizona,inner=ari.inner,outer=ari.outer,modes=ari.mod,scheme="factor",scaled=TRUE,plsr=TRUE)res1summary(res1)例data(arizona)46plot(res1,what="all")plot(res1,what="all")47例

##exampleofPLS-PMinmulti-blockdataanalysis##estimateapathmodelforthewinedataset##requirespackageFactoMineRlibrary(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)#usingfunctionplspm.fit(basicplsalgorithm)res4<-plspm.fit(wine,wine.mat,wine.sets,wine.mods,scheme="centroid")plot(res4,what="all",arr.pos=.4,p=.4,cex.txt=.8)

##End(Notrun)例##exampleofPLS-PMinmult48路径模型和PLSppt课件49路径模型和PLSppt课件50路径模型和PLSppt课件51##Notrun:##examplewithcustomersatisfactionanalysis##groupcomparisonbasedonthesegmentationvariable"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)##reflectiveindicatorspls<-plspm(satisfaction,sat.inner,sat.outer,sat.mod,scheme="factor",scaled=FALSE)##permutationtestwith100permutationsres.group<-plspm.groups(pls,satisfaction$gender,method="permutation",reps=100)res.groupplot(res.group)

##End(Notrun)plspm.groups{plspm}:GroupComparisoninPLS-PM##Notrun:plspm.groups{plsp52路径模型和PLSppt课件53路径模型和PLSppt课件54nipals{plspm}:Non-linearIterativePartialLeastSquares(主成份分析)PrincipalComponentAnalysiswithNIPALSalgorithmlibrary(plspm)data(wines)nip1<-nipals(wines[,-1],nc=5)plot(nip1)nipals{plspm}:Non-linearIte55##USArrestsdatavarynip2<-nipals(USArrests)plot(nip2)##USArrestsdatavary56plsca{plspm}:PLS-CA:PartialLeastSquaresCanonicalAnalysis(典型相关分析)##exampleofPLSCAwiththevehiclesdatasetdata(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])canplot(can)plsca{plspm}:PLS-CA:Partial57路径模型和PLSppt课件58路径模型和PLSppt课件59路径模型和PLSppt课件60semPLSsemPLS61library(semPLS)#下面是如何构建一个模型(以ECSI为例)#gettingthepathtothe.csvfilerepresentingtheinnerModelptf_Struc<-system.file("ECSIstrucmod.csv",package="semPLS")#gettingthepathtothe.csvfilerepresentingtheouterModelsptf_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)library(semPLS)构建一个模型(以ECSI为例)62路径模型和PLSppt课件63ExpectationQualityValueImageSatisfactionComplaintsLoyaltyECSIExpectationQualityValueImageSa64EC