路徑模型和PLS課件

路徑模型和PLS吳喜之路徑模型和PLS吳喜之1基于回歸的傳統(tǒng)方法的假定

(e.g.,multipleregressionanalysis,discriminantanalysis,logisticregression,analysisofvariance)簡單模型結(jié)構(gòu):Thepostulationofasimplemodelstructure(atleastinthecaseofregression-basedapproaches);變量是可觀測的:Theassumptionthatallvariablescanbeconsideredasobservable;所有變量可精確測量:Theconjecturethatallvariablesaremeasuredwithouterror,whichmaylimittheirapplicabilityinsomeresearchsituations.基于回歸的傳統(tǒng)方法的假定

(e.g.,multipler2為克服第一代基于回歸的模型的弱點

Structuralequationmodeling(SEM)SEM僅同時分析自變量和因變量之間的鏈接中的一層.SEM允許多個自變量和因變量結(jié)構(gòu)中的關(guān)系的同時建模.因此不再區(qū)別因變量和自變量,但是區(qū)別外生和內(nèi)生隱變量變量(theexogenousandendogenouslatentvariables),前者不被設(shè)定的模型所解釋(總是因變量),后者為被解釋變量.SEM能夠構(gòu)造由指標變量(indicators,items,manifestvariables,orobservedmeasures)以及可觀測變量的度量誤差來度量的不可觀測變量為克服第一代基于回歸的模型的弱點

Structurale3兩種模型基于協(xié)方差(或最大似然)的方法:Covariance-basedSEM(軟件工具:EQS,AMOS,SEPATH,andCOSAN,theLISREL)基于方差(成分)的方法:Variance-basedSEM(Component-basedSEM),andtopresentpartialleastsquares(PLS)兩種模型基于協(xié)方差(或最大似然)的方法:Covarianc4內(nèi)生和外生隱變量的關(guān)系內(nèi)生隱變量及其指標及測量誤差的關(guān)系外生隱變量及其指標及測量誤差的關(guān)系內(nèi)生和外生隱變量的關(guān)系內(nèi)生隱變量及其指標及測量誤差的關(guān)系外生5名詞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.名詞η(eta)=latentendogenous6內(nèi)生和外生隱變量的關(guān)系:theoreticalequations:representingnonobservationalhypothesesandtheoreticaldefinitions(structuralmodel)內(nèi)生隱變量及其指標及測量誤差的關(guān)系(measurementequations)(measurementmodel)外生隱變量及其指標及測量誤差的關(guān)系(measurementequations)(measurementmodel)矩陣記號結(jié)構(gòu)模型度量模型內(nèi)生和外生隱變量的關(guān)系:theoreticalequat7三種不同類型的不可觀測變量原則上不可觀測變量:variablesthatareunobservableinprinciple(e.g.,theoreticalterms);

原則上不可觀測,但暗含經(jīng)驗概念或能夠從觀測值導出:variablesthatareunobservableinprinciplebuteitherimplyempiricalconceptsorcanbeinferredfromobservations(e.g.,attitudes,whichmightbereflectedinevaluations);用可觀測變量定義的不可觀測變量:unobservablevariablesthataredefinedintermsofobservables.三種不同類型的不可觀測變量原則上不可觀測變量:variab8兩類指標變量:a)reflectiveindicatorsthatdependontheconstruct;b)formativeones(alsoknownascausemeasures)thatcausetheformationoforchangesinanunobservablevariable兩類指標變量:a)reflectiveindicato9二者的區(qū)別Reflectiveindicatorsshouldhaveahighcorrelation(astheyarealldependentonthesameunobservablevariable),formativeindicatorsofthesameconstructcanhavepositive,negative,orzerocorrelationwithoneanother(Hulland,1999),whichmeansthatachangeinoneindicatordoesnotnecessarilyimplyasimilardirectionalchangeinothers(Chin,1998a).二者的區(qū)別Reflectiveindicatorssho10基于協(xié)方差(SEM-ML)和基于方差(SEM-PLS)的兩種建?；趨f(xié)方差方法試圖減少樣本協(xié)方差和理論預測的協(xié)方差的區(qū)別,因此參數(shù)估計過程試圖重新產(chǎn)生觀測到協(xié)方差矩陣(先計算模型參數(shù),然后用回歸得到個體估計值)基于方差的方法:使得被自變量解釋的因變量方差最大,而不是再生經(jīng)驗協(xié)方差矩陣.除了結(jié)構(gòu)模型和測量模型之外,PLS有第三部分:用來估計隱變量的個體值的加權(quán)關(guān)系(weightrelations)(先計算個體值—不可觀測變量值用他們的指標變量的線性組合表示,所用權(quán)重使得最終的個體值反映了因變量的大多數(shù)方差,再估計不可觀測變量的估計值.最后確定結(jié)構(gòu)模型的參數(shù).)基于協(xié)方差(SEM-ML)和基于方差(SEM-PLS)的兩種11PLS估計步驟:兩步確定權(quán)重(wi):第一步:外部近似(類似于主成份分析forreflective,回歸forformativeindicators)

第二步:內(nèi)部近似(三種方法:centroid,factor,andpathweightingscheme)

得到更新的重復這兩步直到收斂PLS估計步驟:兩步確定權(quán)重(wi):得到更新的重復這兩步12 PLS優(yōu)點:沒有總體假定或度量標度的假定,因此也沒有分布假定.然而需要某些假定,如線性回歸的系統(tǒng)部分等于因變量的條件期望.根據(jù)MonteCarlo模擬,PLS非常穩(wěn)健,而且隱變量的得分總是和真值吻合.

由于隱變量的個體值為顯變量的整合,由于后者的度量誤差,該值為不相合的(但漸近相合).由于樣本及每個隱變量的指標的有限性,PLS有低估隱變量之間的相關(guān)及高估載荷(測量變量的系數(shù))的傾向. PLS優(yōu)點:沒有總體假定或度量標度的假定,因此也沒有13在基于協(xié)方差和基于方差的SEM之間的選擇在每個隱變量的指標變量數(shù)目太大時,基于協(xié)方差的SEM就沒有辦法了.而實際上,如果沒有足夠的指標變量(有時達到500個),不能做任何嚴肅的路徑模型研究.由于有充分多的指標變量,選擇權(quán)重不會對路徑系數(shù)有任何影響,相合性問題就不是問題了.Therefore,theresearcherwouldbewelladvisedtousePLSinsteadofcovariance-basedSEMinsuchsituations.RecapitulatingtheseargumentsbyusingthewordsofS.Wold(1993),H.Wold’sson,onecansaythat“thenaturaldomainforLV[latentvariable]modelssuchasPLS…iswherethenumberof‘significant’LV’sissmall,muchsmallerthanthenumberofmeasuredvariables…andthanthenumberofobservations.”(p.137).在基于協(xié)方差和基于方差的SEM之間的選擇在每個隱變量的指標變14其它PLS占優(yōu)勢的情況Constructsaremeasuredprimarilybyformativeindicators.那時基于協(xié)方差的方法(LISREL)會有嚴重的識別困難LISREL至少要100,甚至200個觀測值,但PLS只需50(甚至在兩個隱變量,27個顯變量時只有10個觀測值的情況).其它PLS占優(yōu)勢的情況Constructsaremeas15Sohn&Park(2001)[3]的蒙特卡羅模擬比較表明：（1）以均方誤差和對因子載荷的方差為標準，在數(shù)據(jù)量小，而且表現(xiàn)出稍微非正態(tài)時，ML性能最差；當數(shù)據(jù)是正態(tài)或近似正態(tài)時，在ML和PLS之間沒有顯著差別，（2）以因子載荷的偏差為標準，無論數(shù)據(jù)量大小，ML隨著非正態(tài)增加而性能變差，（3）以回歸系數(shù)的均方誤差為標準，PLS比ML要好。

Sohn&Park(2001)[3]的蒙特卡羅模擬比較表16顧客滿意度模型顧客滿意度模型17瑞典顧客滿意度指數(shù)模型感知表現(xiàn)顧客預期質(zhì)量顧客滿意度顧客抱怨顧客忠誠SCSB感知表現(xiàn)顧客預期質(zhì)量顧客滿意度顧客抱怨顧客忠誠五個隱含變量中，顧客預期質(zhì)量為外生隱變量(exogenouslatentvariable)，其余為內(nèi)生隱變量(endogenouslatentvariable)。瑞典顧客滿意度指數(shù)模型感知表現(xiàn)顧客預期質(zhì)量顧客滿意度顧客抱怨18感知質(zhì)量軟件預期質(zhì)量顧客滿意度顧客忠誠感知價值感知質(zhì)量硬件形象ECSI歐洲顧客滿意度指數(shù)模型感知質(zhì)量軟件感知質(zhì)量硬件感知價值預期質(zhì)量形象顧客滿意度顧客忠誠感知質(zhì)量軟件預期質(zhì)量顧客滿意度顧客忠誠感知價值感知質(zhì)量硬件形19感知質(zhì)量（可分為產(chǎn)品和服務兩部分）預期質(zhì)量顧客滿意度(ACSI)顧客抱怨顧客忠誠度感知價值A(chǔ)CSI美國顧客滿意度指數(shù)模型感知質(zhì)量感知價值預期質(zhì)量顧客滿意度顧客抱怨顧客忠誠度感知質(zhì)量預期質(zhì)量顧客滿意度(ACSI)顧客抱怨顧客忠誠度感知20感知質(zhì)量（可分為產(chǎn)品和服務兩部分）預期質(zhì)量顧客滿意度(ACSI)顧客抱怨顧客忠誠度感知價值A(chǔ)CSI滿足顧客需求程度整體印象滿足顧客需求程度可靠性可靠性整體印象質(zhì)量價格比未確認期望值與理想之距離總體滿意度向經(jīng)理抱怨向雇員抱怨再購可能性價格承受度價格質(zhì)量比美國顧客滿意度指數(shù)模型感知質(zhì)量預期質(zhì)量顧客滿意度(ACSI)顧客抱怨顧客忠誠度感知21感知質(zhì)量h2預期質(zhì)量h1顧客滿意度h4顧客忠誠度h5感知價值h3品牌形象h6中國耐用消費品滿意度指數(shù)框圖總體感知質(zhì)量x5自定義感知質(zhì)量x6可靠性感知質(zhì)量x7服務感知質(zhì)量x8可靠性預期質(zhì)量x3品牌總體印象x17品牌特征顯著度x18價格質(zhì)量比x9再購可能性x15與理想之距離x14總體滿意度x11與其他品牌距離x13與期望之距離x12質(zhì)量價格比x10價格承受度x16總體預期質(zhì)量x1自定義預期質(zhì)量x2服務預期x4中國耐用消費品顧客滿意度指數(shù)模型感知質(zhì)量h2預期質(zhì)量h1顧客滿意度h4顧客忠誠度h5感知價值22感知質(zhì)量顧客滿意度顧客忠誠感知價值品牌形象中國非耐用消費品顧客滿意度指數(shù)框圖總體感知質(zhì)量感知質(zhì)量指標1感知質(zhì)量指標2感知質(zhì)量指標n品牌總體印象品牌特征顯著度價格質(zhì)量比再購可能性與理想之距離總體滿意度與其他品牌距離質(zhì)量價格比價格承受度中國非耐用消費品顧客滿意度指數(shù)模型感知質(zhì)量顧客滿意度顧客忠誠感知價值品牌形象中國非耐用消費品顧23感知質(zhì)量預期質(zhì)量顧客滿意度顧客忠誠感知價值品牌形象中國服務行業(yè)顧客滿意度指數(shù)框圖總體感知質(zhì)量響應性感知質(zhì)量可靠性感知質(zhì)量保證性感知質(zhì)量移情性感知質(zhì)量有形性感知質(zhì)量總體預期質(zhì)量品牌總體印象品牌特征顯著度價格質(zhì)量比回頭可能性與理想之距離總體滿意度與其他品牌距離與期望之距離質(zhì)量價格比價格承受度中國服務行業(yè)顧客滿意度指數(shù)模型感知質(zhì)量預期質(zhì)量顧客滿意度顧客忠誠感知價值品牌形象中國服務行24感知質(zhì)量h2預期質(zhì)量h1顧客滿意度h4顧客忠誠度h5感知價值h3品牌形象h6中國耐用消費品滿意度指數(shù)框圖總體感知質(zhì)量x5自定義感知質(zhì)量x6可靠性感知質(zhì)量x7服務感知質(zhì)量x8可靠性期質(zhì)量x3品牌總體印象x17品牌特征顯著度x18價格質(zhì)量比x9(Pricegivenquality)再購可能性x15與理想之距離x14總體滿意度x11與其他品牌距離x13與期望之距離x12質(zhì)量價格比x10(Qualitygivenprice)價格承受度x16總體預期質(zhì)量x1自定義預期質(zhì)量x2服務預期x4中國耐用消費品顧客滿意度指數(shù)模型感知質(zhì)量h2預期質(zhì)量h1顧客滿意度h4顧客忠誠度h5感知價值25這里，包含有b的B矩陣、h及z是未知的。而B矩陣的形式完全被圖模型所確定。這里，包含有b的B矩陣、h及z是未知的。而B矩陣的形式完全被26這里，包含有l(wèi)的L矩陣、h是未知的，而x是可觀測的。而L矩陣的形式完全被圖模型所確定。這里，包含有l(wèi)的L矩陣、h是未知的，而x是可觀測的。而L矩陣27偏最小二乘(PLS)法

解

路徑模型(PathModel)吳喜之(plspm)偏最小二乘(PLS)法

解

路徑模型(PathModel)28例子（先不看數(shù)字）例子（先不看數(shù)字）29其中：reflectiveindicators

“l(fā)oadings”其中：reflectiveindicators

“l(fā)oad30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輸出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:輸出outer.modResultsoftheoute34輸出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:輸出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路徑模型和PLSppt課件37res2$unidimres2$unidim38res2$outer.modres2$out.weights輸出第1列res2$loadings輸出第2列res2$outer.modres2$out.weights39路徑模型和PLSppt課件40res2$inner.modres2$path.coefsres2$r.sqrres2$inner.modres2$path.coefsr41res2$inner.sumres2$gofres2$inner.sumres2$gof42res2$latents：輸出所有觀測值的latent值res2$scores：輸出所有觀測值的latentscores值res2$latents：輸出所有觀測值的latent值43res2$effects#即路徑系數(shù)path.coefres2$effects#即路徑系數(shù)path.coef44路徑模型和PLSppt課件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路徑模型和PLSppt課件49路徑模型和PLSppt課件50路徑模型和PLSppt課件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路徑模型和PLSppt課件53路徑模型和PLSppt課件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(典型相關(guān)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路徑模型和PLSppt課件58路徑模型和PLSppt課件59路徑模型和PLSppt課件60semPLSsemPLS61library(semPLS)#下面是如何構(gòu)建一個模型(以ECSI為例)#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))構(gòu)建一個模型(以ECSI為例)library(semPLS)構(gòu)建一個模型(以ECSI為例)62路徑模型和PLSppt課件63ExpectationQualityValueImageSatisfactionComplaintsLoyaltyECSIExpectationQualityValueImageSa64EC