1、路徑模型和PLS吳喜之基于回歸的傳統(tǒng)方法的假定(e.g., multiple regression analysis, discriminant analysis, logistic regression, analysis of variance)a) 簡(jiǎn)單模型結(jié)構(gòu): The postulation of a simple model structure (at least in the case of regression-based approaches); b) 變量是可觀測(cè)的: The assumption that all variables can be considered a

2、s observable; c) 所有變量可精確測(cè)量: The conjecture that all variables are measured without error, which may limit their applicability in some research situations.為克服第一代基于回歸的模型的弱點(diǎn) Structural equation modeling (SEM)SEM僅同時(shí)分析自變量和因變量之間的鏈接中的一層. SEM允許多個(gè)自變量和因變量結(jié)構(gòu)中的關(guān)系的同時(shí)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(the exogenou

3、s and endogenous latent variables), 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(biāo)變量(indicators, items, manifest variables, or observed measures)以及可觀測(cè)變量的度量誤差來(lái)度量的不可觀測(cè)變量?jī)煞N模型 基于協(xié)方差基于協(xié)方差(或最大似然或最大似然)的方法的方法: Covariance-based SEM (軟件工具: EQS, AMOS, SEPATH, and COSAN, the LISREL) 基于方差基于方差(成分成分)的方法的方法: Variance-

4、based SEM (Component-based SEM), and to present partial least squares (PLS)內(nèi)生和外生隱變量的關(guān)系內(nèi)生隱變量及其指標(biāo)及測(cè)量誤差的關(guān)系外生隱變量及其指標(biāo)及測(cè)量誤差的關(guān)系名詞 (eta) = latent endogenous variable; (xi) = latent exogenous (i.e., independent) variable; (zeta) = random disturbance term; “errors in equations” (gamma) = path coefficient; (ph

5、i) 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) = measurm

6、ent errors for indicators of exogenous variable; xi = (lambda x) loadings of indicators of exogenous variable.內(nèi)生和外生隱變量的關(guān)系: theoretical equations: representing nonobservational hypotheses and theoretical definitions (structural model)內(nèi)生隱變量及其指標(biāo)及測(cè)量誤差的關(guān)系(measurement equations) (measurement model)外生隱變量及其

7、指標(biāo)及測(cè)量誤差的關(guān)系(measurement equations) (measurement model)矩陣記號(hào)矩陣記號(hào)結(jié)構(gòu)模型結(jié)構(gòu)模型度量模型度量模型三種不同類型的不可觀測(cè)變量a) 原則上不可觀測(cè)變量: variables that are unobservable in principle (e.g., theoretical terms);b) 原則上不可觀測(cè), 但暗含經(jīng)驗(yàn)概念或能夠從觀測(cè)值導(dǎo)出: variables that are unobservable in principle but either imply empirical concepts or can be infe

8、rred from observations (e.g., attitudes, which might be reflected in evaluations); c) 用可觀測(cè)變量定義的不可觀測(cè)變量: unobservable variables that are defined in terms of observables. 兩類指標(biāo)變量?jī)深愔笜?biāo)變量: a) reflective indicators that depend on the construct; b) formative ones (also known as cause measures) that cause the

9、 formation of or changes in an unobservable variable 二者的區(qū)別 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),

10、 which means that a change in one indicator does not necessarily imply a similar directional change in others (Chin, 1998a).基于協(xié)方差(SEM-ML)和基于方差(SEM-PLS)的兩種建模 基于協(xié)方差方法基于協(xié)方差方法試圖減少樣本協(xié)方差和理論預(yù)測(cè)的協(xié)方差的區(qū)別, 因此參數(shù)估計(jì)過(guò)程試圖重新產(chǎn)生觀測(cè)到協(xié)方差矩陣(先計(jì)算模先計(jì)算模型參數(shù)型參數(shù), 然后用回歸得到個(gè)體估計(jì)值然后用回歸得到個(gè)體估計(jì)值) 基于方差的方法基于方差的方法: 使得被自變量解釋的因變量方差最大, 而不是再生經(jīng)驗(yàn)

11、協(xié)方差矩陣. 除了結(jié)構(gòu)模型和測(cè)量模型之外, PLS有第三部分: 用來(lái)估計(jì)隱變量的個(gè)體值的加權(quán)關(guān)系(weight relations)(先計(jì)算個(gè)體值先計(jì)算個(gè)體值不可觀測(cè)不可觀測(cè)變量值用他們的指標(biāo)變量的線性組合表示變量值用他們的指標(biāo)變量的線性組合表示, 所用權(quán)重使得最終的個(gè)體值反映了因變量所用權(quán)重使得最終的個(gè)體值反映了因變量的大多數(shù)方差的大多數(shù)方差, 再估計(jì)不可觀測(cè)變量的估計(jì)再估計(jì)不可觀測(cè)變量的估計(jì)值值. 最后確定結(jié)構(gòu)模型的參數(shù)最后確定結(jié)構(gòu)模型的參數(shù).)PLS估計(jì)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for reflective, 回歸 for formative

12、indicators ) 第二步: 內(nèi)部近似 (三種方法: centroid, factor, and path weighting scheme)得到更新的重復(fù)這兩步直到收斂重復(fù)這兩步直到收斂PLS 優(yōu)點(diǎn): 沒(méi)有總體假定或度量標(biāo)度的假定, 因此也沒(méi)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)Monte Carlo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(gè)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(gè)隱變量的指標(biāo)的有限性, PLS有低估隱變量之間的相關(guān)及高估載荷(測(cè)量變量的系數(shù))的傾

13、向.在基于協(xié)方差和基于方差的在基于協(xié)方差和基于方差的SEM之間的選擇之間的選擇 在每個(gè)隱變量的指標(biāo)變量數(shù)目太大時(shí), 基于協(xié)方差的SEM就沒(méi)有辦法了. 而實(shí)際上, 如果沒(méi)有足夠的指標(biāo)變量(有時(shí)達(dá)到500個(gè)), 不能做任何嚴(yán)肅的路徑模型研究. 由于有充分多的指標(biāo)變量, 選擇權(quán)重不會(huì)對(duì)路徑系數(shù)有任何影響, 相合性問(wèn)題就不是問(wèn)題了. Therefore, the researcher would be well advised to use PLS instead of covariance-based SEM in such situations. Recapitulating these argu

14、ments 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占優(yōu)勢(shì)的情況 Const

15、ructs are measured primarily by formative indicators. 那時(shí)基于協(xié)方差的方法(LISREL)會(huì)有嚴(yán)重的識(shí)別困難 LISREL至少要100, 甚至200個(gè)觀測(cè)值, 但PLS只需50 (甚至在兩個(gè)隱變量, 27個(gè)顯變量時(shí)只有10個(gè)觀測(cè)值的情況).Sohn & Park(2001)3的蒙特卡羅模擬比較表明：（1）以均方誤差和對(duì)因子載荷的方差為標(biāo)準(zhǔn)，在數(shù)據(jù)量小，而且表現(xiàn)出稍微非正態(tài)時(shí)，ML性能最差；當(dāng)數(shù)據(jù)是正態(tài)或近似正態(tài)時(shí)，在ML和PLS之間沒(méi)有顯著差別，（2）以因子載荷的偏差為標(biāo)準(zhǔn)，無(wú)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

16、方誤差為標(biāo)準(zhǔn)，PLS比ML要好。 顧客滿意度模型瑞典顧客滿意度指數(shù)模型瑞典顧客滿意度指數(shù)模型感知表現(xiàn)顧客預(yù)期質(zhì)量顧客滿意度顧客抱怨顧客忠誠(chéng)SCSB感知表現(xiàn)感知表現(xiàn)顧客預(yù)期質(zhì)量顧客預(yù)期質(zhì)量顧客滿意度顧客滿意度顧客抱怨顧客抱怨顧客忠誠(chéng)顧客忠誠(chéng)五個(gè)隱含變量中，顧客預(yù)期質(zhì)量為外生隱變量五個(gè)隱含變量中，顧客預(yù)期質(zhì)量為外生隱變量(exogenous latent variable)，其余為內(nèi)生隱變量，其余為內(nèi)生隱變量(endogenous latent variable)。感知質(zhì)量軟件預(yù)期質(zhì)量顧客滿意度顧客忠誠(chéng)感知價(jià)值感知質(zhì)量硬件形象ECSI歐洲顧客滿意度指數(shù)模型歐洲顧客滿意度指數(shù)模型感知質(zhì)量軟件感知質(zhì)量

17、軟件感知質(zhì)量硬件感知質(zhì)量硬件感知價(jià)值感知價(jià)值預(yù)期質(zhì)量預(yù)期質(zhì)量形象形象顧客滿意度顧客滿意度顧客忠誠(chéng)顧客忠誠(chéng)感知質(zhì)量感知質(zhì)量（可分為產(chǎn)品和服務(wù)兩部分）（可分為產(chǎn)品和服務(wù)兩部分）預(yù)期質(zhì)量預(yù)期質(zhì)量顧客滿意度顧客滿意度(ACSI)顧客抱怨顧客抱怨顧客忠誠(chéng)度顧客忠誠(chéng)度感知價(jià)值感知價(jià)值A(chǔ)CSI美國(guó)顧客滿意度指數(shù)模型感知質(zhì)量感知質(zhì)量感知價(jià)值感知價(jià)值預(yù)期質(zhì)量預(yù)期質(zhì)量顧客滿意度顧客滿意度顧客抱怨顧客抱怨顧客忠誠(chéng)度顧客忠誠(chéng)度感知質(zhì)量感知質(zhì)量（可分為產(chǎn)品和（可分為產(chǎn)品和服務(wù)兩部分）服務(wù)兩部分）預(yù)期質(zhì)量預(yù)期質(zhì)量顧客滿意度顧客滿意度(ACSI)顧客抱怨顧客抱怨顧客忠誠(chéng)度顧客忠誠(chéng)度感知價(jià)值感知價(jià)值A(chǔ)CSI滿足顧客需求程度滿

18、足顧客需求程度整體印象整體印象滿足顧客需求程度滿足顧客需求程度可靠性可靠性可靠性可靠性整體印象整體印象質(zhì)量?jī)r(jià)格比質(zhì)量?jī)r(jià)格比未確認(rèn)期望值未確認(rèn)期望值與理想之距與理想之距離離總體滿意度總體滿意度向經(jīng)理抱怨向經(jīng)理抱怨向雇員抱怨向雇員抱怨再購(gòu)可能性再購(gòu)可能性價(jià)格承受度價(jià)格承受度價(jià)格質(zhì)量比價(jià)格質(zhì)量比美國(guó)顧客滿意度指數(shù)模型感知質(zhì)量h h2預(yù)期質(zhì)量h h1顧客滿意度h h4顧客忠誠(chéng)度h h5感知價(jià)值h h3品牌形象h h6中國(guó)耐用消費(fèi)品滿意度指數(shù)框圖中國(guó)耐用消費(fèi)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(wù)感知質(zhì)量x8可靠性預(yù)期質(zhì)量x3品牌總體印象x17品牌特征顯著度x18價(jià)格質(zhì)量

19、比x9再購(gòu)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?jī)r(jià)格比x10價(jià)格承受度x16總體預(yù)期質(zhì)量x1自定義預(yù)期質(zhì)量x2服務(wù)預(yù)期x4中國(guó)耐用消費(fèi)品顧客滿意度指數(shù)模型中國(guó)耐用消費(fèi)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(chéng)感知價(jià)值品牌形象中國(guó)非耐用消費(fèi)品顧客滿意度指數(shù)框圖中國(guó)非耐用消費(fèi)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(biāo)1感知質(zhì)量指標(biāo)2感知質(zhì)量指標(biāo)n品牌總體印象品牌特征顯著度價(jià)格質(zhì)量比再購(gòu)可能性與理想之距離總體滿意度與其他品牌距離質(zhì)量?jī)r(jià)格比價(jià)格承受度中國(guó)非耐用消費(fèi)品顧客滿意度指數(shù)模型中國(guó)非耐用消費(fèi)品顧客滿意度指數(shù)模型感知質(zhì)量預(yù)期質(zhì)量顧客滿意度顧客

20、忠誠(chéng)感知價(jià)值品牌形象中國(guó)服務(wù)行業(yè)顧客滿意度指數(shù)框圖中國(guó)服務(wù)行業(yè)顧客滿意度指數(shù)框圖總體感知質(zhì)量響應(yīng)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(yù)期質(zhì)量品牌總體印象品牌特征顯著度價(jià)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?jī)r(jià)格比價(jià)格承受度中國(guó)服務(wù)行業(yè)顧客滿意度指數(shù)模型中國(guó)服務(wù)行業(yè)顧客滿意度指數(shù)模型感知質(zhì)量h h2預(yù)期質(zhì)量h h1顧客滿意度h h4顧客忠誠(chéng)度h h5感知價(jià)值h h3品牌形象h h6中國(guó)耐用消費(fèi)品滿意度指數(shù)框圖中國(guó)耐用消費(fèi)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(wù)感知質(zhì)量x8可靠性期質(zhì)量x3品牌總體印象

21、x17品牌特征顯著度x18價(jià)格質(zhì)量比x9 (Price given quality)再購(gòu)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?jī)r(jià)格比x10(Quality given price)價(jià)格承受度x16總體預(yù)期質(zhì)量x1自定義預(yù)期質(zhì)量x2服務(wù)預(yù)期x4中國(guó)耐用消費(fèi)品顧客滿意度指數(shù)模型中國(guó)耐用消費(fèi)品顧客滿意度指數(shù)模型這里，包含有這里，包含有b b的的B B矩陣、矩陣、h h及及z z是未知是未知的。而的。而B B矩陣的形式完全被圖模型所矩陣的形式完全被圖模型所確定。確定。這里，包含有這里，包含有l(wèi) l的的L L矩陣、矩陣、h h是未知的，是未知的，而而x是

22、可觀測(cè)的。而是可觀測(cè)的。而L L矩陣的形式完全矩陣的形式完全被圖模型所確定。被圖模型所確定。偏最小二偏最小二乘乘(PLS)法法解解路徑模型路徑模型(Path Model)吳喜之吳喜之( (plspm) )Inner ModelPath Coefficients0.57890.20070.27520.84830.10550.00270.67670.12220.58930.4954IMAGEXPEQUALVALSATLOY例子（先不看數(shù)字）IMAGloadings0.70950.87730.84170.56940.7783imag1imag2imag3imag4imag5IMAGEXPEloadi

23、ngs0.76580.83740.75980.71840.8373expe1expe2expe3expe4expe5EXPEQUALloadings0.78150.88150.7940.7890.8075qual1qual2qual3qual4qual5QUALVALloadings0.86480.79630.75010.8445val1val2val3val4VALSATloadings0.91980.9160.82590.8175sat1sat2sat3sat4SATLOYloadings0.90650.67120.90490.682loy1loy2loy3loy4LOY其中：reflec

24、tive indicators“l(fā)oadings”IMAGweights0.09830.15740.15670.07680.1842imag1imag2imag3imag4imag5IMAGEXPEweights0.10630.14070.11870.09950.1384expe1expe2expe3expe4expe5EXPEQUALweights0.10670.13460.11710.09570.1157qual1qual2qual3qual4qual5QUALVALweights0.17490.11770.12080.1665val1val2val3val4VALSATweights0.

25、16640.16260.12110.1321sat1sat2sat3sat4SATLOYweights0.15860.08180.16160.0808loy1loy2loy3loy4LOY其中：reflective indicators“weights”Inner ModelPath Coefficients0.57890.20070.27520.84830.10550.00270.67670.12220.58930.4954IMAGEXPEQUALVALSATLOY library(plspm) # typical example of PLS-PM in customer satisfac

26、tion 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

27、,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

28、=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) xA numeric matrix or data frame containing the manifest variables.inner.matA square (lower triangular) boolean matrix indicating the pa

29、th relationships betwenn latent variables.setsList of vectors with column indices from x indicating which manifest variables correspond to the latent variables.modesA character vector indicating the type of measurement for each latent variable. A for reflective measurement or B for formative measure

30、ment (NULL by default).schemeA string of characters indicating the type of inner weighting scheme. Possible values are centroid or factor.scaledA logical value indicating whether scaling data is performed (TRUE by default).boot.valA logical value indicating whether bootstrap validation is performed

31、(FALSE by default).brAn integer indicating the number bootstrap resamples. Used only when boot.val=TRUE.plsrA logical value indicating whether pls regression is applied (FALSE by default).輸出outer.modResults of the outer (measurement) model. Includes: outer weights, standardized loadings, communaliti

32、es, and redundancies.inner.modResults of the inner (structural) model. Includes: path coefficients and R-squared for each endogenous latent variable.latentsMatrix of standardized latent variables (variance=1 calculated divided by N) obtained from centered data (mean=0).scoresMatrix of latent variabl

33、es 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.weightsVector of outer weights.loadingsVector of standardized loadings (i.e. correlations with L

34、Vs.)path.coefsMatrix of path coefficients (this matrix has a similar form as inner.mat).r.sqrVector of R-squared coefficients.An object of class plspm. When the function plspm.fit is called, it returns a list with basic results: 輸出outer.corCorrelations between the latent variables and the manifest v

35、ariables (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 extractedeffectsPath effects of the structural relationsh

36、ips. Includes: direct, indirect, and total effects.unidimResults for checking the unidimensionality of blocks (These results are only meaningful for reflective blocks).gofTable with indexes of Goodness-of-Fit. Includes: absolute GoF, relative GoF, outer model GoF, and inner model GoF.dataData matrix

37、 containing the manifest variables used in the model.bootList 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

38、 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

39、(A,6) # reflective indicators res2 - plspm(satisfaction, sat.mat, sat.sets, sat.mod, scaled=FALSE) summary(res2) plot(res2)res2$unidimres2$outer.modres2$out.weights輸出第1列res2$loadings輸出第2列res2$inner.modres2$path.coefsres2$r.sqrres2$inner.sumres2$gofres2$latents：輸出所有觀測(cè)值的latent值res2$scores：輸出所有觀測(cè)值的late

40、nt scores值 res2$effects#即路徑系數(shù)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

41、.outer, modes=ari.mod, scheme=factor, scaled=TRUE, plsr=TRUE) res1 summary(res1)Inner ModelPath Coefficients 0.7960.0932ENVSOILDIVplot(res1,what=all)ENVweights1.05150.3242env.elevenv.incliENVSOILmatsoil.nitroSOILDIVweights0.38160.68860.0515div.treesdiv.shrubsd

42、iv.herbsDIVENVloadings0.95138e-04env.elevenv.incliENVSOILmatsoil.nitroSOILDIVloadings0.83650.96180.3589div.treesdiv.shrubsdiv.herbsDIV例 # example of PLS-PM in multi-block data analysis # estimate a path model for the wine data set # requires package FactoMine

43、R 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

44、, wine.mods, scheme=centroid) plot(res4, what=all, arr.pos=.4, p=.4, cex.txt=.8) # End(Not run)Inner ModelPath Coefficients0.73450.53640.23260.45070.410.7727SMELLVIEWSHAKETASTESMELLloadings0.71560.91270.84420.41730.0391Odor.Intensity.before.shakingAroma.quality.before.shakingFruity.before.sha

45、kingFlower.before.shakingSpice.before.shakingSMELLVIEWloadings0.98250.98030.9527VensityNuanceSurface.feelingVIEWSHAKEloadings0.57870.84180.78630.23630.21320.5460.44340.9280.9270.8195Odor.IntensityQuality.of.odourFruityFlowerSpicePlantePhenolicAensityAroma.persistencyAroma.qualitySHA

46、KETASTEloadings0.93780.22630.78760.78780.82560.88460.40110.97020.9476AensityAcidityAstringencyAlcoholBalanceSmoothBitternessIntensityHarmonyTASTESMELLweights0.29980.42670.35280.23240.0318Odor.Intensity.before.shakingAroma.quality.before.shakingFruity.before.shakingFlower.before.shakingSpice

47、.before.shakingSMELLVIEWweights0.33360.32370.3726VensityNuanceSurface.feelingVIEWSHAKEweights0.15080.17250.160.03010.07570.10710.08670.20820.21240.1604Odor.IntensityQuality.of.odourFruityFlowerSpicePlantePhenolicAensityAroma.persistencyAroma.qualitySHAKETASTEweights0.15480.0260.1559

48、0.14950.14120.15220.07360.17380.1678AensityAcidityAstringencyAlcoholBalanceSmoothBitternessIntensityHarmonyTASTE# 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

49、) 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=fact

50、or, scaled=FALSE) # permutation test with 100 permutations res.group EXPEIMAG-SATIMAG-LOYEXPE-QUALEXPE-VALEXPE-SATQUAL-VALQUAL-SATVAL-SATSAT-LOYnipals plspm: Non-linear Iterative Partial Least Squares(主成份分析主成份分析)Principal Component Analysis with NIPALS algorithmlibrary(plspm) data(wines) nip1 - nipa

51、ls(wines,-1, nc=5) plot(nip1)-3-2-10123-1012Graphic of components t1,t2Component t1Component t2AlbmAlskArznArknClfrClrdCnncDlwrFlrdGergHawaIdahIllnIndnIowaKnssKntcLosnMainMrylMsscMchgMnnsMsssMssrMntnNbrsNevdNwHmNwJrNwMxNwYrNrtCNrtDOhioOklhOrgnPnnsRhdISthCSthDTnnsTexsUtahVrmnVrgnWshnWstVWscnWymn0.300

52、.350.400.450.500.55-0.8-0.6-0.4-0.20.00.20.4Graphic of loadings p1,p2Loading p1Loading p2MrdrAsslUrbPRape-1.0-0.50.00.51.0-1.0-0.50.00.51.0Circle of CorrelationsComponent t1Component t2MrdrAsslUrbPRape# USArrests data vary nip2 - nipals(USArrests) plot(nip2)plsca plspm: PLS-CA: Partial Least Squares

53、 Canonical Analysis(典型相關(guān)分析典型相關(guān)分析)# example of PLSCA with the vehicles datasetdata(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, ve

54、hicles,13:16) can plot(can)v1v2v3v4v5Screeplot of eigenvaluesvalues01234v1v2v3v4v5Screeplot of eigenvaluesPercentage of explained variance020406080100-1.0-0.50.00.51.0-1.0-0.50.00.51.0Circle of CorrelationsComponent t1Component t2alchmlc.ashalclmgnsphnlflvnnfl.prntcl.nhuedltdprlnv1v2Screeplot of eig

55、envaluesvalues0.00.51.01.52.0v1v2Screeplot of eigenvaluesPercentage of explained variance020406080100-1.0-0.50.00.51.0-1.0-0.50.00.51.0Circle of CorrelationsComponent t1Component t2MrdrAsslUrbPRape-1.0-0.50.00.51.0-1.0-0.50.00.51.0Circle of Correlations (X-components)X-component t1X-component t2dies

56、elturbotwo.doorshatchbackwheel.baselengthwidthheightcurb.weighteng.sizehorsepowerpeak.rpmpricesymbolcity.mpghighway.mpg-1.0-0.50.00.51.0-1.0-0.50.00.51.0Circle of Correlations (Y-components)Y-component u1Y-component u2pricesymbolcity.mpghighway.mpgdieselturbotwo.doorshatchbackwheel.baselengthwidthhe

57、ightcurb.weighteng.sizehorsepowerpeak.rpm-2024-201234Graphic of PLS components t1,t2X-component t1X-component t2alfraudibmwchvrddg1ddg2hnd1hnd2isuzjagrmazdmrcdmrcrmtsbnss1nss2plympegtprscsaabsubrtyt1tyt2tyt3tyt4vlk1vlk2vlv1vlv2vlv3-3-2-10123-2-1012Graphic of PLS components u1,u2Y-component u1Y-component u2alfraudibmwchvrddg1ddg2hnd1hnd2isuzjagrmazdmrcdmrcrmtsbnss1nss2plympegtprscsaabsubrtyt1tyt2tyt3tyt4vlk1vlk2vlv1vlv2vlv3t1t2t3t4Explained variance of X-scores0.00.8u1u2u3u4Explained variance of Y-scores0.00.81.0u1u2u3u4Communality of