路徑模型和PLS教學(xué)提綱

1、路徑(ljng)模型和PLS吳喜之第一頁，共79頁?；诨貧w的傳統(tǒng)(chuntng)方法的假定(e.g., multiple regression analysis, discriminant analysis, logistic regression, analysis of variance)a) 簡單模型結(jié)構(gòu): The postulation of a simple model structure (at least in the case of regression-based approaches); b) 變量(binling)是可觀測的: The assumption that

2、all variables can be considered as observable; c) 所有變量(binling)可精確測量: The conjecture that all variables are measured without error, which may limit their applicability in some research situations.第二頁，共79頁。為克服第一代基于回歸的模型(mxng)的弱點 Structural equation modeling (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

3、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(the exogenous and endogenous latent variables), 前者不被設(shè)定的模型(mxng)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)以及可觀測變量的度量誤差來度量的不可觀測變量第三頁，共79頁。兩種模型(mxng) 基于協(xié)方差基于協(xié)方差(fn ch)(或最大似然或最大似然)的的方法方法: Covariance-based

4、 SEM (軟件工軟件工具具: EQS, AMOS, SEPATH, and COSAN, the LISREL) 基于方差基于方差(fn ch)(成分成分)的方法的方法: Variance-based SEM (Component-based SEM), and to present partial least squares (PLS)第四頁，共79頁。內(nèi)生和外生隱變量(binling)的關(guān)系內(nèi)生隱變量及其指標(biāo)(zhbio)及測量誤差的關(guān)系外生隱變量及其指標(biāo)(zhbio)及測量誤差的關(guān)系第五頁，共79頁。名詞(mng c) (eta) = latent endogenous variabl

5、e; (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

6、 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.第六頁，共79頁。內(nèi)生和外生(wi shn)隱變量的關(guān)系: theoretical equa

7、tions: representing nonobservational hypotheses and theoretical definitions (structural model)內(nèi)生隱變量(binling)及其指標(biāo)及測量誤差的關(guān)系(measurement equations) (measurement model)外生(wi shn)隱變量及其指標(biāo)及測量誤差的關(guān)系(measurement equations) (measurement model)矩陣記號矩陣記號結(jié)構(gòu)模型結(jié)構(gòu)模型度量模型度量模型第七頁，共79頁。三種(sn zhn)不同類型的不可觀測變量a) 原則上不可觀測變量: v

8、ariables that are unobservable in principle (e.g., theoretical terms);b) 原則上不可觀測, 但暗含經(jīng)驗概念或能夠(nnggu)從觀測值導(dǎo)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); c) 用可觀測變量定義的不可觀

9、測變量: unobservable variables that are defined in terms of observables. 第八頁，共79頁。兩類指標(biāo)兩類指標(biāo)(zhbio)變量變量: 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 第九頁，共79頁。二者的區(qū)別(qbi) Reflectiv

10、e 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 imp

11、ly a similar directional change in others (Chin, 1998a).第十頁，共79頁。基于(jy)協(xié)方差(SEM-ML)和基于(jy)方差(SEM-PLS)的兩種建模 基于協(xié)方差方法試圖減少樣本協(xié)方差和理論基于協(xié)方差方法試圖減少樣本協(xié)方差和理論預(yù)測預(yù)測(yc)的協(xié)方差的區(qū)別的協(xié)方差的區(qū)別, 因此參數(shù)估計過因此參數(shù)估計過程試圖重新產(chǎn)生觀測到協(xié)方差矩陣程試圖重新產(chǎn)生觀測到協(xié)方差矩陣(先計算模先計算模型參數(shù)型參數(shù), 然后用回歸得到個體估計值然后用回歸得到個體估計值) 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使得被自變量解釋的因變量方差最大方

12、差最大, 而不是再生經(jīng)驗協(xié)方差矩陣而不是再生經(jīng)驗協(xié)方差矩陣. 除了除了結(jié)構(gòu)模型和測量模型之外結(jié)構(gòu)模型和測量模型之外, PLS有第三部分有第三部分: 用用來估計隱變量的個體值的加權(quán)關(guān)系來估計隱變量的個體值的加權(quán)關(guān)系(weight relations)(先計算個體值先計算個體值不可觀測變量值用不可觀測變量值用他們的指標(biāo)變量的線性組合表示他們的指標(biāo)變量的線性組合表示, 所用權(quán)重使所用權(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再估計不可觀測變量的估計值. 最后確定結(jié)最后確定結(jié)構(gòu)模型的參數(shù)構(gòu)模型的參數(shù).)第十一頁，共79頁。PLS估計

13、(gj)步驟: 兩步確定權(quán)重 (wi): 第一步: 外部近似(類似于主成份(chng fn)分析for reflective, 回歸 for formative indicators ) 第二步: 內(nèi)部近似 (三種方法: centroid, factor, and path weighting scheme)得到(d do)更新的重復(fù)這兩步直到收斂重復(fù)這兩步直到收斂第十二頁，共79頁。PLS 優(yōu)點: 沒有總體假定或度量標(biāo)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)Monte Carlo模擬, PLS非常穩(wěn)健, 而且隱變量的得分總是(zn

14、 sh)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(biāo)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.第十三頁，共79頁。在基于在基于(jy)協(xié)方差和基于協(xié)方差和基于(jy)方差的方差的SEM之間的選之間的選擇擇 在每個隱變量的指標(biāo)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(biāo)變量(有時達(dá)到(d do)500個), 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)重不會對路徑系數(shù)有任何影響, 相合性問題就不是問題了. Therefor

15、e, 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 L

16、Vs is small, much smaller than the number of measured variables and than the number of observations.” (p. 137).第十四頁，共79頁。其它(qt)PLS占優(yōu)勢的情況 Constructs are measured primarily by formative indicators. 那時基于協(xié)方差的方法(LISREL)會有嚴(yán)重的識別困難 LISREL至少要100, 甚至(shnzh)200個觀測值, 但PLS只需50 (甚至(shnzh)在兩個隱變量, 27個顯變量時只有10個觀測值的情

17、況).第十五頁，共79頁。Sohn & 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(biāo)準(zhǔn)，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(dāng)數(shù)據(jù)是正態(tài)或近似正態(tài)時，在ML和PLS之間沒有(mi yu)顯著差別，（2）以因子載荷的偏差為標(biāo)準(zhǔn)，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(biāo)準(zhǔn)，PLS比ML要好。 第十六頁，共79頁。顧客(gk)滿意度模型第十七頁，共79頁。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SCSB感知感知(gnzh)表現(xiàn)表現(xiàn)顧客顧客(gk)預(yù)期質(zhì)量

18、預(yù)期質(zhì)量顧客顧客(gk)滿意度滿意度顧客抱怨顧客抱怨顧客忠誠顧客忠誠五個隱含變量中，顧客預(yù)期質(zhì)量為外生隱變量五個隱含變量中，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)。第十八頁，共79頁。感知質(zhì)量軟件預(yù)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歐洲顧客歐洲顧客(gk)滿意度指滿意度指數(shù)模型數(shù)模型感知感知(gnzh)質(zhì)量軟件質(zhì)量軟件感知質(zhì)量感知質(zhì)量(zhling)硬件硬件感知價值感知價值預(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顧客忠誠第十九頁，

19、共79頁。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度顧客忠誠度感知價值感知價值A(chǔ)CSI美國顧客滿意度指數(shù)(zhsh)模型感知感知(gnzh)質(zhì)量質(zhì)量感知感知(gnzh)價值價值預(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度顧客忠誠度第二十頁，共79頁。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度顧客忠誠度感知價值感知價值A(chǔ)CSI滿足顧客需求程度滿足顧客需求程度整體印象整體印象滿足顧客

20、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)量價格比質(zhì)量價格比未確認(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可能性再購可能性價格承受度價格承受度價格質(zhì)量比價格質(zhì)量比美國顧客(gk)滿意度指數(shù)模型第二十一頁，共79頁。感知質(zhì)量h h2預(yù)期質(zhì)量h h1顧客滿意度h h4顧客忠誠度h h5感知價值h h3品牌形象h h6中國耐用消費品滿意度指數(shù)框圖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(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價格質(zhì)量比x9再

21、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(yù)期質(zhì)量x1自定義預(yù)期質(zhì)量x2服務(wù)預(yù)期x4中國耐用消費品顧客中國耐用消費品顧客(gk)滿意度指數(shù)模型滿意度指數(shù)模型第二十二頁，共79頁。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(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)中國非耐用消費品顧客滿意度指數(shù)(zhsh)模型

22、模型第二十三頁，共79頁。感知質(zhì)量預(yù)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(wù)行業(yè)顧客滿意度指數(shù)框圖中國服務(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(wù)行業(yè)中國服務(wù)行業(yè)(fw hngy)顧客滿意度指數(shù)模型顧客滿意度指數(shù)模型第二十四頁，共79頁。感知質(zhì)量h h2預(yù)期質(zhì)量h h1顧客滿意度h h4顧客忠誠度h h5感知價值h h3品牌形象h h6中國耐用消費品滿意度指數(shù)框圖中國耐用消費品滿意度指數(shù)框圖

23、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x17品牌特征顯著度x18價格質(zhì)量比x9 (Price given quality)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(Quality given price)價格承受度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中國耐用消費品顧客滿意度指數(shù)中國耐用消費品顧客滿意度指數(shù)(zhsh)模型模型第二十五頁，共79頁。這里，包含有這里，包含有b的的B矩陣、矩陣、h及及z是未知是未知的。而的。而B矩陣的形式矩陣的形式(xngsh)完

24、全被圖完全被圖模型所確定。模型所確定。第二十六頁，共79頁。這里，包含有這里，包含有l(wèi)的的L矩陣、矩陣、h是未知的，而是未知的，而x是可觀測的。而是可觀測的。而L矩陣的形式完全矩陣的形式完全(wnqun)被圖模型所確定。被圖模型所確定。第二十七頁，共79頁。偏最小二乘偏最小二乘(PLS)法法解解路徑路徑(ljng)模型模型(Path Model)吳喜之吳喜之( (plspm) )第二十八頁，共79頁。例子(l zi)（先不看數(shù)字）第二十九頁，共79頁。其中(qzhng)：reflective indicators“l(fā)oadings”第三十頁，共79頁。其中(qzhng)：reflective

25、indicators“weights”第三十一頁，共79頁。Inner ModelPath Coefficients0.57890.20070.27520.84830.10550.00270.67670.12220.58930.4954IMAGEXPEQUALVALSATLOY 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,

26、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,

27、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)第三十二頁，共79頁。程序(chngx)plspm(x, inner.mat, sets, modes

28、 = 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 path relationships betwenn latent variables.setsList of vectors with column indic

29、es 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 measurement (NULL by default).schemeA string of characters indicating the type of inne

30、r 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 (FALSE by default).brAn integer indicating the number bootstrap resamples. Used

31、 only when boot.val=TRUE.plsrA logical value indicating whether pls regression is applied (FALSE by default).第三十三頁，共79頁。輸出(shch)outer.modResults of the outer (measurement) model. Includes: outer weights, standardized loadings, communalities, and redundancies.inner.modResults of the inner (structural

32、) 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 variables used to estimate the inner model. If scaled=FALSE then scor

33、es 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 LVs.)path.coefsMatrix of path coefficients (this matrix has a s

34、imilar 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: 第三十四頁，共79頁。輸出(shch)outer.corCorrelations between the latent variables and the manifest variables (also called crossloadings).inner.su

35、m 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 relationships. Includes: direct, indirect, and total ef

36、fects.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 containing the manifest variables used in th

37、e 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: 第三十五頁，共79頁。 # typical example of PLS-PM in customer satisfaction analysis # model with six LVs and reflective indi

38、cators 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 res

39、2 - plspm(satisfaction, sat.mat, sat.sets, sat.mod, scaled=FALSE) summary(res2) plot(res2)第三十六頁，共79頁。第三十七頁，共79頁。res2$unidim第三十八頁，共79頁。res2$outer.modres2$out.weights輸出(shch)第1列res2$loadings輸出(shch)第2列第三十九頁，共79頁。第四十頁，共79頁。res2$inner.modres2$path.coefsres2$r.sqr第四十一頁，共79頁。res2$inner.sumres2$gof第四十二頁，共7

40、9頁。res2$latents：輸出(shch)所有觀測值的latent值res2$scores：輸出(shch)所有觀測值的latent scores值第四十三頁，共79頁。 res2$effects#即路徑(ljng)系數(shù)path.coef第四十四頁，共79頁。第四十五頁，共79頁。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(

41、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)第四十六頁，共79頁。plot(res1,what=all)第四十七頁，共79頁。例 # example of PLS-PM in multi-block data analysis # estimate a path mode

42、l 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 a

43、lgorithm) 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(Not run)第四十八頁，共79頁。第四十九頁，共79頁。第五十頁，共79頁。第五十一頁，共79頁。# Not run: # example with customer satisfaction analysis # group comparison based on the segmentation v

44、ariable 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 ind

45、icators 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-

46、PM第五十二頁，共79頁。第五十三頁，共79頁。第五十四頁，共79頁。nipals plspm: Non-linear Iterative Partial Least Squares(主成份主成份(chng fn)分析分析)Principal Component Analysis with NIPALS algorithmlibrary(plspm) data(wines) nip1 - nipals(wines,-1, nc=5) plot(nip1)第五十五頁，共79頁。# USArrests data vary nip2 - nipals(USArrests) plot(nip2)第五十

47、六頁，共79頁。plsca plspm: PLS-CA: Partial Least Squares Canonical Analysis(典型相關(guān)典型相關(guān)(xinggun)分分析析)# 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 s

48、ymbol city.mpg 16 highway.mpg can - plsca(vehicles,1:12, vehicles,13:16) can plot(can)第五十七頁，共79頁。第五十八頁，共79頁。-1.0-0.50.00.51.0-1.0-0.50.00.51.0Circle of CorrelationsComponent t1Component t2MrdrAsslUrbPRape第五十九頁，共79頁。第六十頁，共79頁。semPLS第六十一頁，共79頁。library(semPLS)#下面(xi mian)是如何構(gòu)建一個模型(以ECSI為例)# getting the path to the .csv file representing the inner Modelptf_Struc - system.file(ECSIstrucmod.csv, package=semPLS)# getting the pa