侯杰泰结构方程模型-课件

侯杰泰结构方程模型Kit-TaiHau

EducationalPsychologyDept,TheChineseUniversityofHongKong1侯杰泰结构方程模型1侯杰泰结构方程模型I简介IIntroduction

2侯杰泰结构方程模型I简介2精品资料3精品资料3你怎么称呼老师？如果老师最后没有总结一节课的重点的难点，你是否会认为老师的教学方法需要改进？你所经历的课堂，是讲座式还是讨论式？教师的教鞭“不怕太阳晒，也不怕那风雨狂，只怕先生骂我笨，没有学问无颜见爹娘……”“太阳当空照，花儿对我笑，小鸟说早早早……”44100个推理测验分数

21,31,32,05,06,09,10,22,29,18,11,01,39,92,23,27,93,97,30,02,96,40,53,78,04,98,36,07,08,24,54,55,77,99,34,03,86,87,59,60,15,62,63,43,52,28,79,58,65,95,81,85,57,14,17,33,16,19,20,37,25,69,84,61,64,68,70,42,45,72,83,89,44,38,47,71,00,73,12,35,82,56,75,41,46,49,50,94,66,67,76,51,88,90,74,13,26,80,48,91均值Mean=53，标准差SD(StdDev)=15

5100个推理测验分数5侯杰泰结构方程模型6侯杰泰结构方程模型677再生/隐含矩阵

(reproduced/impliedmatrix)

8再生/隐含矩阵(reproduced/impliedm991010检查模型的准确性(accuracy)和简洁性(parsimony)

拟合优度指数（goodnessoffitindex），简称为拟合指数(fitindex):

、NNFI、CFI

df=[不重复元素non-duplicatingelements,

p(p+1)/2]–[估计参数estimatedparameters]

在前面例子

df=9x10/2–21=2411检查模型的准确性(accuracy)和简洁性(parsimo依据及指定模型找出与相距最小的

侯杰泰结构方程模型输出

Output输入InputSEM程式program(e.g.,LISREL)

、各路径参数（因子负荷loading、因子相关系数factorcorrelations等）各种拟合指数12依据及指定模型侯杰泰结构方程模型输出输入SEM程式侯杰泰结构方程模型I简介IIntroduction

13侯杰泰结构方程模型I简介13侯杰泰结构方程模型14侯杰泰结构方程模型141515161617171818191920202121222223232424_________________________________________________________________________________________________(no.ofestimatedparameters)模型df

NNFICFI需要估计的参数个数

______________________________________________________________________________________________

M12440.973.982 21=9Load+

9Uniq+

3Corr

M227 503.294.47118=9Load+

9Uniq

M326 255.647.74519=9Load+9Uniq+

1Corr

M426 249.656.752 19=9Load+

9Uniq+

1CorrM527 263.649 .727 18=9Load+

9Uniq

M624 422.337.558 21=9Load+

9Uniq+

3CorrM7 21 113 .826 .89824=9Load+

9Uniq+

6Corr

______________________________________________________________________________________________25______________________________侯杰泰结构方程模型自由度(df),拟合程度

(fit),不能保证最好，可能存在更简洁(parsimonious)又拟合(fit)得很好的模型

输入Input:相关（或协方差）矩阵correlation/covariancematrix一个或多个有理据的可能模型

(alternativemodels)输出Output:既符合某指定模型，又与差异最小的矩阵估计各路径参数parameter（因子负荷loading、因子相关系数factorcorrelations等）。计算出各种拟合指数(goodnessoffitindexes)26侯杰泰结构方程模型自由度(df),拟合程度(fit),依据及指定模型找出与相距最小的

侯杰泰结构方程模型输出

Output输入InputSEM程式program(e.g.,LISREL)

、各路径参数（因子负荷loading、因子相关系数factorcorrelations等）各种拟合指数27依据及指定模型侯杰泰结构方程模型输出输入SEM程式结构方程模型的重要性

StructuralEquationModel，SEMCovarianceStructureModeling，CSM

LInearStructuralRELationship，

LISREL(EQS,AMOS,Mplus,etc.)28结构方程模型的重要性28侯杰泰结构方程模型测量模型

(measurementmodel)

,,

——外源指标exogenous（如6项社经指标）

—内生指标endogenous（如语、数、英成绩）—因子负荷矩阵

(loading)—误差项

(uniqueness,measurementerrors)

结构模型

(structuralmodel)29侯杰泰结构方程模型测量模型(measurementmod侯杰泰结构方程模型同时处理多个因变量(manydependentvariables)

同时估计因子结构factorstructure和因子关系30侯杰泰结构方程模型同时处理多个因变量(manydepend容许自变量independentvariable和因变量dependentvariable含测量误差measurementerror[传统方法（如回归regression）假设自变量independentvariable没有误差

]_______________________________________

英文

中文_

观察真误差观察

真误差

得分分数得分

分数observedtrueerrorobservedtrueerrorscorescorescorescore

X

TxeY

Tye_

8

7+15

3+2

5

6-16

7-17

5+29

7+2

9

8+15

8-3......X=Tx+e Y=Ty+eifr(X,Y)=0.5r(Tx,Ty)=0.5/[(rXt-t)(rYt-t)]1/2=0.71(assumert-t=0.7)31容许自变量independentvariable和因变量d容许更大弹性的测量模型估计整个模型的拟合程度modelfit[用以比较不同模型]SEM包括:回归分析regression、因子分析(验证性因子分析CFA、探索性因子分析EFA)、ｔ检验t-test、方差分析ANOVA、比较各组因子均值groupmeancomparison、交互作用模型interaction、实验设计exptdesign

32容许更大弹性的测量模型32侯杰泰结构方程模型I简介IIntroduction

33侯杰泰结构方程模型I简介33侯杰泰结构方程模型Intheaboveanalyses,wehaveastructureinmindtotest,thisprocessiscalledconfirmatoryfactoranalysis(CFA)Itisalsopossiblethatwehaveno“theory”inmindtotest,i.e.,wehavethefollowingresearchquestions:Howmanyclusterofsubjectsarethere?Howdothese9subjectsrelatetoeachoftheseclusters(factors)?Whichofthesesubjectsaremorecloselyrelated/correlatedthanothers?34侯杰泰结构方程模型IntheaboveanalysesUsingLISREL,runthefollowingprogramDANI=9NO=100KM1.000.121.000.080.081.000.500.110.081.000.480.030.120.451.000.070.460.150.080.111.000.050.440.150.120.120.441.000.140.170.530.140.080.100.061.000.160.050.430.100.060.080.100.541.00PCNC=6OU35UsingLISREL,runthefollowinTheoutput:PrincipalComponentsAnalysisEigenvaluesandEigenvectors

PC_1PC_2PC_3PC_4PC_5PC_6

------------------------------------------Eigenvalue2.561.661.630.690.590.56%Variance28.4218.4918.157.656.506.18Cum%Var28.4246.9165.0672.7179.2185.3936Theoutput:36侯杰泰结构方程模型37侯杰泰结构方程模型37Assume3factors,werunthefollowingprogramandobtainfurtherinformationDANI=9NO=100KM1.000.121.000.080.081.000.500.110.081.000.480.030.120.451.000.070.460.150.080.111.000.050.440.150.120.120.441.000.140.170.530.140.080.100.061.00.160.050.430.100.060.080.100.541.0FANF=3OU38Assume3factors,werunthefTheOutput:Varimax-RotatedFactorLoadings

Factor1Factor2Factor3UniqueVar----------------------------------VAR10.100.730.040.46

VAR20.090.060.660.55

VAR30.630.050.120.58

VAR40.080.670.080.53

VAR50.040.650.070.57

VAR60.070.050.680.54

VAR70.050.070.650.57

VAR80.820.080.070.32VAR90.650.090.040.56factorsareassumedtobeuncorrelated正交39TheOutput:factorsareassumed

Promax-RotatedFactorLoadings

Factor1Factor2Factor3UniqueVar----------------------------------

VAR10.73-0.030.030.46

VAR20.000.660.020.55

VAR3-0.020.060.640.58

VAR40.680.020.010.53

VAR50.660.01-0.030.57

VAR6-0.010.680.000.54

VAR70.010.66-0.020.57

VAR80.00-0.010.830.32VAR90.03-0.030.660.56

FactorCorrelations

Factor1Factor2Factor3------------------------

Factor11.00Factor20.191.00

Factor30.210.221.00Factorsallowedtobecorrelated斜交40Promax-RotatedFactorLoadingEFA(exploratoryFA)CFA(confirmatoryFA)NospecificideaonhowvariablearerelatedHavesomeguess(hypotheses)onrelationsamongvariables(e.g.,Variables1,4,5shouldloadonFactor3)determinenumberoffactorsusingEigenvalue(EV≧1orscreetest)knowbeforehandthenumberoffactorseachitemloadedonALLfactors,thoughsomeloadingsaresmallItemsloadedontargetedfactorsonly41EFA(exploratoryFA)CFA(conf侯杰泰结构方程模型17个题目:

学习态度及取向

A、B、C、D、E

4、4、3、3、3题

350个学生

ConfirmatoryFactorAnalysis,CFA

42侯杰泰结构方程模型17个题目:

学习态度及取向

A、B、C4343ConfirmatoryFactorAnalysisExample1DANI=17NO=350MA=KMKMSY1.341…MONX=17NK=5LX=FU,FIPH=STTD=DI,FRPALX4(10000)4(01000)3(00100)3(00010)3(00001)OUMISSSC44ConfirmatoryFactorAnalysisE侯杰泰结构方程模型

12

34runningLISREL45侯杰泰结构方程模型

12

3侯杰泰结构方程模型46侯杰泰结构方程模型46什么情况下固定(fixed,FI)？两个变量（指标或因子）间没有关系，将元素固定为0例如，不从属，将因子负荷(LX1,2)固定为0。又如，因子和因子没有相关，PH1,2固定为0。需要设定因子的度量单位(setmetric/scale)因子没有单位(metric)，无法计算。一种将所有因子的方差固定为1(或其他常数)，简称为固定方差法(fixedvariancemethod)一种是在每个因子中选择一个负荷固定为1(或其他常数)，简称为固定负荷法(fixedloading)什么情况下设定为自由(free,FR):所有需要估计的参数47什么情况下固定(fixed,FI)？474848补充例子9个题目:第1个因子:

第1、2、3题第2个因子:

第4、5、6题第3个因子:

第7、8、9题设因子1,2,3互有相关

因子1因子2因子3第1题,x1FRFIFI第2题,x2FRFIFI第3题,x3FRFIFI第4题,x4FIFRFI第5题,x5FIFRFI第6题,x6FIFRFI第7题,x7FIFIFR第8题,x8FIFIFR第9题,x9FIFIFR固定方差法(fixedvariance)49补充例子因子1因子2因子3第1题,x1FRFIFI第2题,固定方差法

(fixedvariance)MOLX=9NK=3LX=FU,FIPH=STTD=DI,FRFRLX1,1LX2,1LX3,1LX4,2LX5,2FRLX6,2LX7,3LX8,3LX9,3固定负荷法(fixedloading)MOLX=9NK=3LX=FU,FIPH=SY,FRTD=DI,FRFRLX2,1LX3,1LX5,2LX6,2LX8,3LX9,3VA1LX1,1LX4,2LX7,350固定方差法(fixedvariance)50设因子1和因子3无关(uncorrelated)，因子1和因子2、因子2和因子3相关(correlated)固定方差法(fixedvariance)MOLX=9NK=3LX=FU,FIPH=STTD=DI,FRFRLX1,1LX2,1LX3,1LX4,2LX5,2FRLX6,2LX7,3LX8,3LX9,3FIPH1,3固定负荷法(fixedloading)MOLX=9NK=3LX=FU,FIPH=SY,FRTD=DI,FRFRLX2,1LX3,1LX5,2LX6,2LX8,3LX9,3VA1LX1,1LX4,2LX7,3FIPH1,351设因子1和因子3无关(uncorrelated)，因子1和因NumberofInputVariables17(读入变量个数)NumberofY-Variables0(Y-变量个数)NumberofX-Variables17(X-变量个数)NumberofETA-Variables0(Y-因子个数)NumberofKSI-Variables5(X-因子个数)NumberofObservations350(样品个数)52NumberofInputVariables17(ParameterSpecifications参数设定

LAMBDA-X

KSI1KSI2KSI3KSI4KSI5----------------------------------------VAR110000VAR220000VAR330000VAR440000VAR505000VAR606000VAR707000VAR808000VAR900900VAR10001000VAR11001100VAR12000120VAR13000130VAR14000140VAR15000015VAR16000016VAR1700001753ParameterSpecifications参数设定5

PHI

KSI1KSI2KSI3KSI4KSI5----------------------------------------KSI10KSI2180KSI319200KSI42122230KSI5242526270THETA-DELTA

VAR1VAR2VAR3VAR4VAR5VAR6VAR7VAR8VAR9VAR1028293031323334353637VAR11VAR12VAR13VAR14VAR15VAR16VAR17

3839404142434454PHI54

NumberofIterations=19

LISRELEstimates(MaximumLikelihood)参数估计

LAMBDA-X

KSI1KSI2KSI3KSI4KSI5

----------------------------------------

VAR10.59--------(0.06)9.49

VAR20.58--------(0.06)9.30

VAR30.62--------(0.06)9.93

VAR40.05--------(0.07)0.81参数(parameter)StandardError,SEt-value=参数

/SE0.59/0.06=9.4955NumberofIterations=19参数(

VAR5--0.64------(0.06)10.46VAR6--0.57------(0.06)9.32VAR7--0.51------(0.06)8.29VAR8--0.28------(0.06)4.41VAR9----0.59----(0.06)9.5656VAR5--0.64

VAR10----0.61----(0.06)9.99VAR11----0.64----(0.06)10.47VAR12------0.62--(0.06)10.28VAR13------0.66--(0.06)10.84VAR14------0.54--(0.06)8.96VAR15--------0.65(0.06)11.14VAR16--------0.72(0.06)12.19VAR17--------0.55(0.06)9.3657VAR10----

PHI

KSI1KSI2KSI3KSI4KSI5----------------------------------------KSI11.00

KSI20.521.00(0.07)7.06

KSI30.400.531.00(0.08)(0.07)5.217.24

KSI40.510.540.481.00(0.07)(0.07)(0.07)6.977.476.60

KSI50.420.500.440.501.00(0.07)(0.07)(0.07)(0.07)5.776.996.227.17

58PHI58

THETA-DELTA

VAR1VAR2VAR3VAR4VAR5VAR6------------------------------------0.650.660.611.000.590.67(0.07)(0.07)(0.07)(0.08)(0.07)(0.07)9.639.859.0213.198.8210.21

VAR7VAR8VAR9VAR10VAR11VAR12------------------------------------0.740.920.660.630.590.61(0.07)(0.07)(0.07)(0.07)(0.07)(0.06)11.0512.709.969.468.809.46

VAR13VAR14VAR15VAR16VAR17------------------------------0.570.700.570.480.69(0.07)(0.07)(0.06)(0.06)(0.06)8.7010.759.137.4910.9159THETA-DELTA59GoodnessofFitStatistics拟合优度统计量DegreesofFreedom=109MinimumFitFunctionChi-Square=194.57(P=0.00)NormalTheoryWeightLeastSqChi-Sq=190.15(P=0.00)EstimatedNon-centralityParameter(NCP)=81.1590PercentConfidenceIntervalforNCP=(46.71;123.45)MinimumFitFunctionValue=

0.56PopulationDiscrepancyFunctionValue(F0)=0.2390PercentConfidenceIntervalforF0=(0.13;0.35)RootMeanSquareErrorofApproximation(RMSEA)=0.04690PercentConfidenceIntervalforRMSEA=(0.035;0.057)P-ValueforTestofCloseFit(RMSEA<0.05)=0.71ExpectedCross-ValidationIndex(ECVI)=0.8090PercentConfidenceIntervalforECVI=(0.70;0.92)ECVIforSaturatedModel=0.88ECVIforIndependenceModel=5.78Chi–df=190.15-1090.56x(N-1)=chi0.56x349=194.5760GoodnessofFitStatisticsChiChi-SquareforIndependenceModelwith136df=1982.04IndependenceAIC=2016.04ModelAIC=278.15SaturatedAIC=306.00IndependenceCAIC=2098.63ModelCAIC=491.90SaturatedCAIC=1049.26NormedFitIndex(NFI)=0.90

Non-NormedFitIndex(NNFI)=0.94ParsimonyNormedFitIndex(PNFI)=0.72

ComparativeFitIndex(CFI)=0.95IncrementalFitIndex(IFI)=0.95RelativeFitIndex(RFI)=0.88CriticalN(CN)=263.34RootMeanSquareResidual(RMR)=0.054

StandardizedRMR=0.054GoodnessofFitIndex(GFI)=0.94AdjustedGoodnessofFitIndex(AGFI)=0.92ParsimonyGoodnessofFitIndex(PGFI)=0.67NNFI=TLICFI=RNIOldestLISRELindexes:RMR,SRMR,GFI,AGFI61Chi-SquareforIndependenceMoModificationIndicesforLAMBDA-X修正指数

KSI1KSI2KSI3KSI4KSI5----------------------------------------VAR1--0.060.660.092.53VAR2--0.380.530.230.11VAR3--0.720.010.031.49VAR4--0.000.030.010.03VAR57.73--9.629.231.50VAR60.01--3.291.071.50VAR70.12--0.250.122.26VAR841.35--3.6622.024.78VAR90.400.02--2.190.22VAR100.030.10--0.300.22…MaximumModificationIndexis41.35forElement(8,1)LX修正指数:该参数由固定改为自由估计，会减少的数值62ModificationIndicesforLAMBDCompletelyStandardizedSolution

LAMBDA-XKSI1KSI2KSI3KSI4KSI5----------------------------------------VAR10.59--------VAR20.58--------VAR30.62--------VAR40.05--------VAR5--0.64------VAR6--0.57------VAR7--0.51------VAR8--0.28------VAR9----0.59----VAR10----0.61----VAR11----0.64----VAR12------0.62--VAR13------0.66--VAR14------0.54--VAR15--------0.65VAR16--------0.72VAR17--------0.5563CompletelyStandardizedSoluti

PHI

KSI1KSI2KSI3KSI4KSI5----------------------------------------KSI11.00KSI20.521.00KSI30.400.531.00KSI40.510.540.481.00KSI50.420.500.440.501.00THETA-DELTA

VAR1VAR2VAR3VAR4VAR5VAR6------------------------------------------------0.650.660.611.000.590.67VAR7VAR8VAR9VAR10VAR11VAR12------------------------------------------------0.740.920.660.630.590.61

VAR13VAR14VAR15VAR16VAR17----------------------------------------0.570.700.570.480.6964PHI6565侯杰泰结构方程模型Q4在A的负荷loading很小

(LX=0.05)，但在其他因子的修正指数（MI,modificationindex）也不高不从属Ａ，也不归属其他因子Q8在B的负荷不高（0.28），但在A的MI是41.4，可能归属A因子间相关很高(0.40至0.54)模型拟合fit相当好：(109)=194.57，RMSEA＝0.046,NNFI=.94.CFI=.95。仔细检查题目内容后，删去Q4,Q8归入A66侯杰泰结构方程模型Q4在A的负荷loading很小(LX侯杰泰结构方程模型DANI=17NO=350KMSY….（此处输入相关矩阵)

SE;123567891011121314151617/MONX=16NK=5PH=STTD=DI,FRPALX3(10000)3(01000)1(10000)3(00100)3(00010)3(00001)OUMISSSCSE1234567891011121314151617/(note:2lineswithout“;”)67侯杰泰结构方程模型DANI=17NO=350SE67Q8归属A，因子负荷很高（.49），

(94)=149.51，RMSEA＝.040，NNFI＝.96，CFI=.97。虽然没有嵌套关系，模型比好Q8同时从属A和B?

68Q8归属A，因子负荷很高（.49），68DANI=17NO=350KMSY…SE;123567891011121314151617/MONX=16NK=5PH=STTD=DI,FRPALX3(10000)3(01000)1(11000)3(00100)3(00010)3(00001)OUMISSSC69DANI=17NO=35069侯杰泰结构方程模型(93)=148.61,RMSEA＝.040,NNFI=.96,CFI=.97。Q8在A负荷为.54，在B负荷为-.08因为概念上Q8应与B成正相关，故不合理。而且这负荷相对低，所以我们选择通常，每题只归属一个因子70侯杰泰结构方程模型(93)=148.61,RMSE修正modification前后模型的拟合指数比较______________________________________模型

df RMSEANNFICFI註______________________________________M-A 109 195.046.94.95原模型M-B 94150.040 .96.97删Q4,Q8-AM-C 93149.040 .96.97删Q4,Q8-A,BMB-299152 .038 .94.952阶因子______________________________________71修正modification前后模型的拟合指数比较71侯杰泰结构方程模型内容

矩阵大小固定负荷法fixedloading固定方差法fixedvarianceLX因子与观察变量(指标)的从属关系(因子负荷)NXxNK000VA1LX11100VA1LX42100VA1LX73000010010000001001100100100010010010001001001PH因子与因子间的相关(协方差)NKxNK111或100111010111001因子间因子间有关无关011或

000101000110000VA1PH11PH22VA1PH33TD指标误差间的关系(协方差)NXxNX100000000010000000001000000000100000000010000……100000000010000000001000000000100000000010000……72侯杰泰结构方程模型内容矩阵大小固定负荷法固定方差法LX因子验证性因子分析(CFA)LX,PH,TD的设定方法A.用固定方差法LX(LAMBDA-X,因子负荷)

KSI1KSI2KSI3KSI4KSI5----------------------------------------VAR110000VAR210000VAR310000VAR410000VAR501000VAR601000VAR701000VAR801000VAR900100VAR1000100VAR1100100VAR1200010VAR1300010VAR1400010VAR1500001VAR1600001VAR170000173验证性因子分析(CFA)LX,PH,TD的设定方法73用PA指令PALX1000010000100001000001000010000100001000001000010000100000100001000010000010000100001亦可简化为PALX4(10000)4(01000)3(00100)3(00010)3(00001)或

FRLX11LX21LX31FRLX41LX52LX62FRLX72LX82LX93FRLX103LX113FRLX124LX134FRLX144LX155FRLX165LX175对应的PH设定:(假设所有因子互有相关):PAPA0111110111110111110111110VA1PH11PH22VA1PH33PH44VA1PH5574用PA指令亦可简化为对应的PH设定:(假设所有因子互有相B.用固定方差法

PALX000001000010000100001000000000010000100001000001000010000100000100001000010000010000100001可用下述指令描述PALX4(10000)4