行为科学研究方法Lesson 6-Research Methods

Research methods inbehavioral scienceLesson 6: Structural Equation Modeling (SEM)

Structural Equation Modeling What is SEM CFA How are estimations obtained Goodness of fit Model identification Testing nested model

Structural ModelPerson-Job Fit Job Stress Turnover Intention

Person-Org. Fit

Structural Model - Correlation

Job Stress

Turnover Intention

rxy=.36

Structural Model - RegressionP-J Fit

P-O Fit

Job Stress

Tenure

Multivariate RegressionP-J FitJob Stress P-O Fit Org. Commitment

Tenure

Path AnalysisPerson-Job Fit Job Stress Turnover Intention

Person-Org. Fit

SEMε1ε2δ1δ2

x1 x2 x3 x4

λ11λ 21λ 32

ξ1

y1γ11λ 51

y2λ 61

δ2β21

η1

η2

λ 72λ 82

y3 y4

ε3ε4

δ3

ξ2

γ21

δ1

δ4

λ 42

Complexity of AnalysisX 1 N N N N N Y 1 1 N N N N Measurement No No No Yes No Yes Relationship No No No No Yes Yes Technique Correlation Regression Multivariate Regression CFA Path analysis SEM

CFA- Two Measurement Models Classical Measurement Model

x1=ξ1+ε1 x2=ξ1+ε2 Measurement Model Used in SEM

ξ1λ11λ 21

x1

x2

x1=λ 1 1ξ1+ε1 x2=λ 2 1ξ1+ε2

ε1

ε2

EFA vs. CFAFactors

F1

F2X1 X2

F1 .84 .79

F2 -.06 .12

X3

.20.15

.73.68

x1

x2

x3

x4

X4

ε

ε

ε

ε

CFA vs.EFAFactors

F1

F2

Var X1 X2

F1 .60 .75

F2 0 0

X3

00

.68.66

x1

x2

x3

x4

X4

ε

ε

ε

ε

CFAξ1λ11λ 21λ 32

ξ2λ 42

x1

x2

x3

x4

x1=λ 11ξ1+ε1 x2=λ 21ξ1+ε2 x3=λ 32ξ2+ε3 x4=λ 42ξ2+ε4

ε1

ε2

ε3

ε4

CFA– Cross Loadingx1=λ 11ξ1+ε1 x2=λ 21ξ1+ε2 x3=λ 32ξ2+λ 21ξ1+ε3 x4=λ 42ξ2+ε4

X

ξ1λ11λ 21

ξ2

X

λ 32

λ 42

x1

x2

x3

x4

ε1

ε2

ε3

ε4

CFA– Error Correlationφ12ξ1λ11λ 21λ 32

ξ2λ 42

x1

x2

x3

x4

ε1

ε2

ε3

ε4

X

X

CFA– Error Correlationφ12ξ1λ11λ 21λ 32

ξ2λ 42

x1

x2

x3

x4

ε1

ε2

ε3

ε4

X

X

How Are Estimations Obtained? Comparison of observation and theoretical model.Procedure: 1. Come up with estimates of the parameters of interest 2. Try to reproduce the observed data using our estimates 3. If we can perfectly reproduce the observation using our estimates, we have an estimated model with 100% fit. The parameters are assumed to be highly believable

Goodness of Fit Index The goodness of fit of a statistical model describes how well it fits a set of observations. Goodness of Fit index: F=min( E= - E)

Goodness-of-fit Statistics

Degree of Freedom& Identification A= Number of variance–covariance terms B= Number of parameters to be estimated Degree of Freedom= A- B

Nested Model Two models are nested within each other if they are exactly the same except that some parameters in one model are fixed. The model with parameters fixed is said to be nested within the model without parameters fixed.

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