STRUCTURAL EQUATIONS

MODELING (SEM)Wei-Jiun, Shen Ph. D.

Measurement model

Confirmatory factor analysis (CFA)

x1

x3

x2

δ1

δ 2

δ 3

ξ1

λ11

λ21

λ31

δ[delta] ; λ[lambda]; ξ[xi]

x1= λ11 ξ1+ δ1

x2= λ21 ξ1+ δ2

x3= λ31 ξ1+ δ3

After CFA…

The goal of SEM is to analyze a set of relationships between one or more IVs, either continuous or discrete, and one or more DVs, either continuous or discrete.

Model examination Observed variable only Latent variable

Graphical representation for SEM

x1

x2

x3

ξ belief η behavior

y1

y2

y3

δ １ ε １λx1

γ

ζ

ε ２

ε ３

δ ２

δ ３

Error

Exogenous observed variable

Factor loading

Exogenous latent variable

Structural parameter

Endogenous latent variable

Factor loading

Endogenous observed variable

Structural model

measurement model

Error

λx2

λx3

λy1

λy2

λy3

measurement model

Model examination

Fit index Absolute fit index Comparative fit index Parsimonious fit index Residual

Coefficients Loading Error Correlation/Regression coefficient

PRACTICE

個人表現與團隊表現 史蒂分 咖哩∙ 的助攻及得分與好鬥者隊的團隊表

現是否有關？ 。

個人表現與團隊表現 以路徑分析檢驗助攻、得分對團隊表現的預測情

形。分析結果顯示助攻能顯著正向預測團隊表現(β= .44, p < .001) ，得分則不會影響團隊表現(β= .01, p = .777)。

MEDIATION EXAMINATIONAPPLYING BOOTSTRAPPING

Mediation

SEM Observed variables

X Y

M

βa βb

βc

Mediation

SEM Observed and latent variables

X Y

Mβa βb

βc

Mediation examination

B-K Regression coefficients

Visual examine? Sobel test

Test the difference between change of coefficient

Biased SE? Bootstrap

More accurate estimation

Bootstrap

Resampling technique

Applied to mediation model SE Confidence interval

Confidence interval

Interval estimation

𝑐𝑜𝑛𝑓𝑖𝑑𝑒𝑛𝑐𝑒𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 (𝐶𝐼 )=𝑀 𝑥± 𝑡∗×𝑆𝐸𝑥

95%

Why bootstrap provides more accurate SE?

Standard error The standard deviation of the sampling

distribution of a statistic

𝑆𝐸𝑥=𝑠√𝑛

Representative sample

PRACTICE