香港中文大学 基于lisrel的SEM讲义 Note1
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自变因子方差/协方差矩阵 自变因子方差 协方差矩阵
φ 11 Φ= φ21 φ22
23
Matrices of the Y-Model
y = Λyη +ε
y λ 0 ε1 1 11 y λ 0 η ε 1 + 2 2 = 21 y 0 λ 2 ε3 η 3 32 ε 42 y4 0 λ 4
1
Classical True Score Model
• X=T+E
▪ X = Observed score ▪ T = True Score ▪ E = Measurement Error
2
Properties of True and Error Scores
• Mean of the error scores for a population is zero ( µE = 0 ) • Correlation (相关系数) between true and error scores for a population is zero ( ρ E =.00) T • Correlation between error scores is zero ( ρE1E2 = 0 )
24
y Λy η ε
observed indicators ofη factor loadings relating y toη latent endogenous variables (内 生变值) measurement errors for y
25
Matrices of the Structural Model
Structural Equation Modeling
结构方程模型
张伟雄博士 香港中文大学工商管理学院副院长 管理学系教授
Gordon W. Cheung, Ph.D Professor, Department of Management Associate Dean, Faculty of Business Administration The Chinese University of Hong Kong
^ Σk
Fitted Covariance Matrix
15
Implied Covariance Matrix
隐含Байду номын сангаас方差矩阵
(I −Β) (ΓΦ ′ +Ψ)(I −Β) Γ Σ(θ) = 1 −′ Φ ′(I −Β) Γ
−1 ′ −1
(I −Β)
where
Φ= covariance matrix of x
11
LISREL is Greek to Me!
Hayduk (1987). Structural Equation Modeling with LISREL. pp.88. Johns Hopkins. 12
Uppercase
Lowercase Name
Uppercase
Lowercase Name
9
Operationalization Choices
• Variations between the Extremes • Range of Variation • Levels of Measurement
– Nominal Measures (定类 定类) 定类 – Ordinal Measures (定序 定序) 定序 – Interval Measures (定距 定距) 定距 – Ratio Measures (定比 定比) 定比
5
Babbie (1992). The Practice of Social Research. Pp. 121. Wadsworth Publishing
6
Babbie (1992). The Practice of Social Research. Pp. 121. Wadsworth Publishing
14
What is SEM
Approximating Models Operating model (form unknown)
?
Specification + parsimony error
etc.
k-1
specifies relationships among...
Population data
• Measurement Model (测量模型) • Path Model (结构模型) • Full Model (全模型) • Model with Mean Structures (均值结构模型)
17
Measurement Model
测量模型
φ12
ξ1
ξ2
λ11 X1 δ1
λ21 X2 δ2
ΓΦ Φ
−1
For Measurement Model
Σ(θ) = ΛxΦ ′ +Θ Λx δ
Bollen (1989). Structural Equations with Latent Variables. Pp. 86 & 236. Wiley. 16
Basic SEM Models
k
Specification + parsimony error
k+1
Sampling Error
POPULATION SAMPLE
etc.
Sample data matrix
Y
S
Sample Covariance Matrix
∆est
Estimated Discrepancy
(Operationalized as a GFI)
Α Β Γ ∆ Ε Ζ Η Θ Ι Κ Λ Μ
α β γ δ ε ζ η θ ι κ λ μ
alpha beta gamma delta epsilon zeta eta theta iota kappa lambda mu
Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω
ν ξ ο π ρ σ τ υ φ χ ψ ω
21
x Λx ξ δ
observed indicators of ξ factor loadings relating x to ξ latent exogenous variables (外 源变值) measurement errors for x
22
Variance/Covariances among the exogenous variables
27
Residuals in the prediction of the endogenous variables
η = Β +Γ +ζ η ξ
η 0 0η γ11 γ 21ξ1 ζ1 1 1 = β 0 + 0 0 ξ +ζ η η 2 2 2 21 2
26
Β Γ ζ
coefficients relatingηtoη coefficients relatingξtoη residuals in equations
3
Construct (Latent Variable) 潜变量
• Concept that the researcher can define in conceptual terms but normally cannot be directly measured or measured without error • Approximately measured by indicators (指 标)
Hair, et al (1995). Multivariate Data Analysis with Readings. Pp. 618 Prentice Hall.
4
Babbie (1992). The Practice of Social Research. Pp. 121. Wadsworth Publishing
• Single or Multiple Indicators (单一指标或多 项指标)
10
Dimension
• A specifiable aspect or facet of a concept • For example: Job Satisfaction
– Satisfaction with supervisor – Satisfaction with co-workers – Satisfaction with environment – Satisfaction with pay – Satisfaction with job content
## #### # ## #### # ## #### # ## #### # ## #### #
Σo
Population Covariance Matrix
∆pop
Population Discrepancy
Σk
Approximate Covariance Matrix
Specification + parsimony error
7
Babbie (1992). The Practice of Social Research. Pp. 121. Wadsworth Publishing
8
Criteria for Measurement Quality
• Reliability (信度 refers to the likelihood that a 信度) 信度 given measurement procedure will yield the same description of a given phenomenon • Validity (效度 refers to the extent to which a 效度) 效度 specific measurement provides data that relate to commonly accepted meanings of a particular concept. Face validity, criterion-related (predictive) validity, content validity, and construct validity
λ31 X3 δ3
λ41 X4 δ4
λ52 X5 δ5
λ62 X6 δ6
λ72 X7 δ7
λ82 X8 δ8
18
Path Model
结构模型
X1
γ11 γ12
ζ1
β31
Y1
γ32
Y3
ζ3
X2
β21
β32
Y2
γ13
X3
γ 23
ζ2
19
Full Model
全模型
δ1 X1 δ2 X2 λ11 λ21 δ3 X3 λ31 δ4 X4 λ41 γ11 γ21 ε1 y1 ε2 y2 λ11 λ21 ε3 y3 λ31 λ41 ε4 y4
nu xi omicron pi rho sigma tau upsilon phi chi psi omega
Hayduk (1987). Structural Equation Modeling with LISREL. pp.89. Johns Hopkins. 13
What is SEM
• Simultaneous regression equations (回归方程) • Modeling latent variables (潜变量 / 因子) from observed variables (指标 / 题目) • Estimate parameters (参数) of the measurement model (测量模型) & structural model (结构模型) • Comparison between implied covariance matrix (隐含协方差矩阵) & observed covariance matrix (样本协方差矩阵)
ξ1
η1 β21
η2
λ52 y5 ε5
λ62 y6 ε6
λ72 y7 ε7
λ82 y8 ε8 20
Matrices of the X-Model
x = Λxξ +δ
x λ 0 δ1 1 11 x λ 0 ξ δ 1 2 2 21 = ξ +δ x3 0 λ32 2 3 x4 0 λ42 δ4
φ 11 Φ= φ21 φ22
23
Matrices of the Y-Model
y = Λyη +ε
y λ 0 ε1 1 11 y λ 0 η ε 1 + 2 2 = 21 y 0 λ 2 ε3 η 3 32 ε 42 y4 0 λ 4
1
Classical True Score Model
• X=T+E
▪ X = Observed score ▪ T = True Score ▪ E = Measurement Error
2
Properties of True and Error Scores
• Mean of the error scores for a population is zero ( µE = 0 ) • Correlation (相关系数) between true and error scores for a population is zero ( ρ E =.00) T • Correlation between error scores is zero ( ρE1E2 = 0 )
24
y Λy η ε
observed indicators ofη factor loadings relating y toη latent endogenous variables (内 生变值) measurement errors for y
25
Matrices of the Structural Model
Structural Equation Modeling
结构方程模型
张伟雄博士 香港中文大学工商管理学院副院长 管理学系教授
Gordon W. Cheung, Ph.D Professor, Department of Management Associate Dean, Faculty of Business Administration The Chinese University of Hong Kong
^ Σk
Fitted Covariance Matrix
15
Implied Covariance Matrix
隐含Байду номын сангаас方差矩阵
(I −Β) (ΓΦ ′ +Ψ)(I −Β) Γ Σ(θ) = 1 −′ Φ ′(I −Β) Γ
−1 ′ −1
(I −Β)
where
Φ= covariance matrix of x
11
LISREL is Greek to Me!
Hayduk (1987). Structural Equation Modeling with LISREL. pp.88. Johns Hopkins. 12
Uppercase
Lowercase Name
Uppercase
Lowercase Name
9
Operationalization Choices
• Variations between the Extremes • Range of Variation • Levels of Measurement
– Nominal Measures (定类 定类) 定类 – Ordinal Measures (定序 定序) 定序 – Interval Measures (定距 定距) 定距 – Ratio Measures (定比 定比) 定比
5
Babbie (1992). The Practice of Social Research. Pp. 121. Wadsworth Publishing
6
Babbie (1992). The Practice of Social Research. Pp. 121. Wadsworth Publishing
14
What is SEM
Approximating Models Operating model (form unknown)
?
Specification + parsimony error
etc.
k-1
specifies relationships among...
Population data
• Measurement Model (测量模型) • Path Model (结构模型) • Full Model (全模型) • Model with Mean Structures (均值结构模型)
17
Measurement Model
测量模型
φ12
ξ1
ξ2
λ11 X1 δ1
λ21 X2 δ2
ΓΦ Φ
−1
For Measurement Model
Σ(θ) = ΛxΦ ′ +Θ Λx δ
Bollen (1989). Structural Equations with Latent Variables. Pp. 86 & 236. Wiley. 16
Basic SEM Models
k
Specification + parsimony error
k+1
Sampling Error
POPULATION SAMPLE
etc.
Sample data matrix
Y
S
Sample Covariance Matrix
∆est
Estimated Discrepancy
(Operationalized as a GFI)
Α Β Γ ∆ Ε Ζ Η Θ Ι Κ Λ Μ
α β γ δ ε ζ η θ ι κ λ μ
alpha beta gamma delta epsilon zeta eta theta iota kappa lambda mu
Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω
ν ξ ο π ρ σ τ υ φ χ ψ ω
21
x Λx ξ δ
observed indicators of ξ factor loadings relating x to ξ latent exogenous variables (外 源变值) measurement errors for x
22
Variance/Covariances among the exogenous variables
27
Residuals in the prediction of the endogenous variables
η = Β +Γ +ζ η ξ
η 0 0η γ11 γ 21ξ1 ζ1 1 1 = β 0 + 0 0 ξ +ζ η η 2 2 2 21 2
26
Β Γ ζ
coefficients relatingηtoη coefficients relatingξtoη residuals in equations
3
Construct (Latent Variable) 潜变量
• Concept that the researcher can define in conceptual terms but normally cannot be directly measured or measured without error • Approximately measured by indicators (指 标)
Hair, et al (1995). Multivariate Data Analysis with Readings. Pp. 618 Prentice Hall.
4
Babbie (1992). The Practice of Social Research. Pp. 121. Wadsworth Publishing
• Single or Multiple Indicators (单一指标或多 项指标)
10
Dimension
• A specifiable aspect or facet of a concept • For example: Job Satisfaction
– Satisfaction with supervisor – Satisfaction with co-workers – Satisfaction with environment – Satisfaction with pay – Satisfaction with job content
## #### # ## #### # ## #### # ## #### # ## #### #
Σo
Population Covariance Matrix
∆pop
Population Discrepancy
Σk
Approximate Covariance Matrix
Specification + parsimony error
7
Babbie (1992). The Practice of Social Research. Pp. 121. Wadsworth Publishing
8
Criteria for Measurement Quality
• Reliability (信度 refers to the likelihood that a 信度) 信度 given measurement procedure will yield the same description of a given phenomenon • Validity (效度 refers to the extent to which a 效度) 效度 specific measurement provides data that relate to commonly accepted meanings of a particular concept. Face validity, criterion-related (predictive) validity, content validity, and construct validity
λ31 X3 δ3
λ41 X4 δ4
λ52 X5 δ5
λ62 X6 δ6
λ72 X7 δ7
λ82 X8 δ8
18
Path Model
结构模型
X1
γ11 γ12
ζ1
β31
Y1
γ32
Y3
ζ3
X2
β21
β32
Y2
γ13
X3
γ 23
ζ2
19
Full Model
全模型
δ1 X1 δ2 X2 λ11 λ21 δ3 X3 λ31 δ4 X4 λ41 γ11 γ21 ε1 y1 ε2 y2 λ11 λ21 ε3 y3 λ31 λ41 ε4 y4
nu xi omicron pi rho sigma tau upsilon phi chi psi omega
Hayduk (1987). Structural Equation Modeling with LISREL. pp.89. Johns Hopkins. 13
What is SEM
• Simultaneous regression equations (回归方程) • Modeling latent variables (潜变量 / 因子) from observed variables (指标 / 题目) • Estimate parameters (参数) of the measurement model (测量模型) & structural model (结构模型) • Comparison between implied covariance matrix (隐含协方差矩阵) & observed covariance matrix (样本协方差矩阵)
ξ1
η1 β21
η2
λ52 y5 ε5
λ62 y6 ε6
λ72 y7 ε7
λ82 y8 ε8 20
Matrices of the X-Model
x = Λxξ +δ
x λ 0 δ1 1 11 x λ 0 ξ δ 1 2 2 21 = ξ +δ x3 0 λ32 2 3 x4 0 λ42 δ4