结构方程模型-CFA

Hair, et al (1995). Multivariate Data Analysis with Readings. Pp. 618 Prentice Hall.
Structural Equation Model
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Babbie (1992). The Practice of Social Research. Pp. 121. Wadsworth Publishing
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Uppercase
Lowercase
Name
Uppercase
Lowercase
Name
Α
α
alpha
Ν
ν
nu
Β Γ Δ Ε Ζ Η Θ Ι
Κ Λ Μ
β γ δ ε ζ η θ ι κ λ μ
beta gamma delta epsilon zeta eta theta iota kappa lambda mu
模型的参数13个:
ቤተ መጻሕፍቲ ባይዱ1 var 1 , 22 var 2 , 21 cov 2 , 1 ii var i , i 1,
,5
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11 , 21 , 31 , 42 , 52
Structural Equation Model
Notations:
ˆ
S
参数向量

的估计量
真实协方差矩阵 样本协方差矩阵
ˆ
x x
理论模型导出的协方差矩阵
样本估计出 差矩阵

ˆ
后得到估计协方
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Structural Equation Model
var( x1 ) cov( x2 , x1 ) cov( x3 , x1 ) cov( x4 , x1 ) cov( x , x ) 5 1
13个变量
2 11 11 11 2 21 11 11 2111 22 2 311111 312111 31 11 33 421121 422121 423121 522121 523121 52 11 21
2 42 22 44
524222
2 5222 55
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Structural Equation Model
Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω
ξ ο π ρ σ τ υ φ χ ψ ω
xi omicron pi rho sigma tau upsilon phi chi psi omega
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Hayduk (1987). Structural Equation Modeling with LISREL. pp.89. Johns Hopkins.
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一、CFA的基本概念 （一）CFA的假设
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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)
E i 0, i 1,
,5;
指标和潜变量均中心
化
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x x
9.2
x1 11 0 1 x 0 2 2 21 1 x x3 , x 31 0 , , 3 , 2 x4 0 42 4 x 0 52 5 5
路径分析
结构方程模型
Structural Equation Model
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1.1 探索性因子分析
Exploratory Factor Analysis
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1.2 验证性因子分析 Confirmatory Factor Analysis
Structural Equation Model
经济管理数学Ｉ
第三讲
结构方程模型原理及其应用
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主要参考书目：
候杰泰. 结构方程模型及其应用，教育科学出 版社，2004年
主要使用软件Lisrel 8.7
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1 结构方程模型统计原理
探索性因子分析 验证性因子分析
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Indicator x1
Loading
2
Error term
x2 x3 x4 x5
3 4 5
11 21 1 31
Latent Variable
42 52
2
一个简单的CFA模型
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测量方程Measurement equation
基本假设：
x1 111 1 x2 211 2 x3 311 3 x4 42 2 4 x5 52 2 5 (9.1)
可放松
Cov i , j 0, i, j Cov i , j 0, i j
var( x2 ) cov( x3 , x2 ) var( x3 ) cov( x4 , x2 ) cov( x4 , x3 ) var( x4 ) cov( x5 , x2 ) cov( x5 , x3 ) cov( x5 , x4 ) var( x5 )
5 1 5 15方程 2