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STRUCTURAL EQUATION MODELING
Kayla Jordan
D. Wayne Mitchell
RStats Institute
Missouri State University
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What is SEM?
Statistical technique useful for testing theoretical models
Theory-driven Confirmatory
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Types of Variables
Latent VariableExogenous Variable
Manifest or Observed Variable Error
Residual
Endogenous
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Types of Models
Measurement Model Structural Model
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Degrees of Freedom
Knowns: n(n+1)/2 -> 8(9)/2 -> 36 Unknowns: 5 factor loadings, 2 path coefficients, 8
error variances, 2 residuals -> 17 total unknowns Degrees of Freedom: Knowns – Unknowns -> 19
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Estimates
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Factor LoadingsRegression Weights: (Group number 1 - Default model)
Estimate S.E. C.R. P Label
H1 <--- Harm 1.000
H2 <--- Harm 1.020 .112 9.105 ***
H3 <--- Harm 1.096 .111 9.843 ***
H4 <--- Harm .883 .112 7.900 ***
H5 <--- Harm .692 .153 4.508 ***
H6 <--- Harm .643 .171 3.754 ***
Standardized Regression Weights: (Group number 1 - Default model)
Estimate
H1 <--- Harm .716 H2 <--- Harm .705 H3 <--- Harm .768 H4 <--- Harm .608 H5 <--- Harm .344 H6 <--- Harm .286
Indicates all observed variables are measuring the latent variable.
Values closer to one indicate that the observed variable is measuring latent better (e.g., H3 is a better item than H6)
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Confirmatory Factor Analysis
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Path Analysis
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Full Structural Model
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Multi-Trait, Multi-Method
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Fit IndicesModel Fit Summary
CMIN
Model NPAR CMIN DF P CMIN/DF Default model 70 1021.692 395 .000 2.587 Saturated model 465 .000 0 Independence model 30 2715.382 435 .000 6.242
Baseline Comparisons
Model NFI
Delta1 RFI
rho1 IFI
Delta2 TLI
rho2 CFI
Default model .624 .586 .730 .697 .725 Saturated model 1.000
1.000
1.000
Independence model .000 .000 .000 .000 .000
RMSEA
Model RMSEA LO 90 HI 90 PCLOSE Default model .089 .082 .096 .000 Independence model .162 .156 .168 .000
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Model Comparisons Need for Multiple Models Chi-Square Difference CFI Difference
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Assumptions Sample Size Normality Outliers Multicollinearity
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Programs