STRUCTURAL EQUATION MODELING

Kayla Jordan

D. Wayne Mitchell

RStats Institute

Missouri State University

What is SEM?

Statistical technique useful for testing theoretical models

Theory-driven Confirmatory

Types of Variables

Latent VariableExogenous Variable

Manifest or Observed Variable Error

Residual

Endogenous

Types of Models

Measurement Model Structural Model

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

Estimates

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)

Confirmatory Factor Analysis

Path Analysis

Full Structural Model

Multi-Trait, Multi-Method

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

Model Comparisons Need for Multiple Models Chi-Square Difference CFI Difference

Assumptions Sample Size Normality Outliers Multicollinearity

Programs

Questions?

Contact: kaylajordan91@gmail.com