10b SOC681 Writing about SEMS 2000

Writing about Structural
Equation Models
R.H. Hoyle
Abigail T. Panter

The Conceptual Model
• Introduce model with a diagram.
• Provide a written explanation in the text for
each relation or path.

The Statistical Model
• Include a path diagram.
• Describe the statistical model in the
Methods section.

Details about the Data
• Include a correlation matrix with standard
deviations of the variables.
• Explain any assumptions about measurement
levels of the raw data.
• Provide information about the distributions of

the individual variables and the multivariate
distribution.
• Include statistics on univariate kurtosis and
multivariate normality.

Describing the Results
• Report results from ML estimation.
• If necessary report results of alternative
estimation procedures.
• Include the Indicators of Fit recommended
in Table 9.1.

Recommended Indexes of Overall Model Fit
Stand-Alone/Absolute Indexes
Index

Reference

Description

Chi-Square
Scaled Chi-square

Bollen (1989b)
Statistical test of the
Sattora & Bentler lack of fit resulting
(1994)
from overidentifying
restrictions placed on a
model

Goodness-of-fit index

Joreskog &
Sorbom (1981)

Indexes the relative
amount of the
observed variances and
covariances accounted

for by a model
Analogous to R2

Recommended Indexes of Overall Model Fit
Type-2 Indexes
Index

Reference

Description

Tucker-Lewis Index Bentler & Bonett Compares the lack of fit
(TLI)/Nonnormed Fit (1980) Tucker & of a target model to the
Index (NNFI)
Lewis (1973)
lack of fit of a baseline
model, usually the
independence model.
Value estimates the
relative improvement per

df of the target model
over a baseline model.
Not recommended for
very small samples
(