Writing about Structural Equation Models

1
Writing about Structural Equation Models

• R.H. Hoyle
• Abigail T. Panter

2
The Conceptual Model

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

3
The Statistical Model

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

4
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.

5
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.

6
Recommended Indexes of Overall Model
FitStand-Alone/Absolute Indexes
7
Recommended Indexes of Overall Model FitType-2
Indexes
8
Recommended Indexes of Overall Model FitType 2
Indexes
9
Recommended Indexes of Overall Model FitType-3
Indexes
10
Parameter Estimates

• Provide all parameter estimates, error variances,
  and variances of latent variables.
• Include standard error of estimates, critical
  ratios and p-values.
• Indicate parameters fixed at specific values.

11
Alternative Models

• The strongest SEM analysis compares competing
  theoretical models.
• Include substantive reasons for post-hoc
  modifications.
• Report any equivalent models.
• If possible, cross-validate the final model.

12
Interpretation

• Directionality is established by logic,
  manipulation, or strong theoretical arguments.
• Associations in SEMs are necessary but not
  sufficient evidence of causal relations.
• Include additional limitations regarding the
  interpretation of the SEM results in the
  discussion.

13
Reference

• R.H. Hoyle and A. T. Panter, Writing about
  Structural Equation models, In R. H. Hoyle
  (ed.), Structural Equation Modeling Concepts,
  Issues and Applications. Sage Publications, 1995,
  pp. 158-176.