1. Writing up results from Structural Equation Models
What to Report, What to Omit

2. Writing up results from Structural Equation Models
Reference: Hoyle and Panter chapter in Hoyle.
Important to note that there is a wide variety of reporting styles (no one “standard”).

3. Writing up results from Structural Equation Models
A Diagram
Construct Equation Model
Measurement Equation model
Some simplification may be required.
Adding parameter estimates may clutter (but for simple models helps with reporting).
Alternatives exist (present matrices).

4. Reporting Structural Equation Models
“Written explanation justifying each path and each absence of a path” (Hoyle and Panter)
(just how much journal space is available here? )
It might make more sense to try to identify potential controversies (with respect to inclusion, exclusion).

5. Controversial paths?

6. What to report and what not to report…..
Present the details of the statistical model
Clear indication of all free parameters
Clear indication of all fixed parameters
It should be possible for the reader to reproduce the model
Describe the data
Correlations and standard errors (or covariances) for all variables ??
Round to 3-4 digits and not just 2 if you do this

7. What to report and what not to report…
4. Describing the data (continued)
Distributions of the data
Any variable highly skewed?
Any variable only nominally continuous (i.e., 5-6 discrete values or less)?
Report Mardia’s Kurtosis coefficient (multivariate statistic)
Dummy exogenous variables, if any
5. Estimation Method
If the estimation method is not ML, report ML results.

8. What to report and what not to report…
6. Treatment of Missing Data
How big is the problem?
Treatment method used?
Pretend there are no missing data
Listwise deletion
Pairwise deletion
FIML estimation (AMOS, LISREL, MPlus, EQS)
Nearest neighbor imputation (LISREL)
EM algorithm (covariance matrix imputation ) (SAS, LISREL/PRELIS)

9. What to report and what not to report…
7. Fit criterion
Hoyle and Panter suggest “.90; justify if lower”.
Choice of indices also an issue.
There appears to be “little consensus on the best index” (H & P recommend using multiple indices in presentations)
Standards:
Bollen’s delta 2 (IFI)
Comparative Fit Index
RMSEA

10. GFI (Joreskog & Sorbom) Bentler’s Normed Fit index Model Chi-Square
Fit indices
Older measures:
GFI (Joreskog & Sorbom)
Bentler’s Normed Fit index
Model Chi-Square

11. What to report & what not to report….
8. Alternative Models used for Nested Comparisons (if appropriate)

12. 9. Plausible explanation for correlated errors
[“these things were just too darned big to ignore”]
Generally assumed when working with panel model with equivalent indicators across time:

13. 10. Interpretation of regression-based model
What to report
10. Interpretation of regression-based model
Present standardized and unstandardized coefficients (usually)
Standard errors? (* significance test indicators?)
R-square for equations
Measurement model too?
(expect higher R-squares)

14. What to report.
Problems and issues
Negative error variances or other reasons for non-singular parameter covariance matrices
How dealt with? Does the final model entail any “improper estimates”?
Convergence difficulties, if any
LISREL: can look at Fml across values of given parameter, holding other parameters constant
Collinearity among exogenous variables
Factorially complex items

15. What to report & what not to report….
General Model Limitations, Future Research issues:
Where the number of available indicators compromised the model
2-indicator variables? (any constraints required?)
Single-indicator variables? (what assumptions made about error variances?)
Indicators not broadly representative of the construct being measured?
Where the distribution of data presented problems
Larger sample sizes can help

16. What to report & what not to report….
General Model Limitations, Future Research issues:
Missing data (extent of, etc.)
Cause-effect issues, if any (what constraints went into non-recursive model? How reasonable are these?)