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

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”).

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).

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).

Controversial paths?

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

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.

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)

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

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

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

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:

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)

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

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

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?)