Writing up results from
Structural Equation Models
What to Report, What to Omit
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Writing up results from Structural Equation Models
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Reference: Hoyle and Panter chapter in
Hoyle.
Important to note that there is a wide
variety of reporting styles (no one
“standard”).
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Writing up results from Structural Equation Models
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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).
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Reporting Structural Equation Models
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“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).
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Controversial paths?
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y1
y2
y3
y4
y5
y6
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LV1
LV3
e1
e2
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LV2
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LV4
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What to report and what not to report…..
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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
4. Describe the data
1. Correlations and standard errors (or
covariances) for all variables ??
Round to 3-4 digits and not just 2 if you do this
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What to report and what not to report…
4. Describing the data (continued)
– Distributions of the data
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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.
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What to report and what not to report…
6. Treatment of Missing Data
– How big is the problem?
– Treatment method used?
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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)
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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
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Fit indices
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Older measures:
– GFI (Joreskog & Sorbom)
– Bentler’s Normed Fit index
– Model Chi-Square
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What to report & what not to report….
8. Alternative Models used for Nested Comparisons (if appropriate)
US South
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US West
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U.S. Midwest
U.S. Rust Belt
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9. Plausible explanation for correlated errors
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[“these things were just too darned big to ignore”]
Generally assumed when working with panel model with equivalent
indicators across time:
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What to report
10. Interpretation of regression-based model
– Present standardized and unstandardized
coefficients (usually)
– Standard errors? (* significance test indicators?)
– R-square for equations
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Measurement model too?
(expect higher R-squares)
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What to report.
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Problems and issues
– Negative error variances or other reasons for
non-singular parameter covariance matrices
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How dealt with? Does the final model entail any
“improper estimates”?
– Convergence difficulties, if any
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LISREL: can look at Fml across values of given
parameter, holding other parameters constant
– Collinearity among exogenous variables
– Factorially complex items
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What to report & what not to report….
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General Model Limitations, Future Research
issues:
– Where the number of available indicators
compromised the model
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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
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Larger sample sizes can help
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What to report & what not to report….
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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?)
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