1. SEM evaluation and rules
Petr Soukup

2. SEM –model evaluation Overall evaluation - test and criterias
Individual parameters – test and CI
Find parameters that should be added to model – modification indeces

3. Overall evaluation of SEM models (model fit)
Chi-squaret test
Relative criterias
AGFI – above 0,9
TLI – above 0,9
CFI - above 0,9
Criteria measuring error
RMSEA – values below 0,05 (0,08) are evaluated as good
Formulas can be found at :

4. Other evaluation tools (model fit)
Ratio Χ2 and df – max 2-3(4)
Information criterias:
Combine likelihood and complexity of model (df)
Mostly AIC or BIC
AIC = Χ2 + k(k - 1) - 2df

5. Evaluatrion continued
Reco for BIC
Difference above 10 – better model with smaller BIC
More: Raftery, A.E. (1995), Bayesian model selection in social research. In P.V.Marsden (Ed.), Sociological Methodology Oxford: Blackwell
Discussion AIC vs. BIC:

6. Evaluation of parameters
Ratio of parameter and std error
Possibility to compute CI – How?

7. Modification indeces For every possible added parameter
Diff in chi-square if parameter would be included
Reco nr.1 – index above 4, from statistical point of view it is good to add parameter
Reco nr. 2 – Add only one parameter in one step and may be use higher level than 4!

8. Six rules for model building (viz SEM_6_rules.pdf)
Rule 1. Variances for exogenous variables are estimated quantities (esp. latent variables in CFA and residuals/random errors)
Note: For every end. var you need random error
Rule 2. Covariancs of exo vars are estimated quantities (if theory does not expect opposite)

9. Six rules for model building (viz SEM_6_rules.pdf)
Rule 3. All possible factor weights in CFAs are estimated (if theory does not expect opposite)
Note: For 2 (3,4..) factor CFAs it ios common that only some items are linked to 1st, nd (3rd, th,..) factor
Rule 4. Regression coefficients between latent or manifest vars are estimated (if theory does not expect opposite)

10. Six rules for model building (viz SEM_6_rules.pdf)
Rule 5. Variances and covariances between endo vars and covariances between exo and ndo vars are never estimated (no exception!!!)
Rule 6. For every latent var we need to set scale. Reason: no scale for latent var. Two options: fix variance (typical at 1), or fix relationship to one manifest var (typical at 1). Second option is default in AMOS (and other packages)

11. Simple example Apply rules 1-6 2 factor CFA How many pars?
Which rules are applied?