SEM evaluation and rules Petr Soukup

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

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 : http://davidakenny.net/cm/fit.htm

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

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 1995. Oxford: Blackwell Discussion AIC vs. BIC: http://emdbolker.wikidot.com/forum/t-81139/

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

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!

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)

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)

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)

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