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This presentation is an introduction to the concept and theory of Structural Equation Modelling.

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- 1. Structural Equation Modelling (SEM) An Introduction (Part 3)
- 2. CFA Models: Important Steps • Model Specification • Model Identification • Model Estimation • Assessment of Model Fit • Model Re-specification
- 3. Step 1: Model Specification • SEM is a confirmatory technique and it Needs a model that delineates the relationships among variables Requires a model that is based on theory (Bollen & Long, 1993)
- 4. Step 1: Model Specification • Exogenous variables • Variables whose causes are unknown and/or not included in the model • Variables that explain other variables in the model (i.e. independent variables (IVs)) • Endogenous variables • Variables that serve as DVs in a model • May also serve as IVs
- 5. Step 2: Model Identification • Model must be specified so that there are enough pieces of information to give unique estimates for all parameters • SEM involves estimating unknown parameters (e.g., factor loadings, path coefficients) based on known parameters (i.e., covariances) • Identification involves whether a unique solution for a model can be obtained • Requires more known vs. unknown parameters • Identification is a property of the model, not the data Does not depend on sample size i.e., if a model is not identified, it remains so regardless of whether the sample size is 100, 1000, 10,000, etc.
- 6. Step 3: Model Estimation • Over-identified models have infinite # of solutions. • Parameters need to be estimated based on a mathematical criterion. • Goal is to minimize differences between the observed and implied covariance matrices. • Process begins with initial estimates- start values. • Is an iterative process – will stop when a minimum fitting criterion is reached. When the difference between the observed and implied covariance matrices are minimized
- 7. Step 4: Assessing Model Fit • Absolute fit • Relative (Comparative) fit
- 8. Common Absolute Fit Indices • Model X2* • Non-significant X2 (p>0.05) indicates good fit • Root Mean Squared Error of Approximation (RMSEA) • Acceptable fit < 0.10; good fit < 0.05 • Goodness of Fit (GFI) • > 0.90 is considered good fit
- 9. Common Relative Fit Indices • Normed Fit Index (NFI) • Incremental Fit Index (IFI) • Comparative Fit Index (CFI) • All range 0-1 • Generally, >0.90 is considered good
- 10. SEM Model Fit: Rules of Thumb • Will often see/hear reference to 0.90 or above indicating acceptable model fit, for indices such as GFI, CFI, NFI, etc. Typically cite Bentler & Bonett (1980) for this assertation • Basis for this is rather thin (Lance et al., 2006) • What Bentler and Bonett (1980) actually said: “experience will be required to establish values of the indices that are associated with various degrees of meaningfulness of results. In our experience, models with overall fit indices of less than 0.90 can usually be improved substantially” (Bentler & Bonett, 1980, p. 600).
- 11. Step 5: Model Re-specification/Modification • Goal is to improve model fit – changing the model to fit the data • Caveats Modifications are post hoc & capitalize on chance! • General guidelines Must be theoretically consistent Must be replicated with new data
- 12. Evaluating Your Model • Theoretical/clinical meaning Guiding principle • Residuals and implied correlations Discrepancies between sample covariance matrix and those implied by the model • Tests of path coefficients Direction, magnitude • Absence of numerical problems Direction and magnitude of residuals Pattern of standardized residuals (z-scores)
- 13. Looking for Online SEM Training? Contact us: info@costarch.com Visit: http://tinyurl.com/costarch-sem www.costarch.com

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