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The General (LISREL) SEM model

The General (LISREL) SEM model. Ulf H. Olsson Professor of statistics . Branch. Loan. Satisfaction. Loyalty. Savings. Making Numbers. CFA and SEM. CFA and SEM. CFA and SEM. No differences in estimation and testing Many estimators ML GLS ULS WLS DWLS. Notation and Background.

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The General (LISREL) SEM model

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  1. The General (LISREL) SEM model Ulf H. Olsson Professor of statistics

  2. Branch Loan Satisfaction Loyalty Savings Making Numbers Ulf H. Olsson

  3. CFA and SEM Ulf H. Olsson

  4. CFA and SEM Ulf H. Olsson

  5. CFA and SEM • No differences in estimation and testing • Many estimators • ML • GLS • ULS • WLS • DWLS Ulf H. Olsson

  6. Notation and Background • Satorra & Bentler, 1988, equation 4.1 Ulf H. Olsson

  7. C1 for ML and GLS Ulf H. Olsson

  8. The four different chi-squares • C1 is N-1 times the minimum value of a fit-function • C2 is N-1 times the minimum value of a weighted (involving a weight matrix) fit function under multivariate normality • C3 is the Satorra-Bentler Scaled chi-square • C4 is N-1 times the minimum value of a weighted (involving a weight matrix) fit function under multivariate non-normality Ulf H. Olsson

  9. ULS GLS ML WLS DWLS C1 0 * * 0 0 C2 * * * 0 0 C3 0 0 0 0 0 C4 0 0 0 0 0 Asymptotic covariance matrix not provided Ulf H. Olsson

  10. ULS GLS ML WLS DWLS C1 0 * * * 0 C2 * * * 0 * C3 * * * 0 * C4 * * * 0 * Asymptotic covariance matrix provided Ulf H. Olsson

  11. ESTIMATORS • If the data are continuous and approximately follow a multivariate Normal distribution, then the Method of Maximum Likelihood is recommended. • If the data are continuous and approximately do not follow a multivariate Normal distribution and the sample size is not large, then the Robust Maximum Likelihood Method is recommended. This method will require an estimate of the asymptotic covariance matrix of the sample variances and covariances. • If the data are ordinal, categorical or mixed, then the Diagonally Weighted Least Squares (DWLS) method for Polychoric correlation matrices is recommended. This method will require an estimate of the asymptotic covariance matrix of the sample correlations. Ulf H. Olsson

  12. Problems with the chi-square test • The chi-square tends to be large in large samples if the model does not hold • It is based on the assumption that the model holds in the population • It is assumed that the observed variables comes from a multivariate normal distribution • => The chi-square test might be to strict, since it is based on unreasonable assumptions?! Ulf H. Olsson

  13. Alternative test- Testing Close fit Ulf H. Olsson

  14. How to Use RMSEA • Use the 90% Confidence interval for EA • Use The P-value for EA • RMSEA as a descriptive Measure • RMSEA< 0.05 Good Fit • 0.05 < RMSEA < 0.08 Acceptable Fit • RMSEA > 0.10 Not Acceptable Fit Ulf H. Olsson

  15. Other Fit Indices • CN • RMR • GFI = 1-(Fm/Fn) • AGFI= 1 – (k(k+1)/(2df)) (1-GFI) • Evaluation of Reliability • MI: Modification Indices Ulf H. Olsson

  16. Nested Models and parsimony • Modification Indices • chi-sq is chi-sq with df= df • Nested Models • Re-specification (Modification indices) Ulf H. Olsson

  17. RMSEA Ulf H. Olsson

  18. RMSEA Ulf H. Olsson

  19. LISREL SYNTAX Ulf H. Olsson

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