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GRA 6020 Multivariate Statistics Confirmatory Factor Analysis

GRA 6020 Multivariate Statistics Confirmatory Factor Analysis. Ulf H. Olsson Professor of Statistics. CFA. The covariance matrices:. CFA and ML. k is the number of manifest variables.

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GRA 6020 Multivariate Statistics Confirmatory Factor Analysis

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  1. GRA 6020Multivariate StatisticsConfirmatory Factor Analysis Ulf H. Olsson Professor of Statistics

  2. CFA • The covariance matrices: Ulf H. Olsson

  3. CFA and ML k is the number of manifest variables. If the observed variables comes from a multivariate normal distribution, then Ulf H. Olsson

  4. Testing Fit Ulf H. Olsson

  5. 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

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

  7. 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

  8. Other Fit Indices • CN • RMR • GFI • AGFI • Evaluation of Reliability • MI: Modification Indices Ulf H. Olsson

  9. Nine Psychological Tests Ulf H. Olsson

  10. Alternative Estimators • Assuming multivariate normality • ML • GLS • ULS • If the model holds, ML and GLS are asymptotically equivalente Ulf H. Olsson

  11. Alternative Estimators S: sample covariance θ: parameter vector σ(θ): model implied covariance Ulf H. Olsson

  12. Alternative Estimators Ulf H. Olsson

  13. Alternative Estimators Ulf H. Olsson

  14. Alternative Estimators Ulf H. Olsson

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