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GRA 6020 Multivariate Statistics Confirmatory Factor Analysis

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This lecture by Professor Ulf H. Olsson covers key concepts of Confirmatory Factor Analysis (CFA) within the realm of multivariate statistics. It addresses covariance matrices, the importance of multivariate normal distribution, and challenges associated with the chi-square test, particularly in large samples where the model may not fit. Additionally, alternative fit indices such as RMSEA, CN, and others are discussed, alongside various estimators. This comprehensive overview is tailored for those seeking to deepen their understanding of CFA methodologies and their applications in psychological testing.

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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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