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GRA 6020 Multivariate Statistics Factor Analysis

GRA 6020 Multivariate Statistics Factor Analysis. Ulf H. Olsson Professor of Statistics. The CFA model.

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GRA 6020 Multivariate Statistics Factor Analysis

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

  2. The CFA model • In a confirmatory factor analysis, the investigator has such a knowledge about the factorial nature of the variables that he/she is able to specify that each xi depends only on a few of the factors. If xi does not depend on faktor j, the factor loading lambdaij is zero Ulf H. Olsson

  3. CFA • If does not depend on then • In many applications, the latent factor represents a theoretical construct and the observed measures are designed to be indicators of this construct. In this case there is only (?) one non-zero loading in each equation Ulf H. Olsson

  4. CFA Ulf H. Olsson

  5. CFA Ulf H. Olsson

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

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

  8. Testing Fit Ulf H. Olsson

  9. 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

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

  11. 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

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

  13. Nine Psychological Tests Ulf H. Olsson

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