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

Ulf H. Olsson Assignment 1 The Country/People Image 12 items was used for the country-people Image: For each item a 7-point semantic differential scale was used 1) Role in world politics 2) Refined taste 3) Likable 4) Trustworthy 5) Industrious 6) Managing the economy well 7) Technological level 8) Ability to handle large and complex projects 9) Would like closer ties 10) Educational level 11) Polluted environment 12) Athletic People Research project: Use the file CI-week11.psf to find a factor structure for the Construct Country Image. Test and evaluate the model.

Ulf H. Olsson Alternative test- Testing Close fit

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

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

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

Ulf H. Olsson Alternative Estimators

Ulf H. Olsson Alternative Estimators

Ulf H. Olsson Alternative Estimators

Ulf H. Olsson Measurement Models Consequences of Measurement Error Biased estimates Does the Model fit the Data The Chi-square test The RMSEA approach Detailed evaluation of the model t.-values Reliability Validity

Ulf H. Olsson Consequences of Measurement Error

Ulf H. Olsson Consequences of Measurement Error

Ulf H. Olsson Cronbach’s alpha One can see from this formula that if you increase the number of items, you increase Cronbach's alpha. Additionally, if the average inter-item correlation is low, alpha will be low. As the average inter-item correlation increases, Cronbach's alpha increases as well.

Ulf H. Olsson Composite Reliability measure