1. Measurement Models and CFA; Chi-square and RMSEA Ulf H. Olsson Professor of Statistics

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

3. Ulf H. Olsson Testing Exact Fit

4. Ulf H. Olsson 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?!

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

6. 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

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

8. Ulf H. Olsson Model evaluation Does the model fit the data Chi-square; RMSEA and other descriptive measures Are the measures reliable? Are the paths (coeffisients) significant? Is it possible to improve fit? Modification indices