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

2. Ulf H. Olsson 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

3. Ulf H. Olsson 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 only (?) one non-zero loading in each equation

4. Ulf H. Olsson CFA

5. Ulf H. Olsson CFA

6. Ulf H. Olsson CFA The covariance matrices:

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

8. Ulf H. Olsson Testing Fit