GRA 6020 Multivariate Statistics Factor Analysis Ulf H

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

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

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 nonzero loading in each equation Ulf H. Olsson

CFA Ulf H. Olsson

CFA Ulf H. Olsson

CFA • The covariance matrices: Ulf H. Olsson

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

Testing Fit 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? ! 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

Nine Psychological Tests Ulf H. Olsson