# Why confirmatory factor analysis has more degrees of freedom?

I am reading the textbook "Multivariate Data Analysis" and I am puzzled by one statement it makes about confirmatory factor analysis, saying that CFA has more degree of freedom than EFA. The following is a related part of the textbook.

The underlined part is where my question lies. The corresponding EFA model is

Thank you.

• There are a lot of books called "Multivariate data analysis". I guess you're talking about Hair, et al, but you could narrow it down. – Jeremy Miles Apr 14 '15 at 4:08

$df = moments - parameters$

You've got 10 parameters to estimate in the $\lambda$ matrix in the EFA, and only 5 parameters in the $\lambda$ matrix in the CFA because constraints are added in the CFA. Hence you have more df in the CFA.

You can't free all of the parameters in the lambda matrix in CFA, because you will end up with negative df. This is the identification problem, in EFA.

• +1. Perhaps, it would makes sense to clarify for the OP that the reduction in the number of parameters in the CFA case is due to imposed constraints (fixed parameters). – Aleksandr Blekh Apr 14 '15 at 4:19