I ran an Exploratory Factor Analysis in SPSS recently with ML as the extraction method, and got the following table in my output:
I was not used to seeing goodness-of-fit tests in the context of EFA (as opposed to CFA), and wondered what the point of it was. The SPSS documentation seems to suggest that it's a way of deciding how many factors to select (number of factors in factor analysis problem).
If you choose maximum likelihood (ML) or generalized least squares (GLS) as your extraction method, you would get a chi-square measure of goodness of fit, which is a test of the null hypothesis that 3 factors were adequate to explain the covariances among your variables. You would not get a test of whether the factor loading matrix conformed to your model.
I also found the formula used, which is as follows
Is it true that what they 'want' me to do is to run this test with increasing numbers of factors selected for extraction, and then to select the number of factors when the test is no longer statistically significant?
If so, is such a method any good? I've heard of all sorts of other ways of deciding the number of factors (scree plots, Kaiser-Guttman rule, MAP test, parallel test) but had never heard of this one before and it seems very problematic.
The Chi Square test is very sensitive to sample size. Is it legitimate/useful to convert this particular Chi Square test to RMSEA?
Why does is the test only available with ML and GLS and not with other methods also offered, e.g. ULS?