I've estimated some alternative CFA models with WLSMV. The indicators are binary. And in some models there are factor correlations greater than 1 (1.035 and so). Is it a symptom of an underidentified model or just an indication that the two factors are indistinguishable? Is it possible to compute a confidence interval for the estimated correlations?
bmuthen posted on Thursday, May 19, 2005 - 8:52 am
Getting factor correlations close to 1 suggests that you work with too many factors.
I am not sure you need confidence intervals for factor correlations, given my comment above, but here are some thoughts. If the factor correlations are raw parameter estimates - as opposed to obtained in the standardized output column - then you simply use the usual approximate confidence interval of +-1.96*SE. If not, you can do either of 2 things. (1) you can reparameterize your model to have unit factor variances in which case the factor correlations come out as estimates. (2) you take the standardized correlations and use the Delta method to compute their SEs (if you don't know the Delta method, don't use alternative (2)).