So I ran CFA on an exhaustion measure comprising of three facets which were specified as first-order latent variables. When I added a secon-order latent variable to the model the correlation between one of the first-order factor and second-order factor exceeded 1. I do not know how to proceed now. If the correlation had occured only between two the first-order latent variables this could have been adress more straightforwardly. But I really need there to be a second-order factor.
welcome to CrossValidated.
This is usually a sign that your model is wrong in some way.
The estimator is trying to maximize the overall fit of the model - if it can do that by pushing a parameter past a boundary, it will do that.
Here's a simple example: Three variables, A, B and C.
A 1 B 0.9 1 C 0.8 0.1 1 A B C
And the model we want to fit looks like:
A -> B -> C
What will the model estimates be:
A -> B: 0.9 (matches the data) B -> C: 0.1 (matches the data)
Then the implied correlation between A and C is 0.9 * 0.1 = 0.09 - completely wrong.
It can try to fix this in two ways. It can raise the estimate for the effect between B and C - but this means that the second parameter doesn't match the data. So it tries to spread the error around - it makes both B -> C higher AND A -> B higher. If that pushes A -> B over 1.00, well, it doesn't care, it just cares about the overall global fit.
A parameter out of bounds like that is the model's way of telling you that it is wrong.