Confirmatory factor analysis with 4 convoluted factors

Question

I'm having some trouble with a Confirmatory Factor Analysis (CFA) and my data. I use a scale of 16 items in which one item always belongs to two out of four latent factors (SE, CE, Goal, indicated by a "g", and Others, indicated by an "o"). If I add a factor for inverse items (_u), the CFA proves a good fit. However, R returns the following warning, "lavaan WARNING: model has NOT converged!", if I try to run the original model. I think it might have to do with the fact that I don't have unique items for factors. But how do I manage this problem? And how can I include a latent factor behind the 4 factors in this model as well?

Original model:

Modell <- 'SE     =~ SEg01_u + SEg02 + SEg03 + SEg04 + SEo01_u + SEo02 + SEo03 + SEo04
           CE     =~ CEg01_u + CEg02 + CEg03 + CEg04 + CEo01_u + CEo02 + CEo03 + CEo04
           Goal   =~ SEg01_u + SEg02 + SEg03 + SEg04 + CEg01_u + CEg02 + CEg03 + CEg04
           Other  =~ SEo01_u + SEo02 + SEo03 + SEo04 + CEo01_u + CEo02 + CEo03 + CEo04'
fit <- cfa(Modell, data = dataset)
summary(fit, fit.measures=TRUE, modindices=TRUE)

I'd be grateful for any help!

Answer 1

I think the problem might be that lavaan is constraining the first loading of the method factor (u) to 1. That means that two factors have fixed loadings.

Free the first loading on the method variable, and either constrain a different one, or constrain the variance of the method factor to 1.

It might be that your data just can't support such a model.

If you can post a reproducible example, that would mean I could test that idea.