I have established that a 2nd-order CFA model fits well. This model has 4 first-order LVs and a single second-order LV. I am now attempting to predict the 2nd-order LV and the 4 first-order LVs simultaneously with single observed variables (e.g., gender, age, etc). Each time I attempt to do so the model does not converge, and MPlus suggests that the model may not be identified. Is it not possible to predict both the first- and second-order LVs simultaneously because of identification problems?
You cannot identify all of the direct effects of the covariates on the first-order factors. You can run the model without them and ask for modification indices to decide which to leave out. This is that same as in a MIMIC model.