I'm attempting to estimate a second order factor model to capture domain-specific attitudes (first-order) and general attitudes (second order) and then using this model to predict an outcome. I am familiar with models that can accomplish this when regressing the outcome on the second order factor exclusively. However, what I am really interested in theoretically is whether domain-specific attitudes also contribute to the outcome above and beyond general attitudes. Thus, I would like to regress the outcome on both the second order factor as well as one or more of the first order factors. Are there any references you have for this type of model and/or do you foresee any problems with this setup?