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?
Is it wrong to regress the outcome variable on a second-order factor and the first-order factors that form the second-order factor. My outcome is an observed variable that measures retained or not retained. For example: F1 by a b c F2 by d e f F3 by g h i F4 by F1 F2 F3 Retained on F4 Retained on F1 F2 F3 I looked at the reference above for Gustafsson and Balke and that seems to only refer to the measurement model and not the structural model. Are you familiar with any references regarding a structural model that regresses the outcome variable on both the second-order factor and the first-order factors that comprise the second-order factor? Thank you.