I'm currently running a series of cross-lagged panel models (3 waves of data - 2 variables). These two variables are Affect (either Positive or Negative Affect) and another psychological variable. Since both PA and NA are likely to account for some of the same variance in my 3rd psychological variable, I'd like to look at the unique effects of PA on this third variable (over and above NA). If I'm doing this in a path analysis, it's simple. Regress NA on PA (for each wave) and create a residual score and use that in the cross-lagged model. However, since I am using a SEM approach (measurement model + cross-lagged paths), the path forward isn't really clear.
If I use a path analysis to do this analysis the TLI takes a serious hit as I have both demographics and personality as control variables at each time point. So I'd like to do it with latent factors, however, I don't know if it is possible to create item specific 'residuals' scores.