Correlate residuals in common pathway model

Dear all,

I have fitted a common pathway model—one latent factor and 7 observed variables.

I have fitted a single-factor common pathway model since the previous literature has suggested this structure and also my confirmatory factor analysis.

As previous publications did in the confirmatory factor analysis, the model improved by correlating the residuals between two subscales since these two components have strong component overlap (one sub-scale is used to calculate the other). My confirmatory factor analysis also improved by doing so.

Therefore, I fitted a single-factor common pathway model. However, I also tried a 3-factor common pathway model (suggested by another publication). I compared this model against my single-factor model and the best fit was provided by the common pathway model with 3 factors.

I wonder if I could correlate the residuals between these two sub-scales in my AE-common pathway model in order to improve the fit of this model. I have tried to do it but I have no idea how to do it. I am not sure if that makes sense or not, or choosing the single-factor model is already supported by the confirmatory factor analysis (better indices for the single-factor model in comparison with the 3-factor model).

Thank you so much in advance.