I have a complex nonrecursive path model (i.e., only latent disturbance terms for endogenous manifests). It has several reciprocal paths and potential feedback loops. The model converges fine with no errors and the fit statistics all look great (X2 = 9.2, P = 0.24, CFI = 0.99, RMSEA = 0.033) and all the correlation residuals are less than 0.10. However, one of the disturbance estimates is slightly higher than the manifest variables actual variance (d = 1.699, s2 = 1.605), which creates a slightly negative R2 value for that endogenous variable. If I constrain the upper bound of this error to var(manifest x), I get some major changes to the coefficients of other paths.
This was such a subtle problem that I didn't even notice it until I was calculating R2 values for the final publication diagram.
1) Would this be considered a Heywood case and thus an inadmissible solution?
2) Does this mean the model is empirically under-identified?
If so, how would you suggest I proceed?
I've attached the script and covariance matrix. Beware, it's huge and ugly but all very justifiable theoretically. I only plan to include paths with p-values < 0.01 in the final diagram.