I have a longitudinal structural model regressing 1 endogenous latent variable at Time 2 on 4 exogenous latent variables at Time 1. The modification indices in Mplus suggest including a direct effect from an indicator of marital quality (overall feeling of marital closeness) at time 1 to an indicator of mental health (depression) at time 2. Is it possible and/or appropriate to include a direct effect from one indicator to another, or is that effect expected to be captured in the path between the latent variables?
This would be pretty unusual, but not unheard of, and it would be possible to rationalize such a finding. However, to take a more agnostic stance, it might make more sense to simply correlate the errors of those two indicators, which should yield the same improvement in fit without requiring the causal assumptions that are laden in a directed path.
If you have a good feeling that the measures are good and you are more concerned with the structural part of the model, you might also consider moving to model-implied instrumental variable 2 stage least squares (MIIV 2SLS) estimation of your model. With this estimator, misspecification of the measurement equations won't spread to the structural equations.