We are conducting a number of LGM in which we predict growth factors with other growth factors.
Specifically: two sets of latent growth factors (I & S) are estimated: one for income and one for children's internalizing symptoms. The structural part of the model includes the following paths: income_i --> internalizing_i income_i --> internalizing_s income_s --> internalizing_s
I want plot internalizing trajectories for children whose family income slope is higher than average, average, and lower than average. If I were conducting a path analysis using manifest predictor and outcome variables, I would to plot the trajectories for subjects with average income, -1 SD income, and +1 SD income.
However, income_s isn't a manifest variable, it's a latent variable, and so I don't have a standard deviation. Is there some analagous way to conceptualize higher than average, average, and lower than average income_s?
It has occurred to me that one possibility would be to calculate an estimated SD using the s.e. for income_s. But I don't know if this is appropriate? Is there another way that I should do this?