We have specified a latent growth model with three individually-varying times of observation (time scores) and time-invariant predictors predicting both the intercept and the slope. When we add one of the predictors we are interested in as a covariate to the model the mean intercept goes from being positive (M = 53.90) and corresponding to the range of the dependent variable (0-100) to being negative (M = -20.20) and outside of this range. The mean slope also changes from 1.04 to .53. We also find that this covariate is a significant predictor of the intercept, but not the slope, and that including it in the model changes the pattern of results for some of the other predictors.
We would greatly appreciate your input on: 1) How to interpret this finding. 2) Whether the other model results can be considered trustworthy. 3) Suggestions on how to proceed.