I have a linear growth curve model with 5 time points, and am interested in how intercept and slope of the growth curve model predict different outcome variables at a later time point. Early on, I recognized that the regression estimates (intercept and slope predicting outcome variables) change depending on how I code time in the growth curve model. For example, if I set the intercept at the first time point (0,1,2,3,4) I get significantly different estimates than if I set the intercept at the last time point (-4,-3,-2,-1,0). I found a paper that explains why this is happening and how to interpret the differing findings:
Biesanz, J. C., Deeb Sossa, N., Papadakis, A. A., Bollen, K. A., & Curran, P. J. (2004). The role of coding time in estimating and interpreting growth curve models. Psychological Methods, 9, 30-52.
So, I decided to run all possible time-coding alternatives and to compare the results between the models. That is when I recognized that only the regression estimates for the slope (slope predicting outcome variables) were changing, while regression estimates for the intercept are identical no matter how time is coded. My question is, why? The intercept mean and variance is changing when changing the time coding, and thus I would expect that also estimates of how the intercept predicts outcome variables would change (at least slightly).