fractions or wholes for the slope in a latent growth model? When trying to model a latent growth model in lavaan and AMOS respectively, they seem to approach the time spacing of the slope estimates differently. Lavaan defaults to whole numbers increasing by time period: 0, 1, 2, 3, ..., while AMOS seems to default to fractions: 0, 0.11, 0.22, 0.33, ... . What differences in results does this create? What is the logic behind each way of modeling time?
 A: Short Answer
Specifying time-scores as 0, 1, 2…, or 0, 0.11, 0.22, 0.33…, or 0, 2, 4, 6… will all let you specify linear models with the same parameter estimates (except the values of any freely estimated time scores) if all time points were measured at equal time intervals.
Longer Answer
Latent Growth Models (LGM) incorporate time through fixed factor loadings.  A typical linear LGM will include two growth factors: an intercept that represents the initial status of the outcome variable, and a slope representing the rate of change over the time period of interest.  Time is coded in a way that expresses hypothesised change trajectory.  The origin (i.e. 0) of the time scale is placed at the time point that represents “initial status”, which could but not necessarily be the first measuring time point.  intercept factor loadings are fixed at zero for all time points while loadings for the slope factor (also known as “time scores”) for each time point increases in a linear fashion.  In a linear model where measurements took place at equal intervals, time scores could be specified as 0, 1, 2, 3…, or 0, .1, .2, .3; if measurement intervals are not equal, time scores could be adjusted to reflect that (e.g. time scores for 1, 4, 8 months after the initial measurement can be specified as 0, 1, 2.33).  This also means that if change is hypothesised to be non-linear, time scores can be adjusted to reflect that as well, e.g. 0, 1, 4, 9 for quadratic, 0, 0.69, 1.10, 1.39 for logarithmic.
If you allow the time score of a certain time point to be freely estimated, the estimated time score will be relative to the scale that you specify your time scale (0, 1, 2... or 0, 0.11, 0.22), so the absolute value of that parameter estimate will be different, but that should not change your overall model results.  This is also why it is important to also report how you have specified your time scores.
It seems you are trying to do LGM in R and AMOS.  However, there are some really helpful materials on Mplus website with video lectures and handouts (Topic 3) very nicely explaining these concepts, and I think they will be quite helpful despite software differences.
