I'm interesting in conducting a latent growth curve analysis to model change in the proportion of days abstinent from alcohol over 4 time points. I was wondering if anyone has suggestions for how to go about modeling a proportion. I have consided an arcsin transformation, however about 40% of the values on the outcome are zero, which makes an arcsin transformation less effective and not worth the difficulty it creates in the substantive interpretation of the coefficients for a change in an arcsin transformed variable. I have also considered creating a binary variable (never abstinent vs. all others), but I am reluctant to do so because there is considerable variation in proportion of days abstinent for the other 60% of the subjects. I would hate to group them together and treat them the same, and I also might have some trouble justifying why I did so.
I assume that you are using a proportion rather than the number of days because the number of days differs for each individual. A transformation, for example a logit transforatmion, will not help with the problem of a preponderance of zeroes. For this problem, I would either use a censored normal model or a two-part model.