In the semi-continuous growth model why is the default scaling for the non-zero part of the continuous variable to take the log? I realize that I can get around this using the transform option, but I'm just curious.
Three reasons. One is that a log normal distribution is in line with the outcome having positive values. The other is that often one wants the tail of the in this case very skewed distribution to not have too large an influence, making linearity more reasonable. Third, Olsen-Schafer recommend it in their JASA article. Other transforms are also possible.