Generalized linear mixed model, continuous variable, zero values


I have conducted a longitudinal study with four waves of data collection. My data have a nested structure: there are four levels in my data (time - level 1, student - level 2, class - level 3, school - level 4). Student sample size = 51 (no missing values)

I want to fit generalized linear mixed models to test fixed and random effects on my dependent variables. I am using SPSS.

I have encountered a problem regarding my dependent variables which are continuous, non-normally distributed and contain 0 values. What type of distribution should I use? I was going to use Gamma (log link) distribution but from what I have seen, there is no distribution in SPSS that "allows" values equal to zero.

As a solution, I tried to transform my data, but log transformation doesn't allow zero values either.

Is there any solution to this?

Thank you for your help.
I think that a zero inflated Poisson model is for count data, but my data are continuous. I guess a zero inflated gamma model could work but there is no such option in SPSS.