[R] lmer model with continuos non normal response variable, transformation needed?

[arams]

Hi.

I want to do an lmer model but have doubts of what family I should use.
My response variable was originally a proportion, however I standarized it
for each year of data collection (20 in total). After standarizing it I 
checked for normality with the Kolmogorov-Smirnov test, and it turns out
it is not normal. It ranges from -3 to 4. 
Since it is no longer a proportion I can't use a binomial distribution nor a
normal distribution. I'm guessing I have to transform it, but this is a
variable
that has already been standarized. Anny suggestions?
Thank you.
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