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

Bert Gunter gunter.berton at gene.com
Thu Jun 26 20:12:58 CEST 2008

If I understand you correctly, then to paraphrase what Brian Ripley has
stated in recent posts, it is not the (possibly transformed) response that
you want to be normal, but rather the error distributions. Your response
presumably contains systematic variation due to your covariates (your
model). So using the K-S test as I think you describe is nonsense.

I suggest you forget about testing for normality, transform your data
"sensibly" (which is quite often not at all, even for proportions or
counts), fit your model, and see what you get. If you're still hung up on
distributional assumptions, check residual plots. Distributional assumptions
are often most critical for inference, which for glmm's is problematic
anyway, due to the crudeness of the asymptotic approximations (paraphrasing
Doug Bates, now). They may or may not have a large impact on estimation,
which is generally the greatest concern. Sensitivity analyses are a way to
examine this.

Bert Gunter
Genentech Nonclinical Statistics

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of arams
Sent: Thursday, June 26, 2008 9:39 AM
To: r-help at r-project.org
Subject: [R] lmer model with continuos non normal response variable,
transformation needed?


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
that has already been standarized. Anny suggestions?
Thank you.
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