Linear (mixed-effects) model for skewed and negative data / residuals

I am currently fitting a linear mixed-effects model to my data where the outcome variable can have both positive and negative values (integers).

The issue now is, that my outcome data is skewed with a heavier tail in the positive direction. As a consequence, my residuals (as plotted with a qqnorm plot) deviate from a qq line in both directions.

Usually, I would go ahead and do something like a log-transformation, but in this case this is not possible as I have both positive and negative data. Using a generalized linear mixed-effects model does not solve my problem as well due to similar reasons (negative data).

A further thing to note is that I have a lot of data (multiple millions of samples).

• 1. If your data is ordinal, "negative" makes no sense. You can just add a constant because the numbers are meaningless. 2. Data cannot be skewed in both directions. 3. Log transformation of ordinal data makes no sense. – Peter Flom Oct 7 '15 at 21:26
• 1.) You are right, it is not ordinal per-se; it is a simple integer variable with positive and negative values. 2.) Skewed positively – apehead Oct 7 '15 at 22:06

• If you actually have ordinal data, you should consider fitting an ordinal model! e.g ordinal::clmm() in R.
• The robustlmm package in R fits robust LMMs (see the vignette, i.e. vignette("rlmer",package="robustlmm") once you have downloaded/installed/loaded the packages).