Does anyone have any suggestions (short of transforming my data) on how to fit a mixed effect model to a continuous response variable that is left-skewed? Other words, what probability density function should be used? My ultimate goal is to fit a nice global model so I can perform model selection using maximum likelihood estimation. Because the data are so left skewed I'm assuming Gaussian is out of the question. I've looked into skew-normal distributions but can't figure out how to incorporate it into a model in R. I'm using lme4 to analyze my data. I've also thought about using generalized linear mixed models with a Gamma distribution but everything I've looked at for gamma distributions are right skewed data. And when I do try to analyze with a Gamma distribution I get an error. Attached is a histogram of my distribution and also my residuals when I fit a linear mixed-effect model. Clearly the residuals are no good. Any advice would be awesome. Thanks!