# Analysis strategy for left skewed percentage response variable

I have a dataset that is made up of percentage values of DNA methylation at a number of loci and we are looking to model the relationship with a) a treatment and b) a genomic annotation. The histogram of the data shows a left skewed data set, and as a percentage it obviously has an upper bound of 100.

The treatment predictor is binary (Y/N) and the annotation predictor can take 4 values.

#As I say above, we are trying to model
methylation~treatment+annotation+annotation:methylation


Given there are 0s and the data is a percentage I have tried arcsine and folded root transformations followed by anova. Unsurprisingly, these have had little effect on the tails of the residuals in the qqplot. There is no missing data. So, are there any other potential transformations here or do I need to take a generalized linear model approach?

• Is this counted percentages, that is, do you know numerator and denominator separately? – kjetil b halvorsen Sep 11 '17 at 14:35
• A semiparametric ordinal regression model is worth entertaining. – Frank Harrell Sep 11 '17 at 15:18
• The answer by @FrankHarrell here looks a good guide – plumb_r Sep 12 '17 at 10:40