# How to deal with a response variable calculated from added percentages

I am analyzing a data set where the response variable is the total non-native plant cover within a plot. There are non-native grasses and non-native herbaceous plants with overlapping canopies, so the response variable comes from adding together two percentages (percent cover in each layer within the plot). Therefore, the variable is bounded between 0 and 200. I also have both random and fixed effects.

Can I run a linear mixed model with this response variable, or would that be invalid? Would a GLMM make more sense, and if so what type of distribution would fit?

• This may have some slightly tricky issues with it, since you're dealing with things with (at least potentially) quite different variances. If there's not a lot of variation in mean you may be able to get away with LMM, but if either of the components gets close to 0 or 1, or varies substantially (say between 1% and 30% or something), you'd be better ooff looking to GLMM (a quasi-binomial model, one with an over-dispersion parameter can approximate the mean-variance relationship of a beta). Do you have any exact 0's in your response? – Glen_b Dec 3 '14 at 22:02
• Yes, there are a lot of 0 data points, lots of low numbers, and very few values approaching 200 – Megan Dec 3 '14 at 23:50

A beta won't work with the zeros, unless you do a zero-inflated model. The big problem with the binomial approach on continuous proportions is the $n$, but if you put in some fixed number, the overdispersion parameter should take care of that.