# 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

With such a wide variation in the sum of proportions, You definitely need to worry about the variance changing.

If you had single proportions rather than a sum, and no zeros you could use a beta model.

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.

The big problem with the sum is that you don't know if "99%" is "50%+49% or "99% + 0%" - and the implied variance of the two is vastly different.

If you have the individual proportions, then you can do it easily enough, as long as you can assume independence (the fact that they can sum to 200% suggests that might be possible)

It's hard to say much more without more details about your data.