# beta regression or glm binomial?

I have a big dataset (first 36 samples in image below) with proportion data (Proportion) that refer to the substrate that some insects eat: for example sample 1 eats 100% wood, sample 25 eats apx 81% wood. These data originate from counts which I transformed to proportions in order to be able to merge with some older data (that were already proportions). As a result of that not every sample is independent because for example samples 19 and 30 refer to the same insect, which does not eat any wood (0%) but eats exclusively (100%) soil.

I would like to examine the effects of the type of substrate and the group (phylogeny) the insects belong to. And in order to do that I would like to fit everything in a model. After looking around a little bit, I realized that my options are either beta regression or glm binomial. I already tried a glm-binomial model but the results made no sense at all! Categories that I expected to see huge differences (and be highly significant) were not significant at all...

On the other hand, I was under the impression that I cannot use beta regression because I have lots of '1' and '0'

Any advice on what to do and how to do it will be greatly appreciated... :)

• You may want to look at Dirichlet regression, which is specifically good for composition data cran.r-project.org/web/packages/DirichletReg/index.html – Sextus Empiricus Nov 9 '17 at 19:54
• Can your huge differences be demonstrated in a simple overview of the data? What went wrong with the binomial data? How did you set it up? – Sextus Empiricus Nov 9 '17 at 19:56
• How does your data really look like? Your current display of the first 36 samples does not show the relation between sample 19 and 30. Do you have somewhere else more data about your experiments? What is exactly known? Or not known, for instance are there gaps in the data? – Sextus Empiricus Nov 9 '17 at 20:01
• thanks everyone for the quick responses. I tried to do it in R using sth like this: code fit <- glm(delta.CT\$Value ~ interaction, family=binomial, data=all_forage) – Panos Sapou Nov 9 '17 at 20:19
• I have now added a figure on top showing how the data look after fitting them in that binomial glm. As you can see (i guess) the biggest problem is the huge error bars that I get for the categories that are absolutely 0. I guess i could solve that by adding sth like 0.0001 to every value? or is this too arbitrary? In addition, I am still not convinced that what I am doing is the right approach! Is binomial the right one? should I do sth else? and how to choose? If someone wants to play with the data, I am happy to send a link – Panos Sapou Nov 9 '17 at 20:24

• Ok, then I would go for a GLM and posthoc comparisons with the R package multcomp. – gaballench Nov 10 '17 at 13:24