# binomial vs betareg? glm for y=ratio

https://docs.google.com/spreadsheets/d/1e_XOgTv1flSFFleHSwUJJPBzBdd9VPXRaZc2oukwtrE/edit#gid=0[data][1]

I'm using glm to evaluate the response of mammal species to different % of forest cover. My response variable is the ratio of: number of species in each site/regional num of species (Patch_richness/Regional_richness). The outcome takes values 0-1 (0, 0.1, 0.5, 0.3, 1, .....). I've been told to use binomial family, but I'm not sure if this is appropiate. For instance, glm with binomial request "y" to be binary, so I can´t do:glm(Richness_prop~FOREST500+km,family=binomial). I've found that I can run the model as: glm(cbind(Patch_Richness, Regional_richness) ~ FOREST500+km, family=binomial) but according to R docs this means: cbind(Success,failures), which I think is not exactly the nature of my data. I was also able to run the model as: glm(Richness_prop~FOREST500+km,family=binomial,weights=Regional_Richness), and these two models provide different outcome (coeff, AIC).

So my question is, is it appropiate to use binomial family? or should I use beta distribution (betareg)? which I understand, it is suitable for a continuous y variable which takes values from 0 to 1.

Thanks!

## 1 Answer

For instance, glm with binomial request "y" to be binary,

The appropriate model call when you have multiple trials is

model = glm(cbind(Patch_Richness, Regional_Richness - Patch_Richness) ~ FOREST500 + km, family = binomial(), data = d)


The model call

glm(Richness_prop~FOREST500+km,family=binomial,weights=Regional_Richness)


Does not do what you want it to.

Beta regression is more appropriate when the denominator of the proportion is not a whole number. The betareg documentation has some good examples to do with oil refining.