Modelling % cover that do not add up to 100% : GLM distribution families

Question

I have an experimental set-up that consists in studying the impact of diversity of plant mixtures on the development of invasive species. On each plot, we recorded the % cover of each species which were then split in two categories: sum of invasives and sum of sown species. The "problem" is that the total cover (invasive + sown) does not add up to 100% because of the different vegetation strata (clover under common yarrow for ex).

Total cover of invasives and sown species is always >0 and not necessarily integers. Total cover of invasives has a mean of 41% and a SD of 29%.

After some research, three solutions (if any) seem to exist to model this:

• GLM with binomial distribution family (to take into account overdispersion)

  glm.1=glm(cbind(Tot_cov_weeds,Tot_cov_sown)~diversity,family=quasibinomial,data=dat)
  

• GLM with quasipoisson distribution family (to take into account the fact the response is not necessarily an integer) and cover of unsown species (or total?) as a offset

  glm.2=glm(Tot_cov_weeds~diversity+offset(Tot_cov_sown),family=quasipoisson,data=dat)
  

• GLM with gamma distribution family

  glm.3=glm(Tot_cov_weeds/Tot_cov_total~diversity,family=gamma,data=dat)
  

According to you, what model (if any) is correct?

Answer 1

To me, none of your options is correct. I didn't quite understood the context, but if your trying to model a PROPORTION, one adequate model is the Beta model, which was proposed by the Professors Silvia P. Ferrari and Francisco Cribari.

Also, if you're trying to model two response variables simultaneously, I recommend a Multivariate Covariance Generalized Linear Models approach, which was introduced by Professor Wagner Hugo Bonat, and can be done in R using the "mcglm" package (available on CRAN).