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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?

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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).

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  • $\begingroup$ Thanks for your answer Bruna. I'm only trying to model total cover of invasives (univariate response). However, due to vegetation stratification, cover of invasives (or total cover) can exceed 100%. Moreover, proportion does not seem adequate because it would down weigh cover of invasives in plots where there is more important cover of sown species and there is not reason to do so; 30% of invasives in a plot of total cover of 110% is the same as 30% in a plot of total cover of 150%. $\endgroup$ Nov 27, 2017 at 14:25
  • $\begingroup$ I'm starting to think the correct way to go would be to consider % cover of invasives as a count and model it with a GLM with Poisson distribution, not taking into account % cover of sown species (or total cover). $\endgroup$ Nov 27, 2017 at 18:11

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