I am trying to test if the proportion of herbivores in spider's diets is related to the proportion of herbivores in their grassland, but am struggling to understand if I should be using a binomial model. Initially I was going to acrsine square root transform the response variable, but having done some further reading, discovered that this transformation is these days superseeded by using a binomial error structure in my model instead. I belive this is correct.... So,
I have 30 spiders per grassland and 5 grasslands.
My current binomial model looks like this:
glm (obs.herbs.in.diet.proportion ~ prop.herb.in.grassland, family=binomial)
The response variable (obs.herbs.in.diet.proportion) is structured by two columns of data along the lines of "successes,failures", using:
obs.herbs.in.diet.proportion<- cbind(proportion.herb.diet, proportion.NOT.herb.diet)
proportion.NOT.herb.diet is obviously not measured, I have just caluclated it to be the inverse of proportion.herb.diet (which I did measure) so that my response variable will work in this R model.
An example of my data is:
grassland proportion.herb.diet proportion.NOT.herb.diet prop.herb.in.grassland 1 0.23 0.77 0.19 1 0.27 0.73 0.19 2 0.49 0.51 0.58 2 0.49 0.51 0.58
As I understand it, I should be using a binomial model because my response variable is bounded by 0 at its lower limit and 1 at its upper limit.
1) Does using a binomial model in this instance sound appropriate, and a better choice than a arcsine squareroot transforamtion?
2) Presumably, having proportional data for a second variable that is the explanatory variable (prop.herb.in.grassland) is not a problem, and does not require any transformation?
Additionally, when I run the model, I received the following warning:
Warning message: In eval(expr, envir, enclos) : non-integer counts in a binomial glm!
3) Does anyone know if this means that my non-integer response variable values are inappropriate in a binomial model?
I used (summary) and get what looks to be a reasonable output and result, except I have large "under-dispersion".... I was worried about overdispersion!
Residual deviance: 5.8082 on 147 degrees of freedom
4) Is under-dispersion a concern and should I take action against it?