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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?

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  • $\begingroup$ #3 is addressed here: stackoverflow.com/q/12953045 $\endgroup$
    – shadowtalker
    Commented Jan 14, 2015 at 12:27
  • $\begingroup$ See also Appropriate GLM when response variable is proportion, but not binomial. (Glen's comment there is a good enough answer.) The binomial model proper is for counting how many times something does happen out of the known number of times it can happen. $\endgroup$
    – Scortchi ♦
    Commented Jan 14, 2015 at 13:16
  • $\begingroup$ Thanks for these points. Each of my spiders is sampled once for the nitrogen in its tissues. So if it has a herb.proportion value of 0.35 that means 35% of its nitrogen is from herbivore sources. So, in this sense, could it be considered that the spider has undergone multiple trials (i.e. all the feeding events within the lifetime of the spider) and these total to 100%, and so we can view this as the spider having 0.35 successes to 65 failures? My apologies I'm unsure how to interpret if my data is actually binomial or not!! Its certainly proportional. $\endgroup$
    – user2890989
    Commented Jan 14, 2015 at 15:35

1 Answer 1

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You can certainly use a binomial model when your response variable is a proportion. However, you then need to weight each observation by the number of trials that each observation represents, if you are to get an equivalent result to the formulation where you supply the positive and negative counts. In your case, you should weight by the number of spiders that are represented by the proportions in each observation.

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  • $\begingroup$ (+1) It could be though, that each observation is a single spider, & there's no "number of trials" associated with the proportion of herbivores in its diet. Perhaps the OP will clarify. $\endgroup$
    – Scortchi ♦
    Commented Jan 14, 2015 at 13:51
  • $\begingroup$ Thanks for these comments. Yes, each observation is a single spider so there are no "number of trials" to weight each spider by. So if a single spider has a proportion of 0.35 then philosophically / biologically, this represents that of 100 food units 35 of these are herbivores. In this context, would 100 be the number by which i could weight each spider observation? And presumably when you mean weight each observation, this is where I weight "successes,failures", so in this instance 35,65 (=100). $\endgroup$
    – user2890989
    Commented Jan 14, 2015 at 15:16
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    $\begingroup$ @user2890989: Why not 10 or 1000 "food units"? It's just not a binomial model, though you could use a quasibinomial GLM: What is Quasibinomial?. And consider robust standard error estimates. $\endgroup$
    – Scortchi ♦
    Commented Jan 14, 2015 at 16:47

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