Comparing different ways of specifying the same response variable

Question

I have a question about different ways of specifying a response variable in a model and what effect this could have on my results.

In my example, I wanted to model the number of times a bird visits a nest to feed its young during a set period of time. So the data would be a set of counts, let's call it Number of Visits. Now one thing that might affect how many visits an adult makes is the size of the brood (Brood Size). I have seen two ways of modeling this in the literature:

1. Have Number of Visits as the response variable and include Brood Size as an explanatory variable.
2. Have Number of Visits/ Brood Size as the response variable and include other explanatory variables as appropriate.

How would these approaches differ and is either superior to the other, would each approach give a different answer?

I can see that using each approach you might be modeling subtly different things. In option 1) you seem to be modeling the overall number of visits while controlling for brood size, whereas in option 2) you seem to be measuring the per capita number of visits.

Answer 1

Unless it is common practice, I would avoid working with ratios as a response. You already have a response rate, visits/per unit of time. This is a typical count regression response-usually but not always fit with Poisson regression. I would build a model with brood size and the other explanatory variables.