Count vs. continuous predictors in Poisson regression with offset

Question

I'm having a conceptual problem related to using different types of predictor variables (i.e., count data vs. continuous data) in Poisson regression.

My field method was walking transects and counting items. For an example, let's imagine we're counting the number of scats as the response variable. Because my transects were different lengths, I used an offset term (reflecting the number of houses along the transect) as follows:

mod1 <- glm(ScatCount ~ [predictors], offset = log(transect_length), data = XX, family = Poisson).

I have two broad types of predictors. One type is items i counted along transects (e.g., number of litter items). The other category of predictors is 'demographic characteristics of the neighbourhood in which the transect was found'. For example, 'average house size'.

I am uncomfortable here because 'count of litter items' is a predictor, but it should also depend on the length of the transect. By contrast, 'average house size' is a predictor, but it should NOT depend on the length of the transect.

I know that including transect length as an offset term accounts for differences in the response variable (i.e., scat count) based on effort (i.e., transect length), but my understanding is that it does not affect predictor variables. (This understanding is supported by this exchange: Does the inclusion of a model offset convert predictor variables from counts to rates?) If this understanding is correct, should I be transforming my count predictor variables (e.g., by dividing by transect length) prior to using them?

Thanks you so much! Also it is my first time posting--sorry if I goofed on anything!

Answer 1

An offset is used when the nature of the study requires a slope of 1 to account for some extensive property of the data. That's true in your case for log(transect_length), but it's not true for count of litter items.

Think about why you used average house size instead of total size of houses as a predictor. Similarly, you should use some form of average litter item count as a predictor once you've dealt appropriately with transect_length. You are correct that the offset term won't do that for you.