Understanding offsets for continuous variables I'm currently trying to write a linear model with data from some behavioural experiments with termites.
I started to read Ben Bolker's "Ecological Models and Data in R", which has been a great help.
My main independent variable is a measure of relatedness, and I'm interested in how behaviour between termites changes in response to relatedness. The response variable is continuous and consists of an aggression index, constructed by counts of differently weighted behaviours divided by the total amount of observed behaviours per experiment.
I realised that considering how the response variable is constructed, we would expect a value of 0.1 as the default, when termites are highly related.  This would be at a relatedness value of 0.5, indicating full siblings.
I was looking into how to specify the intercept in linear models with the offset function, and I found a solution to easily tell the model that the baseline response should be 0.1.
However, this seems to apply to the idea that the intercept is specified for when all dependent variables are 0.
This might be a very trivial issue, but how would you specify an intercept for a specific value of a continuous dependent variable? 0 makes sense in many contexts, but with the relatedness measure we use, a value of 0 and it's effect is what we want to investigate, since it represents no relatedness, and it's not the default.
Or more exact: is there a way of writing the lm formula to specify that for a specific value of x, in this case 0.5, one would expect a response y of 0.1?
 A: It's probably not a good idea to impose your a priori expectation about an intercept on a model, just like it's generally not a good idea to force a linear regression through the origin. It sounds like you have an hypothesis that your outcome measure will be 0.1 when your relatedness predictor has a value of 0.5. It would be much better to let the data help you test that hypothesis. Note that an offset() term models a predictor whose slope is fixed at 1, in any event.
There is, however, an important way that an offset could improve your model. You say:

The response variable is continuous and consists of an aggression index, constructed by counts of differently weighted behaviours divided by the total amount of observed behaviours per experiment.

It's often best to model as closely as possible to the original counts. When the total number of possible counts per observation can differ due to different areas sampled, time spans evaluated, or observed total behaviors (as in your case), including the log of the area/time/total_behaviors in an offset() term with a log-link Poisson generalized linear model lets you model the rate as a function of other predictors (as expressed in the regression coefficients) directly. That's nicely explained on this page. That said, an offset isn't always appropriate, as explained in this answer.
