# Is an offset term necessary for a count model of a behavior where subjects determine trial length?

We are modeling data from a behavioral study in which subject pairs' conversations are coded for specific types of utterances (say "Type A"). Subjects decide when their trial is over and we count Type A utterances.

However, we disagree about whether we need an offset term for total amount of talk to model the amount of A. I understand that it's definitely necessary when causes external to subjects' behavior determine conversation length. But here, conversation length is influenced by subjects and how they were instructed (the type of instruction is a predictor).

So do we need an offset term here?

You don't explain what statistical model you are fitting. I am going to assume that you are fitting a Poisson or negative binomial glm with a log-link to the number of Type A utterances. I assume that you want to compare counts between instruction types and possibly between other experimental conditions as well.

As always, the appropriate analysis depends on what question you want to answer. If you want to assert that the frequency of Type A utterances per unit time differs between conditions, then you need to include log-conversation-length as an offset in the glm model. Including the offset will account for conversation length so that the coefficient for condition in your glm linear predictor will measure changes per unit time.

On the other hand, if you want to assert that the expected number of Type A utterances over a complete trial period differs between conditions, then you should not include conversation-length as an offset. In this case you do not want to penalize counts for the conversation length because conversation length is part of the response you are wanting to measure.

• Your assumptions are correct and I guess your answer is how one would state the problem more clearly. And it seems like my question really is a pre-statistical, theoretical one: "Do we consider trial length as being influenced by the manipulation or as a trait that subjects take into the trial?" I just thought others might have had this issue before. Thanks anyway! – andreas Aug 16 at 8:41
• @andreas Yes, the choice of which hypothesis to test is scientific rather than statistical, but it does not actually depend I think on whether you believe that length is influenced by manipulation or not. It only depends on which question you want to answer. Of course, the question you want to answer might depend on what you believe, but that is at another level. You could of course test whether trial length depends on experimental conditions. – Gordon Smyth Aug 16 at 9:04