I've constructed a Negative Binomial Regression wherein I predict the number of words an individual will find from a set of seven letters based on the average frequency of words that the set of letters can produce, the total number of words that set of letters can produce, and the participant's score on a vocabulary test. In R:
WholeModel <- glm.nb(NumWordsFound ~ AvgFrequency * TotalWords + VocabScore, data = p)
My question is in regards to the inclusion of an offset term. Right now my model does not contain an offset term as the amount of time each participant had to produce words was exactly the same. While I would like to see the effect of the total number of words the set of letters could produce on actual productivity, should I instead include that number as an offset value?