Getting to grips with the shape of item characteristic curves in Baker, I came across the concept of a three parameter model, where the third parameter allows the fact that candidates will successfully guess the right answers to some items, per Birnbaum. This is something I'll get around to researching some day. My preliminary theory is that "guessing" is a fundamental part of candidate performance, not simply because, (say) when doing a multiple choice test I've a one-in-four (or five) chance of getting it right, but because it may not be pure guesswork, but what is usually called an "inspired" guess, the correct answer lurking in the candidate's subconscious and recalled at need. In other words, in a real life language situation, they would recall the correct usage. Most language learners will be able to provide anecdotes of situations where, say, they remembered a bit of vocabulary from God-knows-where, or were unexpectedly able to use the subjunctive when three sheets to the wind.
Baker, Frank (2001). The Basics of Item Response Theory. ERIC Clearinghouse on Assessment and Evaluation, University of Maryland, College Park, MD.
Birnbaum, A. “Some latent trait models and their use in inferring an examinee’s ability.” Part 5 in F.M. Lord and M.R. Novick. (1968).Statistical Theories of Mental Test Scores. Reading, MA: Addison-Wesley.
NB: I'm going to start using the label CALT for this topic, the L being for Language.
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