On interpreting the model parameters for the three parameter logistic model

This paper addresses two problems relating to the interpretability of the model parameters in the three parameter logistic model. First, it is shown that if the values of the discrimination parameters are all the same, the remaining parameters are nonidentifiable in a nontrivial way that involves not only ability and item difficulty, but also the guessing parameters. Second, a situation is considered where different researchers analyze the same test with different instances of the three parameter logistic model. One researcher reaches the conclusion that students guess, whereas the other one concludes that students do not guess. Both examples illustrate the many-one relation between statistical models and the probability distributions they imply, which is the overarching topic of this paper.