A comment on Birnbaum's three-parameter logistic model in the latent trait theory

Birnbaum's three-parameter logistic model for the multiple-choice item in the latent trait theory is considered with respect to the item response information function and the unique maximum condition. It is clarified that with models of knowledge or random guessing nature, which include the three-parameter logistic model, the unique maximum condition is not satisfied for the correct answer, and the item response information function is negative for the interval (− ∞,θg). It is suggested that we should useθg as a criterion in selecting optimal items for a specified group of examinees, so that we can practically avoid the possibility of non-unique maxima of the likelihood function on the response pattern given by an examinee in the group.