Optimal item discrimination and maximum information for logistic IRT models

Items with the highest discrimination parameter values in a logistic item response theory model do not necessarily give maximum information. This paper derives discrimination parameter values, as functions of the guessing parameter and distances between person parameters and item difficulty, that yield maximum information for the three-parameter logistic item response theory model. An upper bound for information as a function of these parameters is also derived. An algorithm is suggested for the maximum information item selection criterion for adaptive testing and is compared with a full bank search algorithm.