Item Pool Construction Using Mixed Integer Quadratic Programming (MIQP)

Overview

This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information functions across pools and within each content area. The study addresses two important practical questions: (a) how many evaluation points should the objective functions of the MIP/MIQP models use when the targets have numerous non~N(0,1) distributions, and (b) how should the solver be structured when an item bank is gigantic? The study finds that all three MIP/MIQP models could be used effectively to construct highly parallel item pools and content bins when five evaluation points were used. Utilization of these techniques can replace current laborious manual pool construction methods.