Item characteristics of tests constructed by linear programming

Abstract

In the present paper, linear programming was used to select items from item pools based on one-, two-, and three-parameter models so that a target test information function was reached. The primary interest was in the distributional characteristics of the items thus selected. The results suggest that the linear programming approach focuses on the "worst feature" of the target information function (i.e., the extremes of a uniform target and the maximum of a peaked target). The values of the parameters of the selected items tend to form clusters. For uniform targets, these clusters are associated with the extremes of the target range, whereas for peaked targets they are associated with the maximum of the target. Selecting items from an item pool by linear programming appears to be a useful addition to the test constructor’s repertoire. However, additional refinement may be needed to obtain a specific distribution of item parameters for a given test. Index terms: Item response theory, Item selection, Linear programming, Target information function.