Multiple Group IRT

Abstract

The extension of item response theory to data from more than one group of persons offers a unified approach to such problems as differential item functioning, item parameter drift, nonequivalent groups equating, vertical equating, two-stage testing, and matrix-sampled educational assessment. The common element in these problems is the existence of persons from different populations responding to the same test or to tests containing common items. In differential item functioning, the populations typically correspond to sex or demographic groups; in item parameter drift, to annual cohorts of students; in vertical equating, to children grouped by age or grade; in nonequivalent groups equating, to normative samples from different places or times; in two-stage testing, to examinees classified by levels of performance on a pretest; and in matrix-sampled educational assessment, to students from different schools or programs administered matrix-sampled assessment instruments. In all these settings, the objective of the multiplegroup analysis is to estimate jointly the item parameters and the latent distribution of a common attribute or ability of the persons in each of the populations.