A comparison of linking and concurrent calibration under item response theory

Applications of item response theory (IRT) to practical testing problems, including equating, differential item functioning, and computerized adaptive testing, require a common metric for item parameter estimates. This study compared three methods for developing a common metric under IRT: (1) linking separate calibration runs using equating coefficients from the characteristic curve method, (2) concurrent calibration based on marginal maximum a posteriori estimation, and (3) concurrent calibration based on marginal maximum likelihood estimation. For smaller numbers of common items, linking using the characteristic curve method yielded smaller root mean square differences for both item discrimination and difficulty parameters. For larger numbers of common items, the three methods yielded similar results.