Enoch O. Oladunmoye

Item Response Theory Calibration and Linking: Establishing a Common Measurement Scale Across Samples, Forms and Time

Item response theory (IRT) parameters are identified only up to a linear transformation of the latent scale, so separate calibrations of the same or overlapping items produce estimates that cannot be compared directly. This note reviews how calibrations are connected: the designs that supply the connection (common items, common persons, equivalent groups), the calibration strategies (separate, concurrent and fixed-parameter), the transformation methods (mean-mean, mean-sigma, Haebara and Stocking-Lord), and the treatment of anchor quality, parameter drift, linking error and chains of links. It separates the linking of parameters from score equating and from measurement invariance, and it corrects several conventions that are often misreported, notably the direction of the transformation. A Monte Carlo illustration (500 replications per condition, 1,000 examinees per calibration) shows four things under the conditions studied. Characteristic-curve methods recovered the transformation constants more accurately than moment methods when anchors were stable. Drift in 20 per cent of the anchors biased every unscreened method by about 0.12 logits in the origin constant, and mean-sigma linking was the least stable. A simple automatic screening rule removed most drifted anchors but also removed stable ones in a large share of replications. Linking error was of similar size to the sampling error of a group mean, and it grew along a chain of links, from 0.030 after one link to 0.108 after six. A minimum reporting standard and a record-keeping architecture for item banks are proposed.