Effects of Calibration Approach and Ability Distribution on IRT Observed-Score Equating

A central question in item calibration concerns the metric on which final item parameter estimates (IPEs) are expressed. One assumes that IPEs are expressed on the scale of the population (prior) distribution, typically N(0,1). Another perspective assumes that this metric is defined by the scale of the posterior ability distribution (PD) produced by the calibration process. While this distinction may have minimal impact in many standard applications of Item Response Theory (IRT), it can have meaningful implications in contexts such as test equating. In IRT observed-score equating, the choice between a prior and a PD can influence the shape of fitted score distributions and, ultimately, the resulting conversion tables. This study investigates the issue by (a) comparing widely used calibration methods and software programs, and (b) examining how resulting differences in IPEs and PDs, combined with different assumptions about the ability distribution, affect fitted score distributions and equating outcomes.