Incomplete data and item parameter estimates under JMLE and MML estimation

Although nonrandomly missing data is readily accommodated by joint maximum likelihood estimation (JMLE), it can theoretically be problematic for marginal maximum likelihood (MML) estimation. One situation of nonrandomly missing data, vertical equating using an anchor test, was simulated for this study under several conditions. The items from two test forms were calibrated simultaneously using JMLE and MML methods. Under MML, when the different ability distributions of the students taking the forms were not taken into account, the item difficulty parameters were overestimated for the items on the less difficult form and underestimated for the items on the more difficult form.