In some tests, examinees are required to choose a ﬁxed number of items from a set of given items to answer. This practice creates a challenge to standard item response models, because more capable examinees may have an advantage by making wiser choices. In this study, we developed a new class of item response models to account for the choice effect of examinee-selected items. The results of a series of simulation studies showed: (1) that the parameters of the new models were recovered well, (2) the parameter estimates were almost unbiased when the new models were ﬁt to data that were simulated from standard item response models, (3) failing to consider the choice effect yielded shrunken parameter estimates for examinee-selected items, and (4) even when the missingness mechanism in examinee-selected items did not follow the item response functions speciﬁed in the new models, the new models still yielded a better ﬁt than did standard item response models. An empirical example of a college entrance examination supported the use of the new models: in general, the higher the examinee’s ability, the better his or her choice of items. Copyright © 2012 by the National Council on Measurement in Education.