A multidimensional Bayesian item response model is proposed for modeling item position effects. The first dimension corresponds to the ability that is to be measured; the second dimension represents a factor that allows for individual differences in item position effects called persistence. This model allows for nonlinear item position effects on the item side as well as on the person side. Moreover, a flexible loading structure on the two dimensions is allowed. A fully Bayesian estimation procedure is proposed, and its performance is investigated by a simulation study. Further, the model is applied to empirical data collected in the Programme for International Student Assessment 2000 in the reading domain. The additional value of the model's extended flexibility compared to more restrictive models is shown. The findings show that the linear hypothesis of change in performance during a test does not hold in general.