In the Bayesian hierarchical approach, item and person parameters are estimated using a Markov Chain Monte Carlo procedure, in which cohort-specific item parameters are considered level-1 parameters randomly distributed around overall mean item parameters at level 2. See Fig. 1 for a graph representation of the hierarchical structure of both item and person parameters across cohorts. As the identification constraint, the average difficulty of the items is assumed equal across cohorts. That is, cohorts may differ in mean and variance of the latent trait, and particular item parameters might be different across cohorts, but the average difficulty of items is the same (for example, in case of an IQ test for males and females: the assumption is that overall the test has the same difficulty, although it can be the case that some items are relatively more difficult for males, and other items are relatively more difficult for females). In addition, to identify the variance of the scale the product of the discrimination parameters was fixed at 1. Allowing for such random fluctuations in difficulty and discrimination across cohorts is
