Item Response Theory (IRT) is the area of psychometry that deals with the problem of constructing and analyzing psychological tests. By applying a fully Bayesian approach to this methodology, we analyze a data set obtained by administering the Italian translation of the Peabody Picture Vocabulary Test - Revised (PPVT-R) to a sample of Italian children. In the original English version, the items are believed to be in increasing difficulty order. Relying on 1PL and 2PL models and some more parametric extensions to adjust for available covariates, we aim at evaluating if and how much the translation leads to violations of such ordering. Several decision rules for the comparison of item difficulties have been discussed and analyzed.
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