Key points are not available for this paper at this time.
Rianne Janssen, Francis Tuerlinckx, Michel Meulders, Paul de Boeck, A Hierarchical IRT Model for Criterion-Referenced Measurement, Journal of Educational and Behavioral Statistics, Vol. 25, No. 3 (Autumn, 2000), pp. 285-306
Janssen et al. (Sat,) studied this question.