On Equivalence between a Partial Credit Item and a Set of Independent Rasch Binary Items

Given a Masters partial credit item with n known step difficulties, conditions are stated for the existence of a set of (locally) independent Rasch binary items such that their raw score and the partial credit raw score have identical probability density functions. The conditions are those for the existence of n positive values with predetermined elementary symmetric functions and include the requirement that the n step difficulties form an increasing sequence.