A note on the interpretation and simulation of reparameterized intercepts in constrained versions of the nominal response model

This is a brief expository paper on reparameterized intercepts under constrained variants of the nominal response model, including the generalized partial credit and partial credit models. Such parameterizations are commonly found in item response theory software packages such as flexMIRT®, IRTPRO, and OpenMx / rpf, and both these models are highly popular in educational and psychological testing. A heuristic graphical interpretation is provided. We give examples of how intercepts may be easily generated for Monte Carlo simulation studies, including a brief study to increase generalizability and explore limitations of a recently developed information matrix test to detect misspecification when collapsing adjacent response categories.