Modelling category inflation with multiple inflation processes: Estimation, specification, and testing

Zero-inflated ordered probit (ZIOP) and middle-inflated ordered probit (MIOP) models are finding increasing favour in the discrete choice literature. We propose generalisations to these models which collapse to their ZIOP/MIOP counterparts under a set of simple parameter restrictions with respect to the inflation process. These generalisations form the basis of a new specification test of the inflation process in ZIOP and MIOP models. Support for our generalisation framework is principally demonstrated by revisiting a key ZIOP application from the economics literature, and reinforced by the reassessment of an important MIOP application from political science. Our specification test supports the generalised models over the original ZIOP/MIOP ones, suggesting an important role for it in modelling zero and middle-inflation processes.