Estimation, Specification and Testing in Middle- and Zero-Inflated Ordered Probit Models

Zero-inflated ordered probit (ZIOP) and middle-inflated ordered probit (MIOP) models are finding increasing favour in the discrete choice literature. Both models consist of a mixture of binary and single ordered probit equations, the combination of which accounts for an "excessive" build-up of observations in a given choice category. 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. The appropriateness and implications of our generalisations are demonstrated by using two key empirical applications from the economics and political science literatures. Likelihood ratio (LR) and Lagrange multiplier (LM) specification tests lead us to support the newly proposed generalised models over the ZIOP/MIOP ones, and suggest a role for our generalisations in modelling zero- and middle-inflation processes.