Modelling Tobacco Consumption with a Zero-Inflated Ordered Probit Model

It is quite often in economics that we wish to model a discrete ordered random variable, such as bond ratings, employment status, consumption levels and so on. However, traditional approaches to modelling such a discrete ordered random variable ignore both the potential build-up of zero obsersavtions typically observed and, relatedly, that these zeros might come from two distinct situations: non-participants and infrequent consumers. Analogously to the zero inflated (augmented) poisson (and negative binomial) count models, we propose a zero inflated Ordered Probit model. Monte Carlo results suggest that the new model performs well when the data is generated according to such a process and that a Likelihood Ratio-type statistic has good properties in selecting the correct model. Finally, the model is applied to a consumer choice problem of tobacco consumption