Data for discrete ordered random variables are often characterised by "excessive" zero observations. Traditional ordered probit models have limited capacity in explaining the preponderance of zero observations, especially when the zeros may relate to two distinct situations of non-participation and infrequent participation (or consumption), for example. We propose a zero-inflated ordered probit (ZIOP) model using a double-hurdle combination of a split (probit) model and an ordered probit model

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... hich, potentially, relate to different sets of covariates. Monte Carlo results suggest that the new model performs well. Finally, the model is applied to a consumer choice problem of tobacco consumption.