A hurdle model is a class of statistical models where a random variable is modelled using two parts, the first which is the probability of attaining value 0, and the second part models the probability of the non-zero values. The use of hurdle models are often motivated by an excess of zeroes in the data, that is not sufficiently accounted for in more standard statistical models.
In a hurdle model, a random variable x is modelled as
where is a truncated probability distribution function, truncated at 0.
Hurdle models were introduced by John G. Cragg in 1971,[1] where the non-zero values of x were modelled using a normal model, and a probit model was used to model the zeros. The probit part of the model was said to model the presence of "hurdles" that must be overcome for the values of x to attain non-zero values, hence the designation hurdle model. Hurdle models were later developed for count data, with Poisson, geometric,[2] and negative binomial[3] models for the non-zero counts .
^Cragg, John G. (1971). "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods". Econometrica. 39 (5): 829–844. doi:10.2307/1909582. JSTOR 1909582.
^Mullahy, John (1986). "Specification and testing of some modified count data models". Journal of Econometrics. 33 (3): 341–365. doi:10.1016/0304-4076(86)90002-3.
^Welsh, A. H.; Cunningham, R. B.; Donnelly, C. F.; Lindenmayer, D. B. (1996). "Modelling the abundance of rare species: statistical models for counts with extra zeros". Ecological Modelling. 88 (1–3): 297–308. doi:10.1016/0304-3800(95)00113-1.
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