
Hurdle model

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 zero's 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 formula_3 is a truncated probability distribution function, truncated at 0.
Hurdle models were introduced by John G. Cragg in 1971, 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, and negative binomial models for the non-zero counts .
Relationship with zero-inflated models.
Hurdle models differ from zero-inflated models in that zero-inflated models model the zeros using a two-component mixture model. With a mixture model, the probability of the variable being zero is determined by both the main distribution and the mixture weight. Specifically, a zero-inflated model for a random variable "x" is
where formula_6 is the mixture weight that determines the amount of zero-inflation. A zero-inflated model can only increase the probability of formula_7, but this is not a restriction in hurdle models.