Hurdle Model for Count Data
Also known as: hurdle count model, two-part count model, zero-truncated count model, Engel Modeli (Hurdle Model)
The hurdle model is a two-part count-data model introduced by Mullahy (1986). A first stage models the binary choice of crossing a hurdle (a zero versus a non-zero count), and a second stage models the strictly positive counts with a zero-truncated distribution such as a zero-truncated Poisson or negative binomial.
Key highlights
- Handles count data with excess zeros by modelling the zero/non-zero gate and the positive counts separately.
- Cleanly separates the hurdle-crossing process from the quantity process, giving two sets of interpretable coefficients.
- Unlike zero-inflated models, all zeros are attributed to a single first-stage process, which can match the data-generating story more directly.
Intuition
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How it works
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When to use it
Use a hurdle model for count outcomes that contain far more zeros than a plain Poisson model can accommodate, especially when the zeros arise from a single process rather than from a mixture. It suits a reasonable sample (at least about 50 observations), cross-sectional or panel data, and settings where the decision to have any count and the decision about how many are plausibly distinct. The hurdle structure assumes the two processes — clearing the hurdle and the quantity afterwards — are separate, so it differs from zero-inflated models in that all zeros come from the first stage. Compare fit against zero-inflated Poisson and negative binomial models using AIC or BIC.
Strengths & limitations
- Handles count data with excess zeros by modelling the zero/non-zero gate and the positive counts separately.
- Cleanly separates the hurdle-crossing process from the quantity process, giving two sets of interpretable coefficients.
- Unlike zero-inflated models, all zeros are attributed to a single first-stage process, which can match the data-generating story more directly.
- Assumes the two processes (crossing the hurdle and the resulting quantity) are independent, which may not hold.
- Requires a reasonable sample size (at least about 50) to estimate both stages reliably.
- Choosing between hurdle, zero-inflated, and ordinary count models needs explicit comparison via AIC or BIC rather than a single fit.
Common pitfalls
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Applications
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Frequently asked
How does a hurdle model differ from a zero-inflated model?
In a hurdle model all zeros come from the first (binary) stage and the positive counts come from a zero-truncated distribution. A zero-inflated model instead mixes two sources of zeros — structural zeros and ordinary count zeros — so its zeros can arise from both the inflation component and the count component.
What distribution does the second stage use?
The positive-count stage uses a zero-truncated count distribution, typically a zero-truncated Poisson or zero-truncated negative binomial. The negative binomial variant is preferred when the positive counts are overdispersed.
How do I choose between hurdle, zero-inflated, and negative binomial models?
Fit the candidate models and compare them with AIC or BIC, alongside checks on how well each reproduces the observed proportion of zeros. The hurdle structure is most appropriate when a single process governs whether any count occurs.
How large a sample do I need?
Because two stages are estimated, a reasonable sample is needed — roughly 50 observations or more — so that both the binary stage and the zero-truncated count stage have enough information.
Sources
- 1.Mullahy, J. (1986). Specification and Testing of Some Modified Count Data Models. Journal of Econometrics, 33(3), 341–365.
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Cite this page
ScholarGate. (2026, June 1). Hurdle Model. ScholarGate. https://scholargate.app/statistics/hurdle-model