Hurdle and Two-Part Models

Hurdle and two-part models split an outcome with many zeros into a binary model for crossing zero and a separate model for the size of positive values, then combine them into an unconditional mean.

허들·이부분 모형은 0이 많은 결과를 '0을 넘는가'의 이항 모형과 양수일 때의 크기 모형으로 나눠 추정하고, 둘을 곱해 무조건 평균을 냅니다.

Many people spent nothing and the rest spent varying amounts; how do I model spending?

지출이 0인 사람이 많고 나머지는 금액이 제각각인데, 지출을 어떻게 모형화하나요?

A logit model estimates the probability of a positive value, and a zero-truncated count model or a log-normal or gamma model describes the positive amounts. Multiplying the two parts gives the expected value, from which average marginal effects of each predictor are computed.

When to use Hurdle and Two-Part Models

• Zeros come from a separate decision process, such as whether to use a service at all.
• Health care costs, expenditures or counts have a spike at zero and a skewed positive part.
• Predictors may affect participation and intensity differently.

When to use something else

• Some zeros are believed to come from the count process itself as well as a structural zero group; use zero-inflated models.
• There are almost no zeros; use a single count or gamma model.

Assumptions and requirements

• The zero and positive parts are conditionally independent given predictors.
• The positive part follows the chosen distribution (truncated Poisson or NB2, log-normal or gamma).
• For log-normal smearing, homoskedastic errors on the log scale.

What the analysis reports

• Logit coefficients for P(y > 0)
• Positive-part coefficients (count, log-OLS or gamma)
• Average marginal effects on the unconditional mean split by part
• Log-likelihood and AIC, with Poisson, negative binomial and zero-inflated AICs for count outcomes

How to report it

A hurdle negative binomial model for [outcome] (N = [value], [value]% zeros; AIC = [value]) gave an average marginal effect of [predictor] on the expected count of [value].

Related methods

• Zero Inflated Poisson Regression
• Zero-Truncated Count Regression
• Tobit Regression

Run Hurdle and Two-Part Models on Quorant