Zero Inflated Negative Binomial Regression

Zero-inflated negative binomial regression models a count outcome as a mixture of structural zeros, predicted by a logistic part, and a negative binomial count process that allows overdispersion.

영과잉 음이항회귀는 구조적 0 집단(로지스틱)과 과산포를 허용하는 음이항 횟수 과정을 섞어 0이 많고 분산이 큰 횟수 자료를 설명하는 모형입니다.

My counts have many zeros and the non-zero counts also vary much more than the mean; which model handles both?

0도 많고 0이 아닌 값의 분산도 평균보다 훨씬 큰 횟수 자료에는 어떤 모형이 맞나요?

Zero-inflated negative binomial regression combines a logistic model for an always-zero group with a negative binomial model whose variance μ + αμ² exceeds the mean. It is preferred over the zero-inflated Poisson model when the dispersion parameter α is clearly above zero.

When to use Zero Inflated Negative Binomial Regression

• Counts show both excess zeros and overdispersion
• A structural-zero group is plausible, such as people who never perform the behaviour
• A zero-inflated Poisson model leaves a Pearson dispersion well above 1

When to use something else

• There is overdispersion but no excess zeros; use negative binomial regression instead
• The variance of the non-zero counts equals the mean; use zero-inflated Poisson regression instead

Assumptions and requirements

• Counts in the at-risk group follow a negative binomial (NB2) distribution
• Membership in the always-zero group follows a logistic model
• Observations are independent
• Both parts are correctly specified

What the analysis reports

• Count-part coefficients with incidence rate ratios
• Inflation-part coefficients with odds ratios
• Dispersion parameter α
• AIC compared with a plain negative binomial model
• Vuong test statistic and p value

How to report it

A zero-inflated negative binomial model (α = [value]) was preferred to a standard negative binomial model (AIC = [value] vs [value]; Vuong z = [value], p = [value]); [predictor] was associated with higher counts, IRR = [value], 95% CI [[value], [value]].

Related methods

• Zero Inflated Poisson Regression
• Negative Binomial Regression Model
• Poisson Regression Model

Run Zero Inflated Negative Binomial Regression on Quorant