Zero Inflated Poisson Regression

Zero-inflated Poisson regression models a count outcome as a mixture of structural zeros, predicted by a logistic part, and a Poisson count process, predicted by a log-linear part.

영과잉 포아송회귀는 항상 0인 구조적 집단(로지스틱)과 포아송 횟수 과정을 섞어 0이 지나치게 많은 횟수 자료를 설명하는 모형입니다.

My count outcome has far more zeros than a Poisson model predicts; how can I model the extra zeros?

횟수 자료에 0이 포아송 모형이 예측하는 것보다 훨씬 많은데, 이 초과 0을 어떻게 모형화하나요?

Zero-inflated Poisson regression treats each unit as belonging either to a group that always reports zero or to a group whose counts follow a Poisson distribution, and models both parts with predictors. The Vuong test, AIC and the observed versus predicted share of zeros help compare it with an ordinary Poisson model.

When to use Zero Inflated Poisson Regression

• Counts contain more zeros than a Poisson model with the same mean would produce
• There is a plausible reason some units can never have the event
• Apart from the extra zeros, the variance of the counts is close to the mean

When to use something else

• Counts remain overdispersed after accounting for the zeros; use zero-inflated negative binomial regression instead
• Zeros arise only from one process with no structural-zero group; use Poisson or negative binomial regression instead

Assumptions and requirements

• Counts in the at-risk group follow a Poisson 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
• Log-likelihood and AIC for the model and a plain Poisson model
• Vuong test statistic and p value
• Observed and predicted proportion of zeros

How to report it

A zero-inflated Poisson model fitted better than a standard Poisson model (AIC = [value] vs [value]; Vuong z = [value], p = [value]); in the count part, [predictor] increased the expected count, IRR = [value], 95% CI [[value], [value]].

Related methods

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

Run Zero Inflated Poisson Regression on Quorant