Negative Binomial Regression Model

Negative binomial regression is a count-data regression model that relates a non-negative integer outcome to predictors while allowing the variance to exceed the mean (overdispersion).

음이항 회귀분석은 분산이 평균보다 큰 과대산포를 허용하면서 음이 아닌 정수 결과변수(빈도)를 예측변수와 연결하는 가산자료 회귀모형이다.

How do I model a count outcome when the variance is larger than the mean?

분산이 평균보다 큰 빈도(카운트) 결과변수는 어떻게 모형화하나요?

Negative binomial regression models counts such as visits, incidents, or citations through a log link and adds a dispersion parameter so the variance can exceed the mean. It fits count outcomes where a Poisson model is overdispersed, which is common in real data.

When to use Negative Binomial Regression Model

• Count outcomes such as number of hospital visits or defects
• Poisson model shows overdispersion (variance much greater than mean)
• Counts recorded over different exposure periods, using an offset

When to use something else

• Variance is roughly equal to the mean: use Poisson regression
• There are more zeros than the model can explain: use a zero-inflated or hurdle negative binomial model

Assumptions and requirements

• Outcome is a non-negative integer count
• Independent observations
• Log of the expected count is linear in the predictors
• Variance is a quadratic function of the mean (NB2)

What the analysis reports

• Coefficients on the log scale and incidence rate ratios (IRR) with confidence intervals
• Dispersion parameter (alpha) and likelihood-ratio test against Poisson
• Log-likelihood, AIC, BIC
• Predicted counts

How to report it

Negative binomial regression indicated that each unit increase in [predictor] was associated with a [value]-fold change in the expected count of [outcome], IRR = [value], 95% CI [[value], [value]], p = [value].

Related methods

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

Run Negative Binomial Regression Model on Quorant