Poisson Regression Model

Poisson regression is a generalized linear model for count outcomes that models the logarithm of the expected count as a linear function of predictors.

포아송 회귀분석은 기대 빈도의 로그를 예측변수의 선형함수로 모형화하는 빈도(count) 결과변수용 일반화선형모형이다.

How do I model a count outcome such as the number of events per person?

1인당 사건 발생 횟수처럼 빈도형 결과변수는 어떻게 모형화하나요?

Poisson regression models non-negative integer counts, such as visits or accidents, using a log link so that exponentiated coefficients are incidence rate ratios. It fits when the mean and variance of the count are roughly equal, and an exposure offset can model rates.

When to use Poisson Regression Model

• Outcomes that are counts of events, such as hospital visits or defects
• Modeling event rates with an exposure or time offset
• Estimating incidence rate ratios for several predictors

When to use something else

• The variance clearly exceeds the mean (overdispersion): use negative binomial regression
• There are more zeros than a count model predicts: use a zero-inflated Poisson or hurdle model

Assumptions and requirements

• Outcome is a non-negative integer count
• Independent observations
• Mean equals variance (equidispersion)
• Log-linear relationship between predictors and expected count

What the analysis reports

• Coefficients and incidence rate ratios with confidence intervals
• Wald or likelihood-ratio tests
• Deviance and Pearson goodness-of-fit statistics
• Dispersion check
• AIC

How to report it

Each one-unit increase in [predictor] was associated with a [value]-fold change in the expected count of [outcome], IRR = [value], 95% CI [[lower], [upper]], p = [value].

Related methods

• Negative Binomial Regression
• Zero-Inflated Poisson Regression
• Binary Logistic Regression

Run Poisson Regression Model on Quorant