Gamma Regression

Gamma regression is a generalized linear model for positive, right-skewed continuous outcomes whose variance increases with the square of the mean, usually fitted with a log link.

감마회귀는 양수이고 오른쪽으로 치우친 연속 결과를 로그 연결로 모형화하며 분산이 평균의 제곱에 비례한다고 보는 일반화선형모형입니다.

My outcome is a positive amount such as cost or duration with a long right tail; how do I model it without log-transforming it?

비용이나 소요시간처럼 양수이고 오른쪽 꼬리가 긴 결과를 로그 변환 없이 어떻게 분석하나요?

Gamma regression models the mean of a positive skewed outcome directly through a log link, so exponentiated coefficients are multiplicative effects on the mean. It assumes the coefficient of variation is constant, which means the standard deviation grows in proportion to the mean.

When to use Gamma Regression

• The outcome is strictly positive and continuous, such as costs, times or concentrations
• The spread of the outcome increases with its mean
• You want effects on the mean scale rather than on the log of the outcome

When to use something else

• The outcome contains exact zeros; use a Tweedie or two-part model instead
• The variance does not depend on the mean; use multiple linear regression instead

Assumptions and requirements

• The outcome is positive and follows a gamma distribution given the predictors
• The log of the mean is linear in the predictors
• Variance is proportional to the squared mean
• Observations are independent

What the analysis reports

• Coefficients on the log scale and mean ratios exp(b) with confidence intervals
• Dispersion and shape parameters
• Deviance and proportion of null deviance explained
• AIC and log-likelihood

How to report it

A gamma regression with a log link showed that each unit increase in [predictor] multiplied the mean [outcome] by [value], 95% CI [[value], [value]], p = [value] (dispersion = [value]).

Related methods

• Multiple Linear Regression
• Poisson Regression Model
• Tobit Regression Model

Run Gamma Regression on Quorant