Generalized Additive Models (GAM)

A generalized additive model (GAM) is a regression model that represents the outcome as a sum of smooth, data-estimated functions of predictors, allowing nonlinear effects within a generalized linear model framework.

일반화가법모형(GAM)은 결과변수를 예측변수들의 매끄러운 함수의 합으로 표현하고 그 함수를 자료로부터 추정하여, 일반화선형모형 틀 안에서 비선형 효과를 허용하는 회귀모형이다.

How do I model a nonlinear relationship between predictors and an outcome without choosing the curve shape in advance?

곡선 형태를 미리 정하지 않고 예측변수와 결과변수의 비선형 관계를 어떻게 모형화하나요?

A generalized additive model fits smooth functions such as penalized splines for each predictor, so nonlinear effects are estimated from the data rather than specified in advance. It fits continuous, binary or count outcomes and keeps each predictor's effect interpretable through partial-effect plots.

When to use Generalized Additive Models (GAM)

• A continuous, binary or count outcome with predictors whose effects may be curved
• Exploring the shape of dose-response, age or time effects
• Wanting flexibility while keeping per-predictor effects interpretable

When to use something else

• Relationships that are clearly linear; use linear or generalized linear regression
• Many high-order interactions and prediction as the only goal; use gradient boosting

Assumptions and requirements

• Independent observations, or an explicit correlation structure
• Outcome distribution correctly specified through the family and link
• Additive effects unless interactions or tensor smooths are included
• Enough unique predictor values to estimate each smooth

What the analysis reports

• Effective degrees of freedom (edf) for each smooth
• Approximate F or chi-square tests for smooth terms
• Parametric coefficients
• Partial-effect plots
• Deviance explained and AIC

How to report it

The smooth term for [predictor] was significant, edf = [value], F = [value], p = [value], and the model explained [value]% of the deviance.

Related methods

• Polynomial Regression
• Spline Regression
• Generalized Linear Model

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