Marginal Effects Analysis

Marginal effects analysis converts model coefficients, especially from nonlinear or interaction models, into the change in the predicted outcome associated with a change in a predictor, such as average marginal effects.

한계효과분석은 특히 비선형모형이나 상호작용모형의 계수를 예측변수 변화에 따른 예측 결과값의 변화, 예컨대 평균한계효과로 변환하여 해석하는 방법입니다.

How do I interpret logistic regression or interaction results as changes in predicted probabilities?

로지스틱 회귀나 상호작용 결과를 예측확률의 변화로 어떻게 해석하나요?

Marginal effects analysis expresses regression results on the outcome's natural scale, for example as percentage-point changes in a predicted probability, by averaging effects across observations or evaluating them at representative values. It fits nonlinear models such as logit, probit, or Poisson, and models with interactions or polynomial terms, where raw coefficients are hard to interpret.

When to use Marginal Effects Analysis

• Logistic or probit models where odds ratios are hard to communicate
• Models with interaction or squared terms
• Comparing predicted outcomes across groups or values of a predictor

When to use something else

• A linear model without interactions, where coefficients are already marginal effects: report multiple linear regression coefficients
• Causal effects under confounding are the goal: use a causal design such as inverse probability weighting

Assumptions and requirements

• Correctly specified underlying regression model
• Clear choice of average marginal effects, effects at the mean, or effects at representative values
• Standard errors from the delta method or bootstrapping
• Causal interpretation only if the design supports it

What the analysis reports

• Average marginal effects with standard errors and confidence intervals
• Predicted probabilities or values at chosen predictor values
• Marginal effects plots
• Contrasts between groups

How to report it

A one-unit increase in [predictor] was associated with an average [value] percentage-point increase in the probability of [outcome], AME = [value], 95% CI [[value], [value]].

Related methods

• Logistic Regression
• Moderation Analysis
• Predicted Probabilities

Run Marginal Effects Analysis on Quorant