marginaleffect

Marginal effect refers to the change in the predicted value of a dependent variable associated with a one-unit change in an independent variable, holding other variables constant. It is used to summarize how small changes in inputs influence outputs, and it can apply to continuous predictors or to discrete changes in binary indicators. For continuous variables, the marginal effect is typically the partial derivative of the expected outcome with respect to the variable. For binary indicators, it often represents the discrete change in the predicted outcome when the variable switches from 0 to 1, evaluated at fixed values of the other covariates.

In linear models, marginal effects are straightforward: they equal the regression coefficients and are constant across observations. In nonlinear models, such as logistic or probit regression, marginal effects vary with the values of the covariates because the relationship between inputs and the outcome is nonlinear. To summarize these varying effects, researchers compute common measures such as average marginal effects (AME), which average the individual marginal effects across observations, and marginal effects at the mean (MEM), which evaluate the derivative at the mean of the covariates. Marginal effects can also be computed at other specified values or ranges to illustrate how effects change with the data.

Calculation typically involves differentiating the model’s predicted outcome with respect to the variable of interest. If the model links a linear predictor η = Xβ to the outcome through a link function, the marginal effect is ∂μ/∂X_j = ∂μ/∂η × β_j, with the specific form depending on the chosen model family. Marginal effects aid interpretation by translating model coefficients into more intuitive, variable-specific impact estimates, while acknowledging model dependence and potential heterogeneity across observations.