# Logistic regression model: interpretation of average marginal effect

This is more a beginner question but I am having trouble finding helpful information.

Could someone explain to me

• how to interpret the "average marginal effects" of independent variables from a logistic regression model

• how they are related to the probability of the dependent variable in the logistic model

Would really appreciate any simple/ intuitive explanations!

• I'm certain this question has been answered many times before. Try searching the site to see the other questions that have been asked that are very similar to yours. – StatsStudent Apr 13 '15 at 1:14

This has been answered before but I will try to include a very simple explanation which can hopefully get you on the right track.

A logit regression model, linking the probability of a dependent variable $y$ to some vector of independent variables $X$ is written as follows

$$Pr(y=1) = \Lambda(X\beta)$$ where $\Lambda()$ represents a logistic c.d.f.

The marginal effect can be though of as the impact a change in some variable $x_j$ has on the response probability $Pr(y=1)$ and can be written as.

$$\frac{\partial Pr(y=1)}{\partial x_j} = \beta_j \lambda(X\beta)$$ where $\lambda$ is the p.d.f of a logistic function (the first derivative of $\Lambda$ w.r.t its argument)

Notice that for different values of X, you get a different values of $\lambda(XB)$, giving you different marginal effects.

To calculate the average marginal effect, you take the average of the logistic p.d.f for all the values of X in your sample and multiply it by your coefficient $\beta_j$.

$$\frac{\partial Pr(y=1)}{\partial x_j} = \beta_j E[\lambda(X\beta)]$$

Aside Note: This is different than the marginal effect at the average.