# Average Marginal Effects interpretation

I ran a regression where the dependent variable is winning (1=win) Given that my regression is probit I want to understand the coefficient. I've done margins, dydx() for my independent variable (average marginal effects). This yielded a result of -.41.

What does this mean? Does it mean that the probability of winning goes down by .41 percentage points? and if so, when does it go down by that much?

I just want a lay person's way to explain this .41 value.

• Welcome to CrossValidated. A screenshot of your results might be a big help. – Ferdi Dec 21 '16 at 9:56
• Use of Stata (not STATA, no such program) is secondary here. If it's central to the question then this is off-topic. I removed mention from the title. – Nick Cox Dec 21 '16 at 10:38

The average marginal effect gives you an effect on the probability, i.e. a number between 0 and 1. It is the average change in probability when x increases by one unit. Since a probit is a non-linear model, that effect will differ from individual to individual. What the average marginal effect does is compute it for each individual and than compute the average. To get the effect on the percentage you need to multiply by a 100, so the chance of winning decreases by 41 percentage points.

• right...but when does it go down by 41 percent? like is this saying in general my independent variable decreases the probability of winning by this much? or is this at the means? – Katie Dec 21 '16 at 10:00
• i guess i'm just wondering: at what value does the chance of winning decrease by 41 percentage points – Katie Dec 21 '16 at 10:18
• @Katie Elementary, but 41 percentage points and .41 (0.41) percentage points are not at all the same. Compare your question and your comment. – Nick Cox Dec 21 '16 at 10:40
• @Katie I edited the answer, is that what you are looking for? – Maarten Buis Dec 21 '16 at 11:02
• @Katie If Maarten's answer helped, please select it by using the checkmark on the left. – Dimitriy V. Masterov Jan 17 '17 at 18:06

These two links can be checked out for detail explanation. Page 8 in https://cran.r-project.org/web/packages/margins/vignettes/TechnicalDetails.pdf and Appendix A in https://www3.nd.edu/~rwilliam/stats3/Margins02.pdf.

Briefly, average marginal effect of a variable is the average of predicted changes in fitted values for one unit change in X (if it is continuous) for each X values, i.e., for each observation.

dydx means the difference in the dependent variable (or regressand) Y for a change in the explanatory variable X (regressor). This is to be interpreted as a regression coefficient in a lineair regression (of which the marginal effect is equal to the coefficient, other than in regressions of binary dependent variables).

A score of .41 means that for a 1 unit increase in X, Y (in a probit, this is your probability), will increase by .41 or 41%-points. eyex would return elasticities.

correct me if I'm wrong