# Logistic regression and marginal effect

I'm doing a logistic regression and I'm using a model where all included variables are dummy variables (0 or 1). Let's say we have a model with four independent variables and let the constant represent the reference category.

Question: How do we calculate the marginal effect of one of the independent variables if the other independent variables also are dummy variables?

• Not sure what your question is. Why not just look at the coefficient of the variable of interest? I don't see how dummy-versus-not-dummy is of any relevance here. – zkurtz Sep 19 '13 at 17:10
• Please refer to this as a possible solution. Because dichotomous variables can't be differentiated, it is suggested to simply use the regression coefficient as the marginal effect. – Penguin_Knight Sep 19 '13 at 17:58

Suppose the variable of interest was an income tercile (1, 2, or 3). Let's make the middle third the omitted category.

I would predict $Pr(y=1)$ for everyone as they are in the data. Then I would flip the dummy variables for the top category $d_3$ to 1 for everyone, and set $d_1$ to zero. Predict again as if everyone was in the top third.

Calculate the difference for each person and then take the average over everyone to get the finite difference effect from being in the top tercile.

Normally, you could take the marginal effect at the means, however this doesn't exactly fly dichotomous explanatory variables.

Rather, recognize that a logistic regression's dependent variable can be rewritten as the log of the odds ratio.

Read this article for a concrete interpretation example using STATA output: http://www.ats.ucla.edu/stat/mult_pkg/faq/general/odds_ratio.htm

Read the first part on odds ratios, then read the section under the header "Logistic regression with a single dichotomous predictor variables"