Logistic regression when all variables are dummies

[Ian Kingsbury]

I'm modeling something that exclusively uses dummy variables, both the dependent and independent variables.

I'm using logit. Doesn't seem as though there is any obvious preference for logit or probit as far as I can tell, though if someone thinks otherwise I'd love to hear it.

However, I'm wondering what makes most sense in terms of predictive margins. dydx(*) default? dydx at means? Something else?

For what it's worth, the coefficients don't change much based upon my selection. But i still want my decision to be defensible in theory.

[Clyde Schechter]

That question does not have a statistical answer. It depends on what kind of marginal effect answers your research question. Which means that it can only be answered in the context of the specific research question you have in mind. And with that context specified, it probably will depend on substantive knowledge of whatever the content area of your research is. In short, you are probably better of consulting a colleague in your field for this question.

By the way, make sure that you properly use the i. prefixes in front of all those predictor dummy variables so that whichever marginal effect you settle on, you get it calculated correctly. If you don't specify that prefix, -margins- will assume that the variable is continuous and will calculate the marginal effect incorrectly.

[Ian Kingsbury]

Appreciate that, Clyde!

[Jeff Wooldridge]

It’s unlikely you want to use at(means) because then you’re evaluating the covariates at values nonexistent in the population. For example, if you have dummy for being in a union, you’d be evaluating the effect at something like unionbar = 0.32.

Are your dummies exhaustive and mutually exclusive? If so, linear regression will give the same answer.

[Ian Kingsbury]

I've constructed them to be exhaustive and mutually exclusive. From what I can tell, linear regression provides remarkably similar estimates, but not precisely the same.

[Jeff Wooldridge]

The discrete margins in logit will be identical to the coefficients in a linear model. No matter what you do, the margins are simple the differences in cell frequencies.