Logistic regression diagnostics

[Nathalie Guibert]

Hey everyone,

I am currently running a logistic regression with several independent variables.

As for the diagnostic requirements, I have to find out if there are no outliers beyond +/-3 (best case scenario +/-2), no multicollinearity and if there's linearity of logits (linear relationship between metric factor & logit function of the dependent variable).

While I have found out how to control for multicollinearity, I still don't know how to do outlier diagnostics and the linearity of logits assumption in the logistic regression with multiple independent variables.

Can somebody shine a light on these two issues?

Thank you.

[Jeff Wooldridge]

Nathalie: Why are you thinking about multicollinearity? Are your estimated coefficients -- or, preferably, average marginal effects -- too imprecise? There can't be the kids of outliers we think about in standard regression because y takes only two values, zero and one. At best, functional form is the only issue if you are treating your explanatory variables as exogenous (as I assume you are).

Here's how to implement a simple RESET-type test proposed in Papke and Wooldridge (1996, Journal of Applied Econometrics). It applies to binary or fractional responses.

logit y x1 ... xK
predict xbhat, xb
logit y x1 ... xK c.xbhat#c.xbhat c.xbhat#c.xbhat#c.xbhat
test c.xbhat#c.xbhat c.xbhat#c.xbhat#c.xbhat

A rejection at a small significance level means the functional form is not entirely correct. But it doesn't mean the average marginal effects are way off. But it is the one test that makes some sense. It does suggest trying some interactions and quadratics in some variables, and that might be interesting in and of itself.

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