Non-linear terms in logistic regression? I have a data set with binary response and several numerical and categorical predictors. I'm looking for ways to test if some of the numerical predictors are non-linear. I've read about lowess and wondering if it would make sense to do the following for each numerical predictors:

plot(x,predict(loess(y~x)))

If so how do I interpret the plot? If it's a straight line it's linear and quadratic if not?
 A: Chuck, assuming you are interested in detecting if any of your numerical predictors have non-linear effects on your binary response, I would recommend that you examine the so-called Component + Residual Plot for each of your numerical predictors. 
Component + Residual Plots help diagnose non-linearities and can be used to suggest alternative functional forms for the effects of interest (e.g., quadratic, cubic). 
In R, you can produce Component + Residual Plots for glm models using the function crPlots in the car package - see http://www.inside-r.org/packages/cran/car/docs/crPlots for further details.
A: Take a look at restricted cubic splines. The rms package for R contains everything you need to test any non-linearities and more. See the examples for lrm(), which does logistic regression, and anova.rms().
A: The R package mgcv should help you. The syntax is quite similar to glms:
m.fit <- gam(y ~ s(x), family="binomial")
summary(m.fit)

A: There is actually a test called the Box-Tidwell test for linearity of the logit that will tell you the proper relationship (linear, quadratic,...etc) between each of your variables and your target. Technically this test should always be performed to verify that key assumption of logistic regression! 
