Quadratic terms in logistic regression I am looking at the results of a logistic regression model (i dont have the data) and the person who has developed the model has included quadratic terms in the model. 
I understand the use of such polynomial terms in a linear model where one can look at the relationship between the response and the predictor. But in case of a binary outcome, is there a way to identify such a trend before hand i.e. without including it in the model and then checking if the variable is significant or not?
 A: During EDA, you can take the (continuous) predictor and discretize it by either creating equal-sized or equal-spaced bins. Then you can plot the event rates across all bins to visually detect a linear or quadratic relationship (if it exists). E.g., an inverted U-shaped curve would suggest the presence of a quadratic relationship. Another way to create such bins is by using CHAID (or other) decision tree algorithm to split your sample into statistically-derived bins.
A: After building a model based on general linear model (as you would typically be doing when you have a binary outcome), you have several methods available for checking for violations of the assumptions supporting statistical validity. The assumption that would be violated when the prediction relationship was polynomial is linearity of residuals (or equivalently the prediction-vs-predictor on the fitted scale, logistic in the case of binary outcomes). The details will vary depending on your computing platform, but you should be thinking of residual (or fitted values) versus predictor plots. The test for needing a polynomial would be "eyeball"-driven. If you get a "smile" or a "frown" then a squared term might be appropriate. If you get a minus-plus-minus-plus sort of pattern then a higher order polynomial might be needed. You should be thinking about the underlying scientific implications during this process of model building. Cubic polynomials should have a higher degree of skepticism. You need to balance the degree of fit against complexity. The other approach is to use regression splines which allow an automatic penalty to be imposed. Frank Harrell's "Regression Modeling Strategies" has many worked examples using the S/R platform.
