Quadratic term in Logistic regression I am fitting a logistic regression model.  After variable selection, I am not sure how to check if I need any quadratic term in my model.  Is it the same as linear regression to check residual plot?  
 A: Problem with residual plots in logistic regression is that there are too many different residuals defined! In linear regression the model has the form $y_i=\beta_0+\beta_1 x_{i1} + \dotsm +\epsilon_i$, so there is an error term ($\epsilon_i$).  The model consists of a systematic part to which is added an error term, and the residual can be seen as an "estimate of the error term."  
Logistic regression do not have this form, it does not consist of an "error term" added to a "systematic part".  So it is not obvious how to define residuals (and it is not clear that they estimate some identifiable part of the model). So interpretation is less clear, and there is no simple distribution theory for residuals.  
The following post:  What is the expected distribution of residuals in a generalized linear model?  has an answer detailing an solution to this problem, using simulated residuals.  That will give much more helpful residual plots, which can help in judging if a quadratic term is needed. An R package implementing this idea is DHARMa (on CRAN). 
An entirely different idea is to simply use a spline. 
