I am looking for the best way to depict a concave, quadratic association. I'm using logistic regression to measure the association between affect and military advancement (yes/no).
The primary predictor centered on the mean squared was significant, and it is graphically clear that Y increases as X increases only to a point, before leveling off and decreasing. I was able to determine at which level of X, Y reaches its maximum by adding the mean to the linear term (centered on the mean), divided by two times the quadratic term (mean + (b1/2b2).
Are results from logistic regression uninterpretable if there is a curvilinear/quadratic association between X and Y?
What would be the best way to determine the slope at different levels of X for a binary outcome? I would like to compare how the slope differs at varying levels of X (low vs. medium vs. high), and specifically how it decreases at higher levels of X.