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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.

Thanks!

Emily

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    – Jan Kukacka
    Mar 13, 2018 at 15:23

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The resulting coefficients of logistic regression are difficult to interpret in general. The coefficient when not squared is the change in log odds for every 1 unit increase in your IV. So if that IV is squared it is still interpreted the much the same way. The coefficient is equal to the change in log odds for every 1 unit increase in the squared IV (controlling for the other predictors in your model including the linear version of the IV).

Because logistic regression follows a logistic curve interpreting the slope as is would be strange. I think your best bet would be to transform to percent likelihood, so that its more interpretable and then use your low, medium, high method. Either that or just graph it, that will provide the most detail.

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