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I want to do a logistic regression, with multiple covariates, where at least one of the covariates is two-sided. When I say that a covariate $x_1$ is "two-sided", I mean that values close to the mean of $x_1$ are likely to be in class 0, whereas values far away from the mean of $x_1$, in any direction, are likely to be in class 1. Furthermore, the distribution of $x_1$ may not be symmetrical about the mean (for example, a high value of $x_1$ might be somewhat indicative of class 1, whereas a low value of $x_1$ might be extremely indicative of class 1).

One way to do this is to simply say that the actual covariate I give to the logistic regression is the absolute departure of $x_1$ from the mean. Another way is to create two such departure variables, to account for non-symmetry in the distribution of $x_1$. A third way would be to use polynomials of $x_1$. I'm sure there are other potential ways of doing this.

Is there a common "best practice" for handling this situation?

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    $\begingroup$ Well, if the effect of "distance from mean" is asymmetrical, simply using as variable $x_i-\bar{x}$ will not do (it assumes symmetrical effect), a quadratic polynomial in $x$ do the same. So a third-order polynomial could do, but I would maybe rather use a spline. To say more we would need some context! $\endgroup$ Jul 5, 2018 at 8:56

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