I’m conducting a multiple logistic regression with 3 predictors (x, y and z). A Box-Tidwell test suggested that the relation between x and the dependent variable is not linear on the logit, so I have added the squared term (x^2) to the equation. All the coefficients are statistically significant, but my question is: how can I compare the relative impact of each predictor, now that x does not have a single coefficient (or odds ratio), but two? Thanks!
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I came across this paper that basically answers my question:
Mize, T. D. (2019). Best practices for estimating, interpreting, and presenting nonlinear interaction effects. Sociological Science, 6, 81-117. (https://sociologicalscience.com/articles-v6-4-81/)
In sum: do not report regression coefficients when curvilinear effects or interaction terms are included in the model. Instead, determine the size and significance of the effects using marginal effects.