# Polynomial term in logistic regression

I've made a logistic regression model that includes a polynomial term to degree 2. I'm aware that logistic regression models the response variable as a non-linear function of the predictors. Does it make sense to include a polynomial term in logistic regression?

• This is fine. If you'd like, you can see an example in my recent answer here: CDF and logistic regression. Mar 31, 2014 at 14:26

[This model is linear in parameters & the predictor: $$\operatorname{logit}\pi_i = \beta_0 + \beta_1 x_i$$ This one is linear in only the parameters: $$\operatorname{logit}\pi_i = \beta_0 + \beta_1 x_i + \beta_2 x_i^2$$ ]
• luciano: If you want to think of it in terms of the probability; then yes, its a curved relationship, but still restricted in form - rotational symmetry around the point of inflection at the inflection point at $\pi=\frac{1}{2}$ - you can only shift or stretch the logistic curve when you fit the two parameters. Polynomials allow more flexibility. See @gung's link for an example. Mar 31, 2014 at 14:55