How to specify a non-linear interaction term in a linear model Say I have 2 continuous variables (x & y) in a logit model. I want to test the following hypotheses in the model:

*

*For low values of x, increasing the value of y will increase the value of the response variable

*For high values of x, increasing the value of y will decrease the value of the response variable

Is there a way to specify this using interaction terms? I have only used interaction terms in which y has a linear impact on the effect of x on the response variable.

X1 =  I(x>a)
X2=  I (x<b)
Logit (Response ) = beta0 + betax * x + betay * x + betax1y * X1 * y + betax2y * X2 * y
Then X1y is activated when x is above a, X2 y when x is below b.
You can exclude betayy if you think that response is only through yx terms.
A and b are exogenous parameters in this model, so either outside knowledge or additional testing on which fit best is needed.
