I'm working with a functional form
$\alpha = F(x,y,t)$ where t represents time and $x,y $ other factors affecting $\alpha$.
I want to find a functional form for F (that also has some parameters) such that
1)The treatment effect with respect to t is higher for medium values of y.
2)The treatment effect with respect to t is higher for medium values of x.
3)The treatment effect varies in a specific way for different values of x and y (e.g., highest for low x and low y, highest for medium x and medium y, and highest for high x and high y).
I need a function that is flexible enough to have these characteristics. I've tried Cobb-Douglass ($x^{\gamma_1}y^{-\gamma_2}z^{\gamma_3}$) and sigmoid form but haven't reached a satisfying function yet.