| Abstract: | In many research areas, especially within social and behavioural sciences, the relationship between predictor and criterion variables is often assumed to have a particular shape, such as monotone, single‐peaked or U‐shaped. Such assumptions can be transformed into (local or global) constraints on the sign of the nth‐order derivative of the functional form. To check for such assumptions, we present a non‐parametric regression method, P‐splines regression, with additional asymmetric discrete penalties enforcing the constraints. We show that the corresponding loss function is convex and present a Newton–Raphson algorithm to optimize. Constrained P‐splines are illustrated with an application on monotonicity‐constrained regression with both one and two predictor variables, using data from research on the cognitive development of children. |
