Simple and multiple P-splines regression with shape constraints.
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.
Bollaerts
Kaatje
K
Katholieke Universiteit Leuven, Belgium. kaatje.bollaerts@uhasselt.be
Eilers
Paul H C
PH
van Mechelen
Iven
I
D000465:Algorithms; D002648:Child; D003196:Computer Graphics; D003198:Computer Simulation; D003210:Concept Formation; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008297:Male; D008960:Models, Psychological; D009716:Numerical Analysis, Computer-Assisted; D011337:Probability Learning; D011340:Problem Solving; D012044:Regression Analysis; D018709:Statistics, Nonparametric