Simple and multiple P-splines regression with shape constraints
Authors: Bollaerts, Kaatje1; Eilers, Paul H. C.2; van Mechelen, Iven3
Source: British Journal of Mathematical and Statistical Psychology, Volume 59, Number 2, November 2006 , pp. 451-469(19)
Publisher: British Psychological Society
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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.Keywords: non-parametric regression; P-splines; shape constraints; monotonicity; one dimension; two dimensions
Document Type: Research article
DOI: 10.1348/000711005X84293
Affiliations: 1: Katholieke Universiteit Leuven, Belgium, Universiteit Hasselt, Belgium 2: Leiden University Medical Centre, The Netherlands 3: Katholieke Universiteit Leuven, Belgium
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