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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/1985

Title: Simple and multiple P-splines regression with shape constraints
Authors: BOLLAERTS, Kaatje
Eilers, PHC
van Mechelen, I
Issue Date: 2006
Publisher: BRITISH PSYCHOLOGICAL SOC
Citation: BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY, 59. p. 451-469
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.
Notes: Univ Hasselt, Ctr Stat, B-3590 Diepenbeek, Belgium. Katholieke Univ Leuven, Louvain, Belgium. Leiden Univ, Med Ctr, Leiden, Netherlands.Bollaerts, K, Univ Hasselt, Ctr Stat, Agoralaan 1 Gebouw D, B-3590 Diepenbeek, Belgium.kaatje.bollaerts@uhasselt.be
URI: http://hdl.handle.net/1942/1985
DOI: 10.1348/000711005X84293
ISI #: 000242713800011
ISSN: 0007-1102
Category: A1
Type: Journal Contribution
Validation: ecoom, 2008
Appears in Collections: Research publications

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