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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 | Source: | 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 | Document URI: | http://hdl.handle.net/1942/1985 | ISSN: | 0007-1102 | e-ISSN: | 2044-8317 | DOI: | 10.1348/000711005X84293 | ISI #: | 000242713800011 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2008 |
Appears in Collections: | Research publications |
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