Title: Simple and multiple P-splines regression with shape constraints
Authors: Bollaerts, Kaatje ×
Eilers, Paul H. C
Van Mechelen, Iven #
Issue Date: Nov-2006
Publisher: J. Wright & Sons
Series Title: British Journal of Mathematical and Statistical Psychology vol:59 pages: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.
ISSN: 0007-1102
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Quantitative Psychology and Individual Differences
× corresponding author
# (joint) last author

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