%0 Journal Article %1 BMSP:BMSP186 %A Bollaerts, Kaatje %A Eilers, Paul H. C. %A van Mechelen, Iven %D 2006 %I Blackwell Publishing Ltd %J British Journal of Mathematical and Statistical Psychology %K monotone Regression %N 2 %P 451--469 %R 10.1348/000711005X84293 %T Simple and multiple P-splines regression with shape constraints %U http://dx.doi.org/10.1348/000711005X84293 %V 59 %X 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.

@article{BMSP:BMSP186, 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.}, added-at = {2014-02-26T14:55:23.000+0100}, author = {Bollaerts, Kaatje and Eilers, Paul H. C. and van Mechelen, Iven}, biburl = {https://www.bibsonomy.org/bibtex/2d3d2c500a839ff5d7fabd7c14c24834a/marsianus}, description = {Simple and multiple P-splines regression with shape constraints - Bollaerts - 2010 - British Journal of Mathematical and Statistical Psychology - Wiley Online Library}, doi = {10.1348/000711005X84293}, interhash = {620c84e98738a26851de7b08c1aa2017}, intrahash = {d3d2c500a839ff5d7fabd7c14c24834a}, issn = {2044-8317}, journal = {British Journal of Mathematical and Statistical Psychology}, keywords = {monotone Regression}, number = 2, pages = {451--469}, publisher = {Blackwell Publishing Ltd}, timestamp = {2014-05-19T19:50:18.000+0200}, title = {Simple and multiple P-splines regression with shape constraints}, url = {http://dx.doi.org/10.1348/000711005X84293}, volume = 59, year = 2006 }