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Three types of polynomial mixed model splines have been proposed: smoothing splines, P-splines and penalized splines using a truncated power function basis. The close connections between these models are demonstrated, showing that the default cubic form of the splines differs only in the penalty used. A general definition of the mixed model spline is given that includes general constraints and can be used to produce natural or periodic splines. The impact of different penalties is demonstrated by evaluation across a set of functions with specific features, and shows that the best penalty in terms of mean squared error of prediction depends on both the form of the underlying function and the signal:noise ratio.
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Keywords: P-splines; best linear unbiased prediction; mixed models; penalized splines; residual maximum likelihood; smoothing splines

Document Type: Research Article

Affiliations: 1: Wagga Wagga Agricultural Institute 2: London School of Hygiene and Tropical Medicine 3: Rothamsted Research

Publication date: March 1, 2007

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