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A COMPARISON OF MIXED MODEL SPLINES FOR CURVE FITTING
Authors:Sue J  Welham  Brian R  Cullis  Michael G  Kenward Robin  Thompson
Institution:Rothamsted Research;, Wagga Wagga Agricultural Institute;and London School of Hygiene and Tropical Medicine
Abstract: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.
Keywords:best linear unbiased prediction  mixed models  penalized splines  P-splines  residual maximum likelihood  smoothing splines
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