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A comparison of mixed model splines for curve fitting

Journal Article


Abstract


  • Three types of polynomial mixed model splines have been proposed: smoothing splines, Psplines 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.

Authors


  •   Welham, S J. (external author)
  •   Cullis, Brian R.
  •   Kenward, M G. (external author)
  •   Thompson, Robin (external author)

Publication Date


  • 2007

Citation


  • Welham, S. J., Cullis, B. R., Kenward, M. G. & Thompson, R. (2007). A comparison of mixed model splines for curve fitting. Australian and New Zealand Journal of Statistics, 49 (1), 1-23.

Scopus Eid


  • 2-s2.0-33846700066

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2094

Has Global Citation Frequency


Number Of Pages


  • 22

Start Page


  • 1

End Page


  • 23

Volume


  • 49

Issue


  • 1

Place Of Publication


  • Australia

Abstract


  • Three types of polynomial mixed model splines have been proposed: smoothing splines, Psplines 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.

Authors


  •   Welham, S J. (external author)
  •   Cullis, Brian R.
  •   Kenward, M G. (external author)
  •   Thompson, Robin (external author)

Publication Date


  • 2007

Citation


  • Welham, S. J., Cullis, B. R., Kenward, M. G. & Thompson, R. (2007). A comparison of mixed model splines for curve fitting. Australian and New Zealand Journal of Statistics, 49 (1), 1-23.

Scopus Eid


  • 2-s2.0-33846700066

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2094

Has Global Citation Frequency


Number Of Pages


  • 22

Start Page


  • 1

End Page


  • 23

Volume


  • 49

Issue


  • 1

Place Of Publication


  • Australia