StatsWAP2009Aug07

Nonlinear Regression Models

• Brian Caffo's websiite: http://www.biostat.jhsph.edu/~bcaffo/
• Series Home: http://putter.ece.jhu.edu/StatsWAP

Resources

• Slides will be available here
• R-code will be available here

Notes

• Not covered: kernel smoothing, local weighting, moving averages, binning, loess (local estimation) etc.
• Non-parametric regression -
  • can factor in <math>y=f(x)+other stuff </math>
  • confounding effects
  • interactions
  • can generalize to discrete and/or multivariate responses (logistic regression, etc.)
• Example bases
  • linear
  • polynomial (Taylor series expansion)
    • why not?
    • it works... sort of
    • not good for smoothing: not "localized", not "parsimonious" ==> takes a lot of terms to get non-exactly polynomial
  • See slide on general functions for tips on selected basis sets.
    • wavelet bases - smooth trends and spikes
      • can be "same" as wavelet transform, slowly
    • trigonometric (Fourier) - "frequency concept"
      • can be "same" as Fourier transform, slowly
    • Spline bases - general smoothing
      • We'll talk about these today. Good for general smoothing. General purpose, but do not preserve spikes.
• Pick the basis for the eventual goal.

Spline Bases

• Highly controversial topic on spline fitting: fun reading [1]
• Gauss and the "invention" of least squares: [2]