Common choices for representing the smooth function f in model (1) include natural splines, penalized splines and smoothing splines. (Other less common choices are LOESS smoothers or harmonic functions.) The first is fully parametric, whereas the last two may be considered more natural splines, we construct a spline basis with knots at fixed locations through- out the range of the data and the choice of knot locations can have a substantial effect on the resulting smooth. Smoothing splines and penalized splines circumvent the problem of choosing the knot locations by constructing a very large spline basis and then penalizing the spline coeffi- cients to reduce the.
