This function performs the computations for the LOWESS smoother which uses locally-weighted polynomial regression (see the references).
lowess(x, y = NULL, f = 2/3, iter = 3, delta = 0.01 * diff(range(x)))
- x, y
- vectors giving the coordinates of the points in the scatter plot. Alternatively a single plotting structure can be specified -- see
- the smoother span. This gives the proportion of points in the plot which influence the smooth at each value. Larger values give more smoothness.
- the number of ‘robustifying’ iterations which should be performed. Using smaller values of
- See ‘Details’. Defaults to 1/100th of the range of
lowess is defined by a complex algorithm, the Ratfor original of which (by W. S. Cleveland) can be found in the R sources as file ‘src/appl/lowess.doc’. Normally a local linear polynomial fit is used, but under some circumstances (see the file) a local constant fit can be used. ‘Local’ is defined by the distance to the
floor(f*n)th nearest neighbour, and tricubic weighting is used for
x which fall within the neighbourhood.
The initial fit is done using weighted least squares. If
iter > 0, further weighted fits are done using the product of the weights from the proximity of the
x values and case weights derived from the residuals at the previous iteration. Specifically, the case weight is Tukey's biweight, with cutoff 6 times the MAD of the residuals. (The current R implementation differs from the original in stopping iteration if the MAD is effectively zero since the algorithm is highly unstable in that case.)
delta is used to speed up computation: instead of computing the local polynomial fit at each data point it is not computed for points within
delta of the last computed point, and linear interpolation is used to fill in the fitted values for the skipped points.
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
Cleveland, W. S. (1979) Robust locally weighted regression and smoothing scatterplots. J. American Statistical Association 74, 829--836.
Cleveland, W. S. (1981) LOWESS: A program for smoothing scatterplots by robust locally weighted regression. The American Statistician 35, 54.
Documentation reproduced from R 3.0.1. License: GPL-2.