R: Scatter Plot Smoothing

lowess {stats} | R Documentation

## Scatter Plot Smoothing

### Description

This function performs the computations for the LOWESS smoother which uses locally-weighted polynomial regression (see the references).

### Usage

    lowess(x, y = NULL, f = 2/3, iter = 3, delta = 0.01 * diff(range(x)))

### Arguments

`x, y` | vectors giving the coordinates of the points in the scatter plot. Alternatively a single plotting structure can be specified – see `xy.coords`.
`f` | the smoother span. This gives the proportion of points in the plot which influence the smooth at each value. Larger values give more smoothness.
`iter` | the number of ‘robustifying’ iterations which should be performed. Using smaller values of `iter` will make `lowess` run faster.
`delta` | See ‘Details’. Defaults to 1/100th of the range of `x`.

### Details

`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.

### Value

`lowess` returns a list containing components `x` and `y` which give the coordinates of the smooth. The smooth can be added to a plot of the original points with the function `lines`: see the examples.

### References

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.

### See Also

`loess`, a newer formula based version of `lowess` (with different defaults!).

### Examples

    require(graphics)

    plot(cars, main = "lowess(cars)")
    lines(lowess(cars), col = 2)
    lines(lowess(cars, f = .2), col = 3)
    legend(5, 120, c(paste("f = ", c("2/3", ".2"))), lty = 1, col = 2:3)

[Package stats version 3.1.2 Index]