TeachingDemos (version 2.13)

loess.demo: Demonstrate the internals of loess curve fits

Description

Creates a scatterplot with a loess fit, then interactively shows the window and case weights used to create the curve at the selected value of x.

Usage

loess.demo(x, y, span = 2/3, degree = 1, nearest = FALSE,
  xlim = numeric(0), ylim = numeric(0), verbose = FALSE)

Value

This function does not return anything, it is run purely for its side effects.

Arguments

x

The x coordinates to be plotted.

y

The y coordinates to be plotted.

span

The relative width of the window, passed on to loess.

degree

Degree of polynomial to use (0, 1, or 2), passed on to loess.

nearest

Logical, should predictions be made at the point where you clicked (FALSE), or at the nearest x value of the data to where you clicked (TRUE).

xlim

Limits of the Horizonal axis.

ylim

Limits of the Vertical axis.

verbose

If true then print the x coordinate being predicted.

Author

Greg Snow

Details

This function demonstrates the underlying calculations of loess curves.

Given x and y vectors it will create a scatterplot and add 2 loess fit lines (one using straight loess smooth with linear interpolation and one that does a spline interpolation of the loess fit).

The function then waits for the user to click on the plot. The function then shows the window of points (centered at the x value clicked on) used in the weighting for predicting that point and shows a circle around each point in the window where the area of the circle is proportional to the weight of that point in the linear fit. The function also shows the linear (or quadratic) fit used to predict at the selected point.

The basic steps of the loess algorithm (as demonstrated by the function) is that to predict the y-value for a given x-value the computer:

1. Find all the points within a window around the x-value (the width of the window is based on the parameter span). 2. Weight the points in the window with points nearest the x-value having the highest weight. 3. Fit a weighted linear (quadratic) line to the points in the window. 4. Use the y-value of the fitted line (curve) at the x-value to give loess prediction at that x-value.

Clicking on another point in the graph will replot with the new situation.

Right click and select 'stop' to end the demonstration.

See Also

loess, locator

Examples

if(interactive()){
data(ethanol, package='lattice')
attach(ethanol)
loess.demo(E, NOx)
# now click a few places, right click to end
loess.demo(E, NOx, span=1.5)
loess.demo(E, NOx, span=0.25)
loess.demo(E, NOx, degree=0)
loess.demo(E, NOx, degree=2)
detach()
}