- Residual plots can be used as a useful diagnostic tool for controlling the LOWESS fitting process (Cleveland, W. S. (1993): Visualizing Data. Hobart Press, Summit, NJ).
This is particularly important for using the appropriate value for the local smoothing width (Alpha).
Example for Illustrating the Effect of Alpha on the LOWESS Fitting Process
The effect of Alpha for controlling the LOWESS fitting process is shown below for a given bivariate data set, using Alpha values of 0.1, 0.6, and 0.99.
- In choosing Alpha, we want a curve that is as smooth as possible without introducing lack of fit, i.e., the main structure within the data should
be by and large represented, with no remaining residual dependence.