Fits an increasing monotonic regression of y on x.
No options
Parameters
Y = variates |
Y-values of the data points |
|---|---|
X = variates |
X-values of the data points; default is to assume that the x-values are monotonically increasing |
RESIDUALS = variates |
Variate to save the residuals from each fit |
FITTEDVALUES = variates |
Variate to save the fitted values from each fit |
Description
Monotonic regression plays a key role in non-metric multidimensional scaling, which is available in Genstat via the MDS directive. However, it can be useful in its own right, so the method has been made accessible by the MONOTONIC directive. A monotonic regression through a set of points is simply the line that best fits the points subject to the constraint that it never decreases: of course the line need not be straight, in fact it rarely will be. If you need a monotonically decreasing line, you can simply subtract all the y-values from their maximum, find the monotonically increasing regression, and then back-transform the data and fitted line, and change the sign of the residuals.
The MONOTONIC directive has no options. It has four parameters: Y to specify the y-values, X for the x-values, RESIDUALS to save the residuals, and FITTEDVALUES to save the fitted values. The x-values need not be supplied, in which case the directive assumes that the y-values are in increasing order of the x-values. In common with the other regression directives, the variates to save the residuals and fitted values need not be declared in advance.
Options: none.
Parameters: Y, X, RESIDUALS, FITTEDVALUES.
Action with RESTRICT
MONOTONIC ignores any restrictions on the variates.
See also
Directives: MDS, FIT, FITCURVE, FITNONLINEAR.
Commands for: Multivariate and cluster analysis, Regression analysis.
Example
" Example 1:4.5.2 "
VARIATE [VALUES=2,6,4,4, 9,1,12,15,13,18] X
& [VALUES=1,5,3,6,10,0,11,14,16,18] Y
MONOTONIC Y=Y; X=X; FITTED=Fvals
LPGRAPH [TITLE='Monotonic regression'; NROWS=25; NCOLUMNS=61]\
Fvals,Y; X; METHOD=line,point
SORT X,Y
MONOTONIC Y; RESIDUALS=Res; FITTED=Fvals
PRINT X,Y,Fvals,Res