SAS Macro Programs: resline

resline macro ( get resline.sas)

Fit a resistant line to bivariate data

Method

The data points are divided into thirds, based on the sorted values of the X= variable. The median X and Y value within each third define "summary points" which are used to calculate robust estimates of slope and intercept.

Power transformations are found by calculating a "ratio of slopes" table, transforming the X and Y coordinates of summary points to all powers in the list [ -1.0, -0.5, log, sqrt, raw, 2.0], and forming the ratio of the slopes of the lines connecting the first pair of summary points and the second pair of summary points. The optimal transformation is the one whose slope ratio is closest to 1 (or whose log is closest to zero).

The resline macro requires that all values for the X and Y variables are positive. If any data values are negative, the recommended solution is to add a constant to all values to make them positive.

Parameters

DATA=_LAST_

Name of the input data set.

X=

The name of the independent variable.

Y=

The name of the response variable.

ID=

The name of a character variable to identify each observation, used to label points in the output.

ENDS=.5

The greatest range of either end-third.

PLOT=FIT RESID,

Keywords to request one or more printer plots to show.
FIT requests a plot of observed and fitted values vs. X for the raw data. RESID requests a plot of residuals vs X.

OUT=_FIT_

The name of an output data set containing fitted values (FIT) and residuals (RESIDUAL), in addition to the X=, Y=, and ID= variables for all non-missing observations. Note that the ID variable is named ID

OUTSUM=_SUMVAL_

The name of an output data set containing median summary values for the thirds (THIRD) of the data.

Missing data

Example

%include data(nations);
*include macros(resline);    *-- included in autocall library;

%resline(data=nations, x=income, y=imr, id=nation);

Warning:         4 row(s) with missing data have been removed.

        Summary Values

              X        Y      n   

Low     101.000  131.150     34  
Mid     426.000   51.700     51  
High   3574.500   14.850     16 R

('R' -> half-range rule;  '=' -> equal X value rule)

      Parameters of fitted resistant line
           slope  intercept

       -0.033482  111.67558

     ----- Ratio of Slopes table ------
     Rows are powers of X, columns are powers of Y

         -1.0     -0.5      log     sqrt      raw      2.0

-1.0    2.163    1.921    1.708    1.521    1.356    1.081
-0.5    1.898    1.685    1.499    1.334    1.189    0.948
log     1.663    1.477    1.314    1.169    1.042    0.831
sqrt    1.457    1.294    1.151    1.024    0.913    0.728
raw     1.275    1.132    1.007    0.896    0.799    0.637
 2.0    0.975    0.866    0.770    0.685    0.611    0.487

     ------- 5 Best powers -------
      Power of X Power of Y   Slope Ratio   log Ratio

     raw        log                 1.007       0.003
     sqrt       sqrt                1.024       0.010
      2.0       -1.0                0.975      -0.011
     log        raw                 1.042       0.018
     -0.5        2.0                0.948      -0.023

See also