resline | Fit a resistant line to bivariate data | resline |
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.
%include data(nations); *include macros(resline); *-- included in autocall library; %resline(data=nations, x=income, y=imr, id=nation);The printed output includes the following:
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 111.67558plus tables of fitted values and residuals, and plots. In addition, the following table indicates that a log transformation of IMR comes closest to having a linear relationship to (raw) INCOME.
----- 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