"Vitaly Kupisk" <[EMAIL PROTECTED]> wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... > Hi, > > I am looking for a good orthogonal linear regression (L1) algorithm > and have been pointed to Bargiela and Hartley > www.doc.ntu.ac.uk/RTTS/Papers/rttg-publ02.ps. I don't quite get what > they mean by "solving equation 29" -- obviuosly a 0 vector is a > solution (often the only one); they must mean something else, so I > can't reconstruct the algorithm. > > Can anyone explain their algorithm, or does anyone know of an > available implementation of it, or for that matter any good orthogonal > linear L1 regression algorithm/implementation? > > I saw some references in the group (e.g Jackson, J. E. (1991), "A > Users Guide To Principal Components", John Wiley and Sons, New York, > chapter 15.) but haven't looked at them yet. Are these older > algorithms much inferior to Bargiela-Hartley's? > > Please copy me on your replies to the group. > > Thank you > > Vitaly Kupisk > [EMAIL PROTECTED] -------------------------------------------------------------- The basic problem with orthogonal regression is that it minimizes the sum of the square of the error as measured by a vector perpendicular to the regression line through each point. This is an assumption about the variance of the X and Y values, which cannot be verified from the data. The better method is to make an assumption on the ratio of the variances, or to assume that the X values have no errors. In many cases, where the X values are instrument measurements, the X variance can be estimated prior to collecting the data, and the regression based on minimizing the Y variance.
With orthogonal regression, one depends on the validity of the linearity assumption. Slight non-linearity can give problems. As Woodhouser points out, scaling (or normalizing) the X and Y values can have a very profound effect on the values of the regression coefficients. David Heiser . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
