Saturday, January 8, 2011
OLS Is Still Useful
The alternative least squares fit was intended for experimental situations where there were errors in the measurements of both dimensions of a two dimensional fit. There are situations where ordinary least squares gives a better fit and that is when the errors in one dimension dominate that of the other. If we treat y as a function of x then y is the dependent variable and x the independent variable. If the errors are predominately in the dependent variable then OLS is probably the method of choice. This can occur when the independent variable is precisely known. But one cannot rightfully assume that this is true when there are measurement errors also present in its values. If one uses two data points equally spaced above and below some line at a number of fixed points along the line then OLS will give a better estimate of the slope of the line. The newer method will try to get a better fit by assigning some error in the horizontal direction and the variance that results is lower but the fit is poorer when compared with the original line. So one needs to exercise some judgement in deciding which method to use.