I have a situation that when I fit a robust regression line (least trimmed squares) to a set of data a lot of the residuals are in fact zero.
This occurs mainly in the situation where the slope is zero and the y values are integers. When the line is fitted it runs right through the majority of the values. I am happy with this fit as a traditional least squares line is incorrect due to a few errors in the data.
However now I've fitted the line I want to analyze the residuals and detect the outliers (possibly automatically). I intended to compute a 'score' perhaps based on Tukey's technique of using the upper and lower quartile plus 1.5 times the inter-quartile range. However this approach won't work if many of the residuals are zero because the IQR is also zero.
What should I do? Just base the score on something like the number of standard deviations from the mean? Thanks.