NimbleThink Posted May 14, 2010 Report Share Posted May 14, 2010 (edited) Has anyone coded up an orthogonal fit regression? This is a Model II regression (error in both Y and X variables). It may be known by references to Deming models or to early published work by York [1]. It is used to perform a linear fit when you have error in both X and Y. Thanks. [1] LEAST-SQUARES FITTING OF A STRAIGHT LINE Derek York Can. J. Phys./Rev. can. phys. 44(5): 1079-1086 (1966) Edited May 14, 2010 by NimbleThink Quote Link to comment
vugie Posted May 14, 2010 Report Share Posted May 14, 2010 Has anyone coded up an orthogonal fit regression? This is a Model II regression (error in both Y and X variables). I made something like this, but not very general - just for one case. I was minimizing sum of squared euclidean distances from measurement point to curve and from error rectangle to curve (weighting both - weight for distance from error rectangle was higher). I coded it using my genetic algorithm (Waptia), but it should be doable also with Unconstrained Optimization.vi. Quote Link to comment
Anders Björk Posted May 14, 2010 Report Share Posted May 14, 2010 I made something like this, but not very general - just for one case. I was minimizing sum of squared euclidean distances from measurement point to curve and from error rectangle to curve (weighting both - weight for distance from error rectangle was higher). I coded it using my genetic algorithm (Waptia), but it should be doable also with Unconstrained Optimization.vi. This is the orginal reference Pearson, K. (1901). "On Lines and Planes of Closest Fit to Systems of Points in Space" (PDF). Philosophical Magazine 2 (6): 559–572. http://stat.smmu.edu.cn/history/pearson1901.pdf Actually I think the best implementation would be to autoscale the variables (to unitvariance and zero mean) and then do SVD and some arranging of terms. Look for instance at the code at http://www.mathworks.com/matlabcentral/fileexchange/16800 Quote Link to comment
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