Orthogonal/Model II/Deming regression

[NimbleThink]

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

[vugie]

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.

[Anders Björk]

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