I am trying to find an R function to calculate the linear least-square fitting of two variables when both have an error (expressed as standard deviation). I have found this problem referred to in half a dozen different ways: Williamson-York method, RMA, Deming regression, bivariate fit, weighted least squares, etc...
I am no statistician, so this may seem like a stupid question, but are all these names referring to the same methodology? And what is the correct name for it if one needs to look for information?
I need to use the procedure described in this paper: https://acp.copernicus.org/articles/8/5477/2008/acp-8-5477-2008.pdf. The assumptions are that the distribution of errors is normal and and the fit parameters do not depend on the choice of units. The R
deming package seems to give the same results as in the paper, at least on the example dataset, so I think it is okay. But it does not return a Pearson correlation coefficient, like
Is it that this type of regression cannot calculate the correlation coefficient or is it just the particular implementation of the
deming package that does not?
EDIT: in a related paper, I found reference to this C function http://numerical.recipes/webnotes/nr3web19.pdf. It seems to be doing what I want but it is unclear to me if it is the same fitting method.
EDIT 2: specific questions:
- Are these terms referring to the same method: Williamson-York method, RMA, Deming regression, bivariate fit, weighted least squares?
- It the methods are equivalent, which one is the correct term to use?
- Are the methods described in the two linked pdf the same?
- The R package
demingimplements a Deming regression. Why does it not return a correlation coefficient? Is it the method or its implementation in the package?