There is the lmodel2 package... http://cran.r-project.org/web/packages/lmodel2/vignettes/mod2user.pdf
Geometric mean regression has been discussed on this list in the past, for example: https://stat.ethz.ch/pipermail/r-help/2005-June/072927.html I've used that approach with nls (rightly or wrongly I'm not sure :) http://lastresortsoftware.blogspot.com/2010/08/meeting-in-middle-or-fudging-model-ii.html Hope this helps Michael On 1 October 2010 23:11, Ted Harding <[email protected]> wrote: > On 27-Sep-10 08:55:13, Maayt wrote: >> As this forum proved to be very helpful, I got another question... >> I'd like to fit data points on which I have an error, dx and dy, >> on each x and y. What would be the common procedure to fit this >> data by a linear model taking into account uncertainty on each point? >> Would weighting each point by 1/sqrt(dx2+dy2) (and taking dx and dy >> as relative errors) in a lm() fit do the job? I would like to >> propagate uncertainty of the points into the uncertainty of the fit, >> would that be the case? >> >> Thanks for all the help >> -- > > It would seem that there has been no response yet to this query. > > This type of problem falls under various headers, typically > > [A] Fitting a linear functional relationship > [B] Regression with errors in both variables > > For [A], it is envisaged that x and y are, in the real world, > related by an exact lnear equation > > y = a + b*x or x = a' + b'y or A*x + B*y = C > > and that data (X1,X2,...), (Y1,Y2,...) are obtained by simultaneously > measuring the exact values (x1,x2,...), (y1,y2,...) where measurement > errors result in: > > Xi = xi + e.Xi Yi = yi + e.Yi > > where, for each i, e.X is (say) distributed as N(0,s.X^2) and > e.Y as N(0,s.Y^2), where s.X and s.Y are the standard deviations > of the errors of measurement in X and Y. > > Then it is a question of estimating a and b from the data. > This can be done by Maximum Likelihood, which requires taking > as parameters not only a and b, and s.X and s.Y, but also the > unknown (only observed with error) exact values (x1,x2,...) and > (y1,y2,...). > > This case will not fit into the standard lm() method of fitting. > > For [B], whereas in standard regression it is taken that the > observed X values are used as they stand (i.e. taken as fixed), > here it is accepted that they two are subject to error (similar > to [A]). So, whereas (for given values of {Xi}, {Yi}) a standard > lm(Y ~ X) will give an answer, the X-values on which the result > depends will themselves be uncertain and this uncertainty has > to be taken into account, in the sense that it is uncertain what > values of X Y is being regressed on. > > The conceptual difference between [A] and [B] is that, in [A}, > there is no "directional" aspect: x and y are simply being > considered as related by y = a + b*x, or x = a' + b'*y, with > no preference between either way of expressing it. The linear > relationship can be used for any appropriate purpose. > > However, in [B] we are looking at a regression problem: y is > being regressed on x: lm(Y ~ X), and the primary purpose is > to predict the value of y that would result from a given value > of x. So it is "directional": x --> y. If we were interested > in predicting x from y, then we would do it the other way round: > lm(X ~ Y), so Y --> X, and the respective coefficients of the two > different regression equations cannot be deduced from each other. > > So, in choosing between approach [A] and approach [B], you would > need to consider what you want to use the results for. > > I think the Maximum Likelihood approach to [A] was first properly > considered by D.V. Lindley in 1947: > > D. V. Lindley. > Regression lines and the linear functional relationship. > Suppl. J. Roy. Statist. Soc., 9:218-244, 1947. > > For this to work properly (i.e. be "consistent" in the technical > sense), you need to know the ratio of the two standard errors > (lambda = s.Y/s.X). From your statement of your problem, it looks > as though you would know this ratio. > > The study of [B], regression with errors in both variables, goes > back a very long way, and many approaches have been considered. > These include several studies by J.B. Copas. > > Neither [A] nor [B] is, in general, a straightforward problem! > > A useful overview of approaches to both [A] and [B] can be found > in the freely downloadable: > > An historical overview of regression with errors in both variables. > J.W. Gillard (Cardiff University) > > http://www.cardiff.ac.uk/maths/resources/Gillard_Tech_Report.pdf > > Now, as to what may be available in R: > > I was a bit surprised to find that a full R site search on either of > > "linear functional relationship" > "errors in both variables" > > yielded nothing relevant. It may be that using different search > terms would find appropriate methods (such as considered by Gillard, > or the Lindley approach for [A]), but I'm having difficulty > thinking what such might be! > > So I hope that R-help readers who have used R for this category > of problem can help! > > Ted. > > -------------------------------------------------------------------- > E-Mail: (Ted Harding) <[email protected]> > Fax-to-email: +44 (0)870 094 0861 > Date: 01-Oct-10 Time: 14:10:54 > ------------------------------ XFMail ------------------------------ > > ______________________________________________ > [email protected] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
