# [R] orthogonal distance regression package?

Wed Feb 29 20:42:54 CET 2012

```Thanks all.  This is tremendously helpful.

Best,

On Feb 29, 2012, at 12:58 PM, David Reiner wrote:

> My understanding is that TLS, EIV, and orthogonal regression are closely related but separate concepts.
> If you read the  'Talk' at the Wikipedia page referenced below, you will see that many people have
> terminology problems as well.
> My take is that TLS is a special case of EIV and orthogonal linear regression is a special case of TLS.
> ** If your data is centered, then the orthogonal regression slope is just the ratio of the standard deviations of the two variables. **
> You can get the same thing from PCA if you first scale by the SD's and then restore them after finding the first eigenvector.
> The TLS and EIV approaches are more general, but assuming that the relative errors in the variables are equal, and things are 'nice' gives the simple result above.
>
> The page Mark refers to from Sabine van Huffel's book on TLS is visible in Google books.
>
> HTH,
> -- David
>
>
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Mark Leeds
> Sent: Wednesday, February 29, 2012 12:37 PM
> Cc: <r-help at r-project.org>; Bert Gunter
> Subject: Re: [R] orthogonal distance regression package?
>
> Hi: I can't find it anywhere on the internet but I have a book that shows that, as long as the SVD of the X matrix can be obtained, then the coefficient solution to TLS ( least angle regression )  is only a function of the eigenvectors.
> Therefore, principal components can be used to obtain the coefficients in TLS which could be why there may not be an R package out there.
>
> The book is titled "The Total Least Squares Problem" Huffel and Vandewalle.
>
> Paul Teetor's paper ( see link below ) has an example of using principal components to calculate the coefficients in a univariate TLS.
>
> Disclaimer: I've never used TLS regression and never studied it so there could be subtlleties where the result doesn't hold. The result is on page
> 37 of the book and the book is almost 300 pages so the SVD approach must not work all the time.
>
> ''
>
>
>
>
>
>
>
> On Wed, Feb 29, 2012 at 1:19 PM, Adam Waytz < a-waytz at kellogg.northwestern.edu> wrote:
>
>>
>> In the age of google, I have found that concepts such as these are
>> more complex than what Wikipedia provides. Going far beyond a cursory
>> search, it appeared to me there are subtle differences between these
>> terms. I was hoping this knowledgeable community could provide insight
>> on an R package to perform ODR. Thank you.
>>
>> On Feb 29, 2012, at 12:07 PM, "Bert Gunter" <gunter.berton at gene.com>
>> wrote:
>>
>>> On Wed, Feb 29, 2012 at 7:53 AM, Adam Waytz
>>> <a-waytz at kellogg.northwestern.edu> wrote:
>>>>
>>>> Hello,
>>>>
>>>> I am extremely new to R and have found some leads to this question
>>>> in
>> the archives, but I am still a bit uncertain.
>>>> I am looking for an R package to carry out orthogonal distance
>> regression.  I found some answers regarding Deming
>>>> regression and Total Least Squares regression, but I was unclear if
>> these are identical terms.
>>>
>>> In the age of Google?!
>>>
>>> Searching on "orthogonal regression" brought up:
>>>
>>> http://en.wikipedia.org/wiki/Total_least_squares
>>>
>>> which provides info. Sheesh!
>>>
>>> I suggest you also check the ChemPhys and Econometrics task views on
>>> CRAN to see what they have to offer.
>>>
>>> Incidentally, my very limited understanding is that orthogonal
>>> regression (for errors in variables) can be problematic. The
>>> wikipedia article provides more details.
>>>
>>> -- Bert
>>>
>>> Please let me know if
>>>> a package is available.
>>>>
>>>> Thank you,
>>>>
>>>> ______________________________________________
>>>> R-help at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>> http://www.R-project.org/posting-guide.html
>>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>>
>>>
>>> --
>>>
>>> Bert Gunter
>>> Genentech Nonclinical Biostatistics
>>>
>>> Internal Contact Info:
>>> Phone: 467-7374
>>> Website:
>>>
>> -biostatistics/pdb-ncb-home.htm
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
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> and provide commented, minimal, self-contained, reproducible code.
>
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