# Re: [R] non parametric linear regression

From: Greg Snow <Greg.Snow_at_imail.org>
Date: Thu, 28 Feb 2008 11:41:35 -0700

These methods are more commonly called robust regression or resistant regression (it is not really non-parametric since you are trying to estimate the slope which is a parameter, just not of a normal distribution).

There are many methods for doing robust regressions, the book Modern Applied Statistics with S (MASS) has a good discussion on some different techniques.

Running the command:

Gives several hits, one of which is the mblm function in the mblm package which, based on its description, does the calculations you mention.

Hope this helps,

```--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow_at_imail.org
(801) 408-8111

> -----Original Message-----

> From: r-help-bounces_at_r-project.org
> [mailto:r-help-bounces_at_r-project.org] On Behalf Of Jeanne Vallet
> Sent: Thursday, February 28, 2008 7:07 AM
> To: r-help_at_r-project.org
> Subject: [R] non parametric linear regression
>
> Dear all,
>
> I am looking for if non parametric linear regression is
> available in R. The method I wish to use is described in the
> help of statsdirect statistical software like this : "This is
> a distribution free method for investigating a linear
> relationship between two variables Y (dependent, outcome) and
> X (predictor, independent). The slope b of the regression
> (Y=bX+a) is calculated as the median of the gradients from
> all possible pairwise contrasts of your data. A confidence
> interval based upon
> <http://www.statsdirect.com/help/nonparametric_methods/kend.ht
> m> Kendall's t is constructed for the slope. Non-parametric
> linear regression is much less sensitive to extreme
> observations (outliers) than is
> <http://www.statsdirect.com/help/regression_and_correlation/sr
> eg.htm> simple linear regression based upon the least squares
> method. If your data contain extreme observations which may
> be erroneous but you do not have sufficient reason to exclude
> them from the analysis then non-parametric linear regression
> may be appropriate. This function also provides you with an
> approximate two sided Kendall's rank correlation test for
> independence between the variables. Technical Validation :
> Note that the two sided confidence interval for the slope is
> the inversion of the two sided Kendall's test. The
> approximate two sided P value for Kendall's t or tb is given
> but the
> <http://www.statsdirect.com/help/distributions/pk.htm> exact
> quantile from Kendall's distribution is used to construct the
> confidence interval, therefore, there may be slight
> disagreement between the P value and confidence interval. If
> there are many ties then this situation is compounded (
> <http://www.statsdirect.com/help/references/refs.htm> Conover, 1999)."
>
>
>
>
> Regards,
>
> Jeanne Vallet
>
> PhD student,
>
> Angers, France
>
>
>
>
>
>
> 	[[alternative HTML version deleted]]
>
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> and provide commented, minimal, self-contained, reproducible code.
>

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