R help - Dec 2003 - add a point to regression line and cook's distance

Hi, 

This is more a statistics question rather than R question. But I thought people
on this list may have some pointers.

MY question is like the following:
I would like to have a robust regression line. The data I have are mostly
clustered around a small range. So
the regression line tend to be influenced strongly by outlier points (with large
cook's distance). From the application
's background, I know that the line should pass (0,0), which is far away
from the data cloud. I would like to add this
point to have a more robust line. The question is: does it make sense to do
this? what are the negative impacts if any?

thanks,
jonathan

What is the context?  What do the "outliers" represent?  If you 
think carefully about the context, you may find the answer. 

      hope this helps.  spencer graves
p.s.  I know statisticians who worked for HP before the split and who 
still work for either HP or Agilent, I'm not certain which.  If you want 
to contact me off-line, I can give you a couple of names if that might 
help. 

jonathan_li at agilent.com wrote:
>Hi, 
>
>This is more a statistics question rather than R question. But I thought
people on this list may have some pointers.
>
>MY question is like the following:
>I would like to have a robust regression line. The data I have are mostly
clustered around a small range. So
>the regression line tend to be influenced strongly by outlier points (with
large cook's distance). From the application
>'s background, I know that the line should pass (0,0), which is far away
from the data cloud. I would like to add this
>point to have a more robust line. The question is: does it make sense to do
this? what are the negative impacts if any?
>
>thanks,
>jonathan
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>  
>

If you know that the line should pass through (0,0), would it make sense to
do a regression without an intercept?  You can do that by putting "-1"
in
the formula, like:  lm(y ~ x - 1).

Hope this helps,

Matt

Matthew Wiener
RY84-202
Applied Computer Science & Mathematics Dept.
Merck Research Labs
126 E. Lincoln Ave.
Rahway, NJ 07065
732-594-5303 


-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Spencer Graves
Sent: Wednesday, December 03, 2003 5:51 PM
To: jonathan_li at agilent.com
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] add a point to regression line and cook's distance


      What is the context?  What do the "outliers" represent?  If you 
think carefully about the context, you may find the answer. 

      hope this helps.  spencer graves
p.s.  I know statisticians who worked for HP before the split and who 
still work for either HP or Agilent, I'm not certain which.  If you want 
to contact me off-line, I can give you a couple of names if that might 
help. 

jonathan_li at agilent.com wrote:
>Hi, 
>
>This is more a statistics question rather than R question. But I thought
people on this list may have some pointers.
>
>MY question is like the following:
>I would like to have a robust regression line. The data I have are mostly
clustered around a small range. So
>the regression line tend to be influenced strongly by outlier points (with
large cook's distance). From the application
>'s background, I know that the line should pass (0,0), which is far away
from the data cloud. I would like to add this
>point to have a more robust line. The question is: does it make sense to do
this? what are the negative impacts if any?
>
>thanks,
>jonathan
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>  
>
______________________________________________
R-help at stat.math.ethz.ch mailing list
https://www.stat.math.ethz.ch/mailman/listinfo/r-help

It is likely that the "true" relationship is nonlinear. There
isn't a priori knowledge about linearity. In the small range where we do
have enough data, the relationship
looks linear. Outside the range, the data are very scarse and have high level of
noises too.
This is why adding (0,0) to the data can potentially improve the fit a great
deal. But at the
same time, I have never heard people doing it this way. 

Jonathan

-----Original Message-----
From: Murray Jorgensen [mailto:maj at stats.waikato.ac.nz]
Sent: Wednesday, December 03, 2003 5:18 PM
To: Wiener, Matthew
Cc: jonathan_li at agilent.com; r-help at stat.math.ethz.ch
Subject: Re: [R] add a point to regression line and cook's distance


Not a good idea, unless the regression function is *known* to be linear. 
More likely it is only approximately linear over small ranges.

Murray Jorgensen

Wiener, Matthew wrote:
> If you know that the line should pass through (0,0), would it make sense to
> do a regression without an intercept?  You can do that by putting
"-1" in
> the formula, like:  lm(y ~ x - 1).
> 
> Hope this helps,
> 
> Matt
> 
> Matthew Wiener
> RY84-202
> Applied Computer Science & Mathematics Dept.
> Merck Research Labs
> 126 E. Lincoln Ave.
> Rahway, NJ 07065
> 732-594-5303 
> 
> 
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Spencer Graves
> Sent: Wednesday, December 03, 2003 5:51 PM
> To: jonathan_li at agilent.com
> Cc: r-help at stat.math.ethz.ch
> Subject: Re: [R] add a point to regression line and cook's distance
> 
> 
>       What is the context?  What do the "outliers" represent?  If
you
> think carefully about the context, you may find the answer. 
> 
>       hope this helps.  spencer graves
> p.s.  I know statisticians who worked for HP before the split and who 
> still work for either HP or Agilent, I'm not certain which.  If you
want
> to contact me off-line, I can give you a couple of names if that might 
> help. 
> 
> jonathan_li at agilent.com wrote:
> 
> 
>>Hi, 
>>
>>This is more a statistics question rather than R question. But I thought
> 
> people on this list may have some pointers.
> 
>>MY question is like the following:
>>I would like to have a robust regression line. The data I have are
mostly
> 
> clustered around a small range. So
> 
>>the regression line tend to be influenced strongly by outlier points
(with
> 
> large cook's distance). From the application
> 
>>'s background, I know that the line should pass (0,0), which is far
away
> 
> from the data cloud. I would like to add this
> 
>>point to have a more robust line. The question is: does it make sense to
do
> 
> this? what are the negative impacts if any?
> 
>>thanks,
>>jonathan
>>
>>______________________________________________
>>R-help at stat.math.ethz.ch mailing list
>>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>> 
>>
> 
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> 
> 
-- 
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz                                Fax 7 838 4155
Phone  +64 7 838 4773 wk    +64 7 849 6486 home    Mobile 021 1395 862

jonathan_li at agilent.com wrote:
> Hi, 
> 
> 
> MY question is like the following:
> I would like to have a robust regression line. The data I have are 
 > mostly clustered around a small range. So
> the regression line tend to be influenced strongly by outlier points 
 > (with large cook's distance). From the application's
 > background, I know that the line should pass (0,0), which is far
 > away from the data cloud. I would like to add this
> point to have a more robust line. The question is: 
 > does it make sense to do this? what are the negative impacts if any?

Have you tried a more robust fit (ltsreg() in the package lqs springs to 
mind)?  Using this, without forcing the intercept to zero, might give 
you some idea if your idea makes sense.  Venables and Ripley (Modern 
Applied Statistics with S, Springer-Verlag, 2002) give a good 
introduction to robust linear models, and how to estimate their error 
distribution.  Julian Faraway also gives an overview of the same, in his 
"Practical Regression and ANOVA using R".
http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf

Hope that helps

Jason
-- 
Indigo Industrial Controls Ltd.
http://www.indigoindustrial.co.nz
64-21-343-545
jasont at indigoindustrial.co.nz

One way of implementing some Bayesian techniques is to add data points 
based on prior knowledge.  E.g., see Gelman, Carlin, Stern & Rubin, in 
"Bayesian Data Analysis" (1997) for how a prior on a regression
parameter
can be interpreted as an additional data point.  (Section 8.9 in my 2000 
reprint).

hope this helps,

Tony Plate


At Wednesday 02:31 PM 12/3/2003 -0800, jonathan_li at agilent.com
wrote:
>Hi,
>
>This is more a statistics question rather than R question. But I thought 
>people on this list may have some pointers.
>
>MY question is like the following:
>I would like to have a robust regression line. The data I have are mostly 
>clustered around a small range. So
>the regression line tend to be influenced strongly by outlier points (with 
>large cook's distance). From the application
>'s background, I know that the line should pass (0,0), which is far away
>from the data cloud. I would like to add this
>point to have a more robust line. The question is: does it make sense to 
>do this? what are the negative impacts if any?
>
>thanks,
>jonathan
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
Tony Plate   tplate at acm.org