Re: [R] Interesting behavior of lm() with small, problematic data sets

[Rainer Krug]

Same version on Mac, same results.


> On 6 Sep 2017, at 15:22, JRG  wrote:
> 
> Indeed (version-specific).
> 
> With R 3.4.1 on linux, I get coefficients and residuals that are
> numerically exact, F-statistic = NaN, p-value = NA, R-squared = NaN, etc.
> 
> All of which is what ought to happen, given that the response variable
> (y) is not actually variable.
> 
> 
> ---JRG
> John R. Gleason
> 
> 
> On 09/06/2017 09:10 AM, S Ellison wrote:
>>> I think what you're seeing is
>>> https://en.wikipedia.org/wiki/Loss_of_significance.
>> 
>> Almost. 
>> All the results in the OP's summary are reflections of finite precision in 
>> the analytically exact solution, leading to residuals smaller than the 
>> double precision limit. The summary is correctly warning that it's all 
>> potentially nonsense, and indeed the only things you can trust are the 
>> coefficient values (to within .Machine$double.eps or thereabouts)
>> 
>> Interestingly, though, my current version of R (3.4.0) gives numerically 
>> exact coefficients (c(1,0) and identically zero standard errors.
>> 
>> So this particular example is apparently version-specific.
>> 
>> S Ellison
>> 
>> 
>> ***
>> This email and any attachments are confidential. Any use...{{dropped:8}}
>> 
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Re: [R] Interesting behavior of lm() with small, problematic data sets

[JRG]

Indeed (version-specific).

With R 3.4.1 on linux, I get coefficients and residuals that are
numerically exact, F-statistic = NaN, p-value = NA, R-squared = NaN, etc.

All of which is what ought to happen, given that the response variable
(y) is not actually variable.


---JRG
John R. Gleason


On 09/06/2017 09:10 AM, S Ellison wrote:
>> I think what you're seeing is
>> https://en.wikipedia.org/wiki/Loss_of_significance.
> 
> Almost. 
> All the results in the OP's summary are reflections of finite precision in 
> the analytically exact solution, leading to residuals smaller than the double 
> precision limit. The summary is correctly warning that it's all potentially 
> nonsense, and indeed the only things you can trust are the coefficient values 
> (to within .Machine$double.eps or thereabouts)
> 
> Interestingly, though, my current version of R (3.4.0) gives numerically 
> exact coefficients (c(1,0) and identically zero standard errors.
> 
> So this particular example is apparently version-specific.
> 
> S Ellison
> 
> 
> ***
> This email and any attachments are confidential. Any use...{{dropped:8}}
> 
> __
> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
> 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.
>

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Re: [R] Interesting behavior of lm() with small, problematic data sets

[S Ellison]

> I think what you're seeing is
> https://en.wikipedia.org/wiki/Loss_of_significance.

Almost. 
All the results in the OP's summary are reflections of finite precision in the 
analytically exact solution, leading to residuals smaller than the double 
precision limit. The summary is correctly warning that it's all potentially 
nonsense, and indeed the only things you can trust are the coefficient values 
(to within .Machine$double.eps or thereabouts)

Interestingly, though, my current version of R (3.4.0) gives numerically exact 
coefficients (c(1,0) and identically zero standard errors.

So this particular example is apparently version-specific.

S Ellison


***
This email and any attachments are confidential. Any use...{{dropped:8}}

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Re: [R] Interesting behavior of lm() with small, problematic data sets

[mark . hogue]

Tim,

I think what you're seeing is 
https://en.wikipedia.org/wiki/Loss_of_significance.

Cheers,

Mark



From:   "Glover, Tim" 
To: "r-help@r-project.org" 
Date:   09/05/2017 11:37 AM
Subject:[R] Interesting behavior of lm() with small, problematic 
data sets
Sent by:"R-help" 



I've recently come across the following results reported from the lm() 
function when applied to a particular type of admittedly difficult data. 
When working with
small data sets (for instance 3 points) with the same response for 
different predicting variable, the resulting slope estimate is a 
reasonable approximation of the expected 0.0, but the p-value of that 
slope estimate is a surprising value.  A reproducible example is included 
below, along with the output of the summary of results

# example code
x <- c(1,2,3)
y <- c(1,1,1)

#above results in{ (1,1) (2,1) (3,1)} data set to regress

new.rez <- lm (y ~ x) # regress constant y on changing x)
summary(new.rez) # display results of regression

 end of example code

Results:

Call:
lm(formula = y ~ x)

Residuals:
 1  2  3
 5.906e-17 -1.181e-16  5.906e-17

Coefficients:
  Estimate Std. Errort value Pr(>|t|)
(Intercept)  1.000e+00  2.210e-16  4.525e+15   <2e-16 ***
x   -1.772e-16  1.023e-16 -1.732e+000.333
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Residual standard error: 1.447e-16 on 1 degrees of freedom
Multiple R-squared:  0.7794,Adjusted R-squared:  0.5589
F-statistic: 3.534 on 1 and 1 DF,  p-value: 0.3112

Warning message:
In summary.lm(new.rez) : essentially perfect fit: summary may be 
unreliable


##

There is a warning that the summary may be unreliable sue to the 
essentially perfect fit, but a p-value of 0.3112 doesn?t seem reasonable.
As a side note, the various r^2 values seem odd too.







Tim Glover
Senior Scientist II (Geochemistry, Statistics), Americas - Environment & 
Infrastructure, Amec Foster Wheeler
271 Mill Road, Chelmsford, Massachusetts, USA 01824-4105
T +01 978 692 9090  D +01 978 392 5383  M +01 850 445 5039
tim.glo...@amecfw.com  amecfw.com


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Re: [R] Interesting behavior of lm() with small, problematic data sets

[David Winsemius]

> On Sep 5, 2017, at 6:24 AM, Glover, Tim  wrote:
> 
> I've recently come across the following results reported from the lm() 
> function when applied to a particular type of admittedly difficult data.  
> When working with
> small data sets (for instance 3 points) with the same response for different 
> predicting variable, the resulting slope estimate is a reasonable 
> approximation of the expected 0.0, but the p-value of that slope estimate is 
> a surprising value.  A reproducible example is included below, along with the 
> output of the summary of results
> 
> # example code
> x <- c(1,2,3)
> y <- c(1,1,1)
> 
> #above results in{ (1,1) (2,1) (3,1)} data set to regress
> 
> new.rez <- lm (y ~ x) # regress constant y on changing x)
> summary(new.rez) # display results of regression
> 
>  end of example code
> 
> Results:
> 
> Call:
> lm(formula = y ~ x)
> 
> Residuals:
> 1  2  3
> 5.906e-17 -1.181e-16  5.906e-17
> 
> Coefficients:
>  Estimate Std. Errort value Pr(>|t|)
> (Intercept)  1.000e+00  2.210e-16  4.525e+15   <2e-16 ***
> x   -1.772e-16  1.023e-16 -1.732e+000.333
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> 
> Residual standard error: 1.447e-16 on 1 degrees of freedom
> Multiple R-squared:  0.7794,Adjusted R-squared:  0.5589
> F-statistic: 3.534 on 1 and 1 DF,  p-value: 0.3112
> 
> Warning message:
> In summary.lm(new.rez) : essentially perfect fit: summary may be unreliable
> 
> 
> ##
> 
> There is a warning that the summary may be unreliable sue to the essentially 
> perfect fit, but a p-value of 0.3112 doesn’t seem reasonable.
> As a side note, the various r^2 values seem odd too.

You have an overfitted model with only 3 perfectly fit-able data points and you 
are whinging about a Wald statistic about which you were warned. I think you 
are wasting our time. (But I'm fully retired and I have a lot of time to waste.)

I seem to remember that a t-distribution with 1 degree of freedom is actually 
the Cauchy distribution. I would point out that you can also get:

> 2*pt(-1.732e+00, 1)
[1] 0.414

So maybe from that perspective any value might be "reasonable" from the 
perspective that you have that particular number data points (so one degree of 
freedom) and are using an estimate of the t-statistic which is essentially the 
ratio of 0/0 from a numerical point of view.

-- 
David.

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Re: [R] Interesting behavior of lm() with small, problematic data sets

[Jeff Newmiller]

Why does an unreliable fit have to provide "reasonable" results?

More specifically, p-values arise from observed distributions... if your slopes 
are "in the noise" then the slope estimate's location within that distribution 
could be anywhere relative to the center and spread of that very narrow 
distribution, leading to, ah, what was it... oh, right... "unreliable" results.
-- 
Sent from my phone. Please excuse my brevity.

On September 5, 2017 6:24:30 AM PDT, "Glover, Tim"  
wrote:
>I've recently come across the following results reported from the lm()
>function when applied to a particular type of admittedly difficult
>data.  When working with
>small data sets (for instance 3 points) with the same response for
>different predicting variable, the resulting slope estimate is a
>reasonable approximation of the expected 0.0, but the p-value of that
>slope estimate is a surprising value.  A reproducible example is
>included below, along with the output of the summary of results
>
># example code
>x <- c(1,2,3)
>y <- c(1,1,1)
>
>#above results in{ (1,1) (2,1) (3,1)} data set to regress
>
>new.rez <- lm (y ~ x) # regress constant y on changing x)
>summary(new.rez) # display results of regression
>
> end of example code
>
>Results:
>
>Call:
>lm(formula = y ~ x)
>
>Residuals:
> 1  2  3
> 5.906e-17 -1.181e-16  5.906e-17
>
>Coefficients:
>  Estimate Std. Errort value Pr(>|t|)
>(Intercept)  1.000e+00  2.210e-16  4.525e+15   <2e-16 ***
>x   -1.772e-16  1.023e-16 -1.732e+000.333
>---
>Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
>Residual standard error: 1.447e-16 on 1 degrees of freedom
>Multiple R-squared:  0.7794,Adjusted R-squared:  0.5589
>F-statistic: 3.534 on 1 and 1 DF,  p-value: 0.3112
>
>Warning message:
>In summary.lm(new.rez) : essentially perfect fit: summary may be
>unreliable
>
>
>##
>
>There is a warning that the summary may be unreliable sue to the
>essentially perfect fit, but a p-value of 0.3112 doesn’t seem
>reasonable.
>As a side note, the various r^2 values seem odd too.
>
>
>
>
>
>
>
>Tim Glover
>Senior Scientist II (Geochemistry, Statistics), Americas - Environment
>& Infrastructure, Amec Foster Wheeler
>271 Mill Road, Chelmsford, Massachusetts, USA 01824-4105
>T +01 978 692 9090  D +01 978 392 5383  M +01 850 445 5039
>tim.glo...@amecfw.com  amecfw.com
>
>
>This message is the property of Amec Foster Wheeler plc and/or its
>subsidiaries and/or affiliates and is intended only for the named
>recipient(s). Its contents (including any attachments) may be
>confidential, legally privileged or otherwise protected from disclosure
>by law. Unauthorised use, copying, distribution or disclosure of any of
>it may be unlawful and is strictly prohibited. We assume no
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