[R] Force regression line to a 1:1 relationship

[David Winsemius]

On Sep 13, 2011, at 11:56 AM, David Winsemius wrote:

>
> On Sep 13, 2011, at 11:44 AM, David Winsemius wrote:
>
>>
>> On Sep 13, 2011, at 9:43 AM, RCulloch wrote:
>>
>>> Dear John,
>>>
>>> Thank you for that, and for explaining why the abline() command  
>>> wont/dosen't
>>> work. The approach is based on reviewers comments that I am a tad  
>>> sceptical
>>> about myself but yet curious enough to test their  
>>> suggestion......I don't
>>> think it is very straightforward to explain; however, it involves  
>>> using the
>>> residuals of the lm() and plotting them against a covariate to  
>>> assess
>>> whether or not the deviation from the 1:1 relationship is in someway
>>> influenced by the other covariate.

Is the reviewer perhaps saying this will display departures from a  
"linear" or "straight-line" relationship? If so, then I agree entirely  
with the reviewer.

>>> I hope that shines a small amount of
>>> light on this rather unorthodox approach?!
>>
>> Plotting the residuals against a covariate is a standard way to  
>> assess the assumption that the residuals are distributed normally  
>> around each continuous regressor

I've been corrected offline on this point by another "reviewer", one  
who I consider highly reputable. The regression assumption is that  
residuals are normal around the  "true" relationship, but since we  
only have the predicted relationship, the usual second-best is to look  
at:

  plot( fitted(fit), resid(fit))

Furthermore normality is generally not important. (I did know that.)


>> and have no non-linear relationship around each continuous regressor

That point is still valid.

> Forgot to include homoschedasticity:
>
>  ...and have a reasonably constant standard deviation across the  
> range of the regressor...

Also should be plotting against fitted() rather than regressors. _My_  
external reviewer is of the opinion : "constant variance -- which,  
again, usually is of no importance for estimation anyway unless the  
heteroscedacity is huge-", but I think opinions about what constitutes  
"huge" or "too much" variance may vary.

>
>> . It is not to assess a "1:1 relationship", whatever that is. I  
>> think we would need to  see a complete quotation of the reviewer's  
>> comments before deciding who is confused in this interchange.
>>
>> -- 
>

David Winsemius, MD
West Hartford, CT