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

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