Re: st: non-normal residual

[Fabio Zona <fabio.zona@unibocconi.it>]

That is great! Thank you very much for your clarifiation

By the way: how should one run a regression, if residuals (errors) are not normally distributed (es for P-P plot and Q-Q plot) and tranformation of Y (i.e., log, square root..and the like) does not help to improve this distrubution of residuals??

Thanks a lot



----- Messaggio originale -----
Da: "Robert Ploutz-Snyder (JSC-SK)[USRA]" <robert.ploutz-snyder-1@nasa.gov>
A: statalist@hsphsun2.harvard.edu
Inviato: Giovedì, 29 aprile 2010 20:33:36 GMT +01:00 Amsterdam/Berlino/Berna/Roma/Stoccolma/Vienna
Oggetto: RE: st: non-normal residual

Right...

And having said all of that... the law of large numbers works... with large numbers!  we have SMALL n.  So then, can we "trust" that if we do have normally distributed residuals, (implying betas are too) but not y's and/or one or more x's, are we still ok?  Homoscedasticity must be tested also, and by independence I assume you refer to collinearity problems.  But passing the usual there, I am operating under the assumption that our results are trustworthy even if y's and some X's are not normally distributed, as long as the host of diagnostic plots focusing mainly on residuals and blups look ok.




-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Feiveson, Alan H. (JSC-SK311)
Sent: Thursday, April 29, 2010 1:27 PM
To: statalist@hsphsun2.harvard.edu
Subject: RE: st: non-normal residual

Yes, in a nutshell, all that matters for proper inference in large samples is whether the parameter estimates (regression coefficients, etc) can be considered approximately normally distributed with the appropriate standard errors as their standard deviations. For the most common types of analyses, the parameter estimates tend to be normal as the sample size increases for most (but not all!) distributions that the residuals might have, but the estimates of their standard errors might not be correct if other model assumptions (such as independence or homoscedasticity) do not hold. 

Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Michael Norman Mitchell
Sent: Thursday, April 29, 2010 12:43 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: non-normal residual

Greetings Fabio

   I think that this is an outstanding question, especially since there 
is so much conflicting information on this topic. I feel that the 
following article provides an outstanding presentation of this issue and 
some extremely useful information.

THE IMPORTANCE OF THE NORMALITY
ASSUMPTION IN LARGE PUBLIC
HEALTH DATA SETS
Thomas Lumley, Paula Diehr, Scott Emerson, and Lu Chen

http://works.bepress.com/cgi/viewcontent.cgi?article=1023&context=paula_diehr

   I would recommend this article to anyone who has contemplated the 
issue of the normality assumption.

Best regards,

Michael N. Mitchell
See the Stata tidbit of the week at...
http://www.MichaelNormanMitchell.com

On 2010-04-29 10.19 AM, Fabio Zona wrote:
> Dear statlist
>
> I have a cross-section multiple regression: however,
> - Y is not distributed normally (some say it should be; some say it is not needed! where is the truth? I read residuals must be normally distributed, not the Y...)
> - any tranformation of Y does not allow to approach a normal-distribution
> - beyond Y, residuals are non-normally distributed
>
> Any suggestions on how to handle this situation?
>
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