[R] Testing for normality of residuals in a regression model

[John Fox]

Dear Kjetil,

I don't believe that these are BLUS residuals, but since the last n - r
"effects" are projections onto an orthogonal basis for the residual
subspace, they should do just fine (as long as the basis vectors have the
same length, which I think is the case, but perhaps someone can confirm).
The general idea is to transform the LS residuals into an uncorrelated,
equal-variance set.

Regards,
 John

--------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
http://socserv.mcmaster.ca/jfox 
-------------------------------- 

> -----Original Message-----
> From: Kjetil Brinchmann Halvorsen [mailto:kjetil at acelerate.com] 
> Sent: Friday, October 15, 2004 9:12 AM
> To: John Fox
> Cc: 'Federico Gherardini'; R-help at stat.math.ethz.ch
> Subject: Re: [R] Testing for normality of residuals in a 
> regression model
> 
> John Fox wrote:
> 
> >Dear Federico,
> >
> >A problem with applying a standard test of normality to LS 
> residuals is 
> >that the residuals are correlated and heterskedastic even if the 
> >standard assumptions of the model hold. In a large sample, this is 
> >unlikely to be problematic (unless there's an unusual data 
> >configuration), but in a small sample the effect could be nontrivial.
> >
> >One approach is to use BLUS residuals, which transform the 
> LS residuals 
> >to a smaller set of uncorrelated, homoskedastic residuals 
> (assuming the 
> >correctness of the model).
> >
> I'm not sure if this are BLUE residuals, but the following 
> function transform to a smaller set of independent, 
> homoscedastic residuals and the calls
> shapiro.test:
> I've proposed to make this a method for shapiro.test for "lm" 
> objects, but it is not accepted.
> 
>  shapiro.test.lm
> function (obj)
> {
>     eff <- effects(obj)
>     rank <- obj$rank
>     df.r <- obj$df.residual
>     if (df.r < 3)
>         stop("To few degrees of freedom for residual for the test.")
>     data.name <- deparse(substitute(obj))
>     x <- eff[-(1:rank)]
>     res <- shapiro.test(x)
>     res$data.name <- data.name
>     res$method <- paste(res$method, " for residuals of linear model")
>     res
> }
> 
> Kjetil
> 
> 
> > A search of R resources didn't turn up anything for BLUS, but they 
> >shouldn't be hard to compute. This is a standard topic 
> covered in many 
> >econometrics texts.
> >
> >You might consider the alternative of generating a bootstrapped 
> >confidence envelope for the QQ plot; the qq.plot() function 
> in the car 
> >package will do this for a linear model.
> >
> >I hope this helps,
> > John
> >
> >--------------------------------
> >John Fox
> >Department of Sociology
> >McMaster University
> >Hamilton, Ontario
> >Canada L8S 4M4
> >905-525-9140x23604
> >http://socserv.mcmaster.ca/jfox
> >--------------------------------
> >
> >  
> >
> >>-----Original Message-----
> >>From: r-help-bounces at stat.math.ethz.ch 
> >>[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Federico 
> >>Gherardini
> >>Sent: Friday, October 15, 2004 7:44 AM
> >>To: R-help at stat.math.ethz.ch
> >>Subject: [R] Testing for normality of residuals in a 
> regression model
> >>
> >>Hi all,
> >>
> >>Is it possible to have a test value for assessing the normality of 
> >>residuals from a linear regression model, instead of simply 
> relying on 
> >>qqplots?
> >>I've tried to use fitdistr to try and fit the residuals 
> with a normal 
> >>distribution, but fitdsitr only returns the parameters of the 
> >>distribution and the standard errors, not the p-value. Am I missing 
> >>something?
> >>
> >>Cheers,
> >>
> >>Federico
> >>
> >>______________________________________________
> >>R-help at stat.math.ethz.ch mailing list
> >>https://stat.ethz.ch/mailman/listinfo/r-help
> >>PLEASE do read the posting guide! 
> >>http://www.R-project.org/posting-guide.html
> >>    
> >>
> >
> >______________________________________________
> >R-help at stat.math.ethz.ch mailing list
> >https://stat.ethz.ch/mailman/listinfo/r-help
> >PLEASE do read the posting guide! 
> >http://www.R-project.org/posting-guide.html
> >
> >
> >  
> >
> 
> 
> -- 
> 
> Kjetil Halvorsen.
> 
> Peace is the most effective weapon of mass construction.
>                --  Mahdi Elmandjra
> 
> 
>