Re: Calcuation of STND residuals

# Re: Calcuation of STND residuals

```Dear Bruce,
> X-Authentication-Warning: lamb.chiswick.anprod.csiro.au: petidomo set sender
to asreml-owner@lamb.chiswick.anprod.csiro.au using -f
> Date: Wed, 19 Apr 2000 13:21:22 -0500
> From: Bruce Southey <southey@uiuc.edu>
> MIME-Version: 1.0
Dear Bruce,

It is negligent of me to explain how the STND RES are
calculated.

I wrote this bit of code long before thinking of calculating the HAT
matrix diagonal.  I wanted a robust estimate of the standard error
of the actual values so my criterion is
sum(abs(res))/count/0.8

In this example
S> sum(abs(yht\$Res))/21/.8
[1] 1.2054
S> sum(abs(yht\$Res))/21/.8*3.3
[1] 3.9777
S> yht\$Res[9]/1.2054
[1] 3.3184
S>

21 is the count because I ignore the 3 zero residuals on the [false in this
case] assumption that they relate to missing values.

You are write in that I'm using 3.3 of the standard value.

Now that I calculate the hat diagonal, I could calculate the standardized
residual if I have the information available at the right time.

I'll think about doing that.  In the meantime, it is not difficult
to calc the Stand Res from what is in the yht file

S> yht\$Res/sqrt(1-yht\$Hat)
[1] -0.41775 -0.41775  0.69625  0.69625  0.00000  0.00000  1.07180 -1.07180
[9]  4.28722 -0.41775 -0.41775 -0.41775 -1.07180 -1.07180  1.07180  2.87706
[17] -0.95902 -0.95902  0.69625 -1.07180 -1.07180  0.00000 -1.07180 -0.95902

Arthur

> To: "asreml@chiswick.anprod.csiro.au" <asreml@chiswick.anprod.csiro.au>
> Subject: Calcuation of STND residuals
>
> Hi,
> Could someone please tell me how the STND RES are calculated?
> I can not get these residuals from the .yht file.
> The attached is a simple example with a fixed effects only model.
>
> I ran the analysis with and without the data point - S^2 is the variance
> with it and S(i)^2 is the variance without.  Res and Hat are the
> residuals and Hat value from the .yht file.
>
> As per pg 376-377 of McCullagh and Nelder
> Stand Res was calculated as Res /(sqrt(1-Hat))
> Student Res was calculated as Stand Res/S
> Del Stud Res was calculated as Student Res * S / S(i)
>
> S^2         S(i)^2    Res     Hat      Stand Res        Student Res
> Del Stud Res
> 1.55357	0.758523	4	0.1295	4.287218357	3.439617822
7.044858309
>
> The value from the .res file is 3.32.
>
> Also, in at least this version of ASREML, potential outliers are those
> with STND RES of >3.3 rather than the 3.5 said on page 115 of the March
> 21, 2000 manual.
>
> Thanks
> Bruce

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
Arthur Gilmour PhD                  mailto:Arthur.Gilmour@agric.nsw.gov.au
Principal Research Scientist (Biometrics)            fax: <61> 2 6391 3899
NSW Agriculture                                           <61> 2 6391 3922
Orange Agricultural Institute             telephone work: <61> 2 6391 3815
Forest Rd, ORANGE, 2800, AUSTRALIA                  home: <61> 2 6362 0046

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