Re: why use pi^2/3 replace of error variance 1 in binomial analysis?

2009/4/1 Arthur Gilmour <arthur.gilmour_at_cargovale.com.au>

> The PROBIT transformation maps a probability to an underlying scale
> using the Standard Normal distribution which has a variance of 1.
>
> The LOGIT transformation works in the same way, but is based on a
> Logistic distribution which has a variance of pi^2/3.
>
> Thus, with a logit link, the implicit residual variance on the
> underlying scale is the variance of the logistic distribution.
> This defines the scale on which the other components are estimated.
>
>
> On Tue, 2009-03-31 at 16:41 +0800, luansheng wrote:
> > In the p333 of asreml 3 user guide, it is about an analysis of footrot
> > as a binomial variable using the logistic link. In this example, using
> > pi^2/3 replace of error variance 1. I don't know the reason, anyone
> > tell me? thanks!
> >
> >
> > --
> > Luan sheng
> > ----------------------------------------
> > Yellow Sea Fisheries Research Institute
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> > luansheng_at_ysfri.ac.cn
> > ----------------------------------------
> >
> >
> >
> >
> >
> >
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> Arthur Gilmour
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ok. I have understand this. But why was the variance showed as 1 other
than pi^2/3 in the asr file when using logit link? I think it is more
clear if variance was showed as pi^2/3. I have got wrong heritability
because I always thought that the variance of logit was 1 from the asr
file.

-- 
Luan sheng
----------------------------------------
  Yellow Sea Fisheries Research Institute
  Chinese Academy of Fisheries Sciences
  Nanjing Road 106
  Qingdao 266071
  China
  luansheng_at_gmail.com
  luansheng_at_ysfri.ac.cn
----------------------------------------