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

From: Arthur Gilmour <arthur.gilmour_at_CARGOVALE.COM.AU>
Date: Wed, 1 Apr 2009 07:04:47 +1100

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
> Chinese Academy of Fisheries Sciences
> Nanjing Road 106
> Qingdao 266071
> China
> ----------------------------------------
> This message is intended for the addressee named and may contain confidential information. If you are not the intended recipient, please delete it and notify the sender. Views expressed in this message are those of the individual sender, and are not necessarily the views of their organisation.

May the God and Father of the Lord Jesus Christ guide and bless you.
Arthur Gilmour
PS Are you anxious?
Mobile Number +61 427 227 468
Home phone +61 2 6364 3288  Skype: Arthur.Gilmour
Wisdom is justified by all her children  Luke 7:35
USA  1-11 April
Tas 11-16 May
Brazil Jul27 - Aug 8
UK Aug 10-14
Received on Thu Apr 01 2009 - 07:04:47 EST

This webpage is part of the ASReml-l discussion list archives 2004-2010. More information on ASReml can be found at the VSN website. This discussion list is now deprecated - please use the VSN forum for discussion on ASReml. (These online archives were generated using the hypermail package.)