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

luansheng wrote:
> Dear I.M.S.White:
> I think It should not be difficult. To different link function,using
> different variance. It was simple programming method.

Please stop confusing the statistical methodology with the genetic
interpretation. There is no 'residual variance' associated with models
that do not assume a residual variance like many models used for binary
data (please read the literature). Rather the usage of one stems from
the implementation of generalized linear mixed models that permits using
different distributions in a single application and enables a user to
compute estimates and approximate standard errors of functions the
variance components such as heritability.

There is rather extensive literature of some 50 or more years that
addresses the heritability of binary data but I do not recall exactly
when the variance of link function was first used or became accepted. (I
guess it starts with Dempster and Lerner's 1950 paper and subsequent
papers like Gianola and Foulley and Harville and Mee.) It is related to
the conditional variance given the estimated parameters.

Bruce
>
> Luan sheng
> ----------------------------------------
> Yellow Sea Fisheries Research Institute
> Chinese Academy of Fisheries Sciences
> Nanjing Road 106
> Qingdao 266071
> China
> luansheng_at_gmail.com <mailto:luansheng_at_gmail.com>
> luansheng_at_ysfri.ac.cn <mailto:luansheng_at_ysfri.ac.cn>
> ----------------------------------------
>
>
>
> 2009/4/1 I.M.S.White <i.m.s.white_at_ed.ac.uk <mailto:i.m.s.white_at_ed.ac.uk>>
>
> Dear Luansheng
>
> I agree that it is misleading. However, it might also be misleading
> in some circumstances to replace the one with pi^2/3. The problem
> for the programmers is devising a suitable rule for replacing
> or not replacing.
>
>
>
> Quoting luansheng <luansheng_at_gmail.com <mailto:luansheng_at_gmail.com>>:
>
> Dear White: Thanks for your reply. Then my an other
> question is " 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."
> I have sent this question to the mail list, but nobody answer me.
>
> Luan sheng
> ----------------------------------------
> Yellow Sea Fisheries Research Institute
> Chinese Academy of Fisheries Sciences
> Nanjing Road 106
> Qingdao 266071
> China
> luansheng_at_gmail.com <mailto:luansheng_at_gmail.com>
> luansheng_at_ysfri.ac.cn <mailto:luansheng_at_ysfri.ac.cn>
> ----------------------------------------
>
>
>
> 2009/3/31 I.M.S.White <i.m.s.white_at_ed.ac.uk
> <mailto:i.m.s.white_at_ed.ac.uk>>
>
> One way the probit and logit links arise is when the event
> in question is
> triggered by an unobserved variable exceeding a fixed
> threshold. Fixed
> effects and variances are measured on this underlying
> (threshold,
> liability) scale. If we assume the unobserved threshold
> variable is standard
> normal (with variance one) we get the probit link, and if
> we assume a
> standard logistic
> distribution (which has a variance of pi^2/3) we get the
> logit link.
>
>
>
> Quoting luansheng <luansheng_at_GMAIL.COM
> <mailto:luansheng_at_GMAIL.COM>>:
>
> 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
> luansheng_at_gmail.com <mailto:luansheng_at_gmail.com>
> luansheng_at_ysfri.ac.cn <mailto:luansheng_at_ysfri.ac.cn>
> ----------------------------------------
>
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Received on Thu Apr 01 2009 - 10:43:53 EST