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

From: luansheng <luansheng_at_GMAIL.COM>
Date: Wed, 1 Apr 2009 22:23:04 +0800

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

Luan sheng
----------------------------------------
Yellow Sea Fisheries Research Institute
Qingdao 266071
China
luansheng_at_gmail.com
luansheng_at_ysfri.ac.cn
----------------------------------------

2009/4/1 I.M.S.White <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>:
>
> 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
>> Qingdao 266071
>> China
>> luansheng_at_gmail.com
>> luansheng_at_ysfri.ac.cn
>> ----------------------------------------
>>
>>
>>
>> 2009/3/31 I.M.S.White <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>:
>>>
>>> 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
>>>> Qingdao 266071
>>>> China
>>>> luansheng_at_gmail.com
>>>> luansheng_at_ysfri.ac.cn
>>>> ----------------------------------------
>>>>
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>>>>
>>>
>>> ::::::::::::::::::::::::::::::::::::::::::
>>> : I.White :
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>>> : Ashworth Laboratories, West Mains Road :
>>> : Edinburgh EH9 3JT :
>>> : Tel 0131 650 5490 Fax 0131 650 6564 :
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>>
>
>
> ::::::::::::::::::::::::::::::::::::::::::
> : I.White :
> : University of Edinburgh :
> : Ashworth Laboratories, West Mains Road :
> : Edinburgh EH9 3JT :
> : Tel 0131 650 5490 Fax 0131 650 6564 :
> ::::::::::::::::::::::::::::::::::::::::::
>
> --
> The University of Edinburgh is a charitable body, registered in
> Scotland, with registration number SC005336.
>
>
>
Received on Thu Apr 01 2009 - 22:23:04 EST

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