# Re: problem of estimation VC

From: Bruce Southey <southey_at_UIUC.EDU>
Date: Mon, 10 Dec 2007 08:53:18 -0600

Hi,

Can you explain in biological terms why there is a covariance between additive genetic effects and competitive genetic effect effects in your simulation?

This is different from the standard approach provided by Dr Gilmour and may help understand what you are attempting.

Regards
Bruce

---- Original message ----
>Date: Mon, 10 Dec 2007 10:37:16 +0100
>From: Jiqiu Cheng <Jiqiu.Cheng_at_BIW.KULEUVEN.BE>
>Subject: problem of estimation VC
>To: ASREML-L_at_AGRIC.NSW.GOV.AU
>
>Quoting arthur.gilmour_at_DPI.NSW.GOV.AU:
>Dear sir,
> I simulate the records including fixed effect "sex", direct genetic
>effect (d), competitive genetic effect (c) from penmates and
>independent residual(e). Then I use ASREML to estimate the variance
>components. The estimation of variance components and fixed effect
>show some deviation from the true parameters.
> My question is whether the code I used to estimate the model in
>ASREML is correct? If it is correct, are there some solutions to
>improve the estimation?
>
>Thank you very much for your help.
>Best regards,
>Jiqiu
>
>The model of simulation:
>y1=sex(+d+c2+c3+c4+e1
>
>The parameter of simulation:
>penmates=4
>varA=1250
>varC=62.5
>covAC=-140
>varE=4000
>sex=20 or -20
>The dataset
> Data set:
> Animal Sire Dam Sex Genation Pen Ai Pm1 Pm2 Pm3 adg
>20751 10957 13673 2 3 1491 20751 23621 25420 27847 19.22
>20752 10957 13673 2 3 1036 20752 23635 28874 29512 19.96
>20753 10957 13673 2 3 2327 20753 22409 25602 26703 19.36
>20754 10957 13673 2 3 2326 20754 21148 23208 30172 19.57
>20755 10957 13673 2 3 2401 20755 22852 28577 29107 19.17
>20756 10957 13673 1 3 782 20756 23266 23270 25910 -20.61
>20757 10957 13673 1 3 983 20757 20815 21163 29738 -19.87
>20758 10957 13673 1 3 1676 20758 21985 22899 23182 -19.31
>20759 10957 13673 2 3 421 20759 27356 28702 29785 20.12
>20760 10957 13673 2 3 308 20760 23035 29144 29441 18.84
>
>The code used in ASREML:
>"Sample to make animal model
>Animal !P
>Sire !P
>Dam !P
>Sex 2
>Genation 3
>Pen 2500
>level 4
>Ai
>Pm1 !P
>Pm2 !P
>Pm3 !P
>ped !MAKE
>data !skip1
>adg~Sex !r Animal Pm1 -Pm2 and(Pm2) -Pm3 and(Pm3)
>0 0 1
>Animal 2
>2 0 US !GU
>0.3125 0 0.016
>Animal"
>Part of the Output of ".asr" file
>"Notice: ASReml assumes Pm1 and and(Pm2)
> have the same levels in the same order.
>
> Notice: ASReml assumes Pm1 and and(Pm3)
> have the same levels in the same order.
> 2 UnStructure 0.3125 0.0000 0.0160
> 30750 Ainverse
> Structure for Animal has 61500 levels defined
> Structure for Animal also covers Pm1
> Forming 61502 equations: 2 dense.
> Initial updates will be shrunk by factor 0.316
> Notice: LogL values are reported relative to a base of -40000.000
> 1 LogL=-7423.36 S2= 3825.8 9998 df : 1 components
>constrained
> 2 LogL=-7422.48 S2= 3822.4 9998 df : 1 components
>constrained
> 3 LogL=-7421.96 S2= 3816.8 9998 df : 1 components
>constrained
> 4 LogL=-7421.32 S2= 3812.6 9998 df
> 5 LogL=-7402.47 S2= 3845.0 9998 df
> 6 LogL=-7400.68 S2= 3772.3 9998 df
> 7 LogL=-7400.65 S2= 3760.0 9998 df
> 8 LogL=-7400.65 S2= 3759.4 9998 df
>
> Source Model terms Gamma Component Comp/SE % C
> Variance 10000 9998 1.00000 3759.41 38.44 0 P
> Animal UnStructured 1 1 0.337645 1269.35 10.64 0 U
> Animal UnStructured 2 1 -0.399584E-01 -150.220 -5.98 0 U
> Animal UnStructured 2 2 0.174257E-01 65.5104 4.72 0 U
> Covariance/Variance/Correlation Matrix UnStructured Animal
> 1269. -0.5209
> -150.2 65.51
>
> Analysis of Variance NumDF F_inc
> 4 Sex 2 366.27
>
> Estimate Standard Error T-value T-prev
> 4 Sex
> 1 -18.8178 2.50154 -7.52
> 2 18.1941 2.50098 7.27 27.07
> 1 Animal 30750 effects fitted ( 1018
>are zero)
> 9 Pm1 30750 effects fitted ( 1018
>are zero)"
>
>> Dear Jiqiu,
>>
>> It is NOT true that PenComponent is always positive.
>> This is a restriction which is ofter sensible but not necessary.
>>
>> In ASReml, just follow Pen with !GU to allow the pen component to be
>> negative,
>> implying a negative correlation (strong competion!).
>>
>> adg ~ mu Sex !r Animal Pen !GU
>>
>>
>>> <><><><><><><><><><><><><><><><><><><><><><><>
>>
>>
>>
>> Jiqiu Cheng <Jiqiu.Cheng_at_BIW.KULEUVEN.BE>
>> Sent by: ASReml users discussion group <ASREML-L_at_AGRIC.NSW.GOV.AU>
>> 09/12/2007 11:39 PM
>> ASReml users discussion group <ASREML-L_at_AGRIC.NSW.GOV.AU>
>>
>>
>> To
>> ASREML-L_at_AGRIC.NSW.GOV.AU
>> cc
>>
>> Subject
>> Re: question to specify R structure.
>>
>>
>>
>>
>>
>>
>> Quoting arthur.gilmour_at_DPI.NSW.GOV.AU:
>> Dear gilmour,
>> As you suggested, "Fit Pen as a random factor, the error
>> correlation between pen-mates is given as the
>> PenComponent/(PenComponent+Residual)"
>> However, the variance components of PenComponent and the residual
>> are always positive, which means that the error correlation between
>> pen-mates is always positive. But I think the correlation between
>> pen-mates could be negative too. So what do you think? Thanks.
>> Best regards,
>>
>> Jiqiu
>>
>>
>>
>>> Dear Jiqiu Cheng
>>>
>>> You wrote
>>> A dataset include Animal and Pen effect. Pm1, Pdm2 and Pm3 are three
>>> penmates of the current animal. There are 2500 pens total, 4 animals
>>> each pen. I want to fit an R structure for which, animals within one
>>> pen are correlated and independent among different pens. The pen
>>> effects are independent.
>>>
>>> I tried to code the R structure as below:
>>>
>>> 1 2 0
>>> 2500 Pen ID
>>> CORU
>>>
>>> But it doesn't work. Could anyone give me any suggestions?
>>>
>>> Data set:
>>> Animal Sire Dam Sex Genation Pen Ai Pm1 Pm2 Pm3 adg
>>> 20751 10957 13673 2 3 1491 20751 23621 25420 27847 19.22
>>> 20752 10957 13673 2 3 1036 20752 23635 28874 29512 19.96
>>> 20753 10957 13673 2 3 2327 20753 22409 25602 26703 19.36
>>> 20754 10957 13673 2 3 2326 20754 21148 23208 30172 19.57
>>> 20755 10957 13673 2 3 2401 20755 22852 28577 29107 19.17
>>> 20756 10957 13673 1 3 782 20756 23266 23270 25910 -20.61
>>> 20757 10957 13673 1 3 983 20757 20815 21163 29738 -19.87
>>> 20758 10957 13673 1 3 1676 20758 21985 22899 23182 -19.31
>>> 20759 10957 13673 2 3 421 20759 27356 28702 29785 20.12
>>> 20760 10957 13673 2 3 308 20760 23035 29144 29441 18.84
>>>
>>>
>>> Assuming your data file has 10000 records so that the pen number say
>> 1491
>>> appears 4 times in the file
>>> associated with the four animals 20751 23621 25420 27847
>>>
>>> Then you just need to fit Pen as a random factor
>>>
>>> Animals in Pens
>>> Animal !P Sire !P Dam !P
>>> Sex 2
>>> Genation
>>> Pen *
>>> Ai Pm1 Pm2 Pm3
>>> datafile.txt !skip 1 # read pedigree from data file
>>> datafile.txt !skip 1 # read data from data file
>>>
>>> adg ~ mu Sex !r Animal Pen
>>>
>>>
>>> This will give 3 variance components
>>> Pen
>>> Animal
>>> Residual
>>>
>>> The error correlation between pen-mates is given as
>>> the PenComponent/(PenComponent+Residual)
>>>
>>>
>>>
>>>
>>> May Jesus Christ be gracious to you,
>>>
>>> Arthur Gilmour, His servant .
>>>
>>> Mixed model regression mapping for QTL detection in experimental
>> crosses.
>>> Computational Statistics and Data Analysis 51:3749-3764 now available at
>>> http://dx.doi.org/10.1016/j.csda.2006.12.031
>>>
>>> Personal website: http://www.cargovale.com.au/
>>>
>>> mailto:Arthur.Gilmour_at_dpi.nsw.gov.au, arthur_at_cargovale.com.au
>>> Principal Research Scientist (Biometrics)
>>> NSW Department of Primary Industries
>>> Orange Agricultural Institute, Forest Rd, ORANGE, 2800, AUSTRALIA
>>>
>>> fax: 02 6391 3899; 02 6391 3922 Australia +61
>>> telephone work: 02 6391 3815; home: 02 6364 3288; mobile: 0438 251 426
>>>
>>> ASREML 2 is now available from http://www.VSNi.co.uk/products/asreml
>>> The ASReml discussion group is at ASREML-L_at_dpi.nsw.gov.au
>>> To join it, mailto:arthur.gilmour_at_dpi.nsw.gov.au
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>>>
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>>>> <><><><><><><><><><><><><><><><><><><><><><><>
>>
>>
>>
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Received on Fri Dec 10 2007 - 08:53:18 EST

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