Multivariate Sire Dam model
tag
sire 92 !I
dam 3561 !I
grp 49
sex
brr 4
litter 4871
age wwt !m0 ywt !m0 # !M0 identifies missing values
gfw !m0 fdm !m0 fat !m0
coop.fmt !DOPATH $1 !CONTINUE !MAXIT 20
!PATH 3
!EXTRA 4
!PATH
wwt ywt gfw fdm fat ~ Trait Tr.age Tr.brr Tr.sex Tr.age.sex,
!r Tr.sire,
!{ at(Tr,1).dam at(Tr,2).dam at(Tr,3).dam !},
!{ at(Tr,1).lit at(Tr,2).lit at(Tr,3).lit at(Tr,4).lit !},
at(Trait,1).age.grp .0024,
at(Trait,2).age.grp .0019,
at(Trait,4).age.grp .0020,
at(Trait,5).age.grp .00026,
at(Trait,1).sex.grp .93,
at(Trait,2).sex.grp 16.0,
at(Trait,3).sex.grp .28,
at(Trait,5).sex.grp 1.18,
!f Tr.grp
1 2 3 #1 R structure with 2 dimensions and 3 G structures
0 0 0 #Independent across animals
Tr 0 US #General structure across traits
15*0. #Asreml will estimate some starting values
Tr.sire 2 #Sire effects.
!PATH 1 #Initial analysis ignoring genetic correlations
Tr 0 DIAG #Specified diagonal variance structure
0.608 1.298 0.015 0.197 0.035 #Initial sire variances
!PATH 2 #Factor Analytic model
Tr 0 FA1 !GP
0.5 0.5 -.01 -.01 0.1 #Correlation factors
0.608 1.298 0.015 0.197 0.035 #Variances
!PATH 3 #Unstructured variance model
Tr 0 US
0.6199 #Lower triangle row-wise
0.6939 1.602
0.003219 0.007424 0.01509
-0.02532 -0.05840 -0.0002709 0.1807
0.06013 0.1387 0.0006433 -0.005061 0.03487
!PATH
sire
#Maternal structure covers the 3 model terms
# at(Tr,1).dam at(Tr,2).dam at(Tr,3).dam
at(Tr,1).dam 2 # Maternal effects.
!PATH 1
3 0 CORGH !GU # Equivalent to Unstructured
.9
.1 .1
2.2 4.14 0.018
!PATH 2
3 0 CORGH !GU
.9
.1 .1
2.2 4.14 0.018
!PATH 3
3 0 US !GU
.9
.1 .1
2.2 4.14 0.018
!PATH
dam
#Litter structure covers the 4 model terms at(Tr,1).lit at(Tr,2).lit
#at(Tr,3).lit at(Tr,4).lit
at(Tr,1).lit 2 # Litter effects.
!PATH 1
4 0 DIAG # Diagonal structure
3.74 0.97 0.019 0.941
!PATH 2
4 0 FA1 !GP # Factor Analytic 1
.5 .5 .01 .1
4.95 4.63 0.037 0.941
!PATH 3
4 0 US # Unstructured
5.073
3.545 3.914
0.1274 0.08909 0.02865
0.07277 0.05090 0.001829 1.019
!PATH
lit
Table 3. Variance models fitted for each part of the ASReml job in the analysis of the genetic example
term | matrix | !PATH 1 | !PATH 2 | !PATH 3
| sire | Σs | DIAG | FA1 | US
| dam | Σd | CORGH | CORGH | US
| litter | Σl | DIAG | FA1 | US
| error | Σe | US | US | US
|
In !PATH 1, the error variance model is taken to be unstructured, but
the starting values are set to zero. This instructs ASReml to
obtain starting values from the sample covariance matrix of the
data. For incomplete data the matrix so obtained may not, in general
be positive definite. Care should be taken when using this option for
incomplete multivariate data. The command to run
!PATH 1
is
asreml -nrw64 mt 1
The Loglikelihood from this run is -20000-1444.93.
When the job runs, the message
Non positive definite G matrix: 0 singularities 1 negative pivots; order 3
appears to the screen. This refers to the 3 by 3 dam matrix which is estimated as
Covariance/Variance/Correlation Matrix CORRelation
2.573 1.025 0.6568
3.024 3.382 0.7830
0.1526 0.2086 0.2098E-01
Note the correlation between wwt and ywt is estimated at 1.025.
The results from this analysis can be automatically used by ASReml
for the next part, if the .rsv is copied prior to running the
next part. That is, we add the !PATH 2 coding to the job,
copy mt1.rsv to mt2.rsv so that when we run !PATH 2 it starts from
where !PATH 1 finished, and run the job using
asreml -cnrw64 mt 2
The Loglikelihood from this run is -20000-1427.37.
Finally, we use the !PATH 3 coding to obtain the final analysis,
copy mt2.rsv to mt3.rsv and run the final stage starting from
the stage 2 results. Note that we are using the automatic
updating associated with !CONTINUE.
A portion of the final output file is
Notice: LogL values are reported relative to a base of -20000.00
NOTICE: 76 singularities detected in design matrix.
1 LogL=-1427.37 S2= 1.0000 35006 df : 2 components constrained
2 LogL=-1424.58 S2= 1.0000 35006 df
3 LogL=-1421.07 S2= 1.0000 35006 df : 1 components constrained
4 LogL=-1420.11 S2= 1.0000 35006 df
5 LogL=-1419.93 S2= 1.0000 35006 df
6 LogL=-1419.92 S2= 1.0000 35006 df
7 LogL=-1419.92 S2= 1.0000 35006 df
8 LogL=-1419.92 S2= 1.0000 35006 df
9 LogL=-1419.92 S2= 1.0000 35006 df
10 LogL=-1419.92 S2= 1.0000 35006 df
11 LogL=-1419.92 S2= 1.0000 35006 df
Source Model terms Gamma Component Comp/SE % C
at(Trait,1).age.grp 49 49 0.135360E-02 0.135360E-02 2.03 0 P
at(Trait,2).age.grp 49 49 0.101561E-02 0.101561E-02 1.24 0 P
at(Trait,4).age.grp 49 49 0.176505E-02 0.176505E-02 1.13 0 P
at(Trait,5).age.grp 49 49 0.209279E-03 0.209279E-03 1.68 0 P
at(Trait,1).sex.grp 49 49 0.919610 0.919610 2.89 0 P
at(Trait,2).sex.grp 49 49 15.3912 15.3912 3.50 0 P
at(Trait,3).sex.grp 49 49 0.279496 0.279496 3.71 0 P
at(Trait,5).sex.grp 49 49 1.44032 1.44032 1.80 0 P
Residual UnStru 1 1 9.46220 9.46220 33.30 0 U
: : : : :
Covariance/Variance/Correlation Matrix UnStructured Residual
9.462 0.5691 0.2356 0.1640 0.2183
7.332 17.54 0.4241 0.2494 0.4639
0.2728 0.6686 0.1417 0.3994 0.1679
0.9625 1.994 0.2870 3.642 0.4875E-01
0.8336 2.412 0.7846E-01 0.1155 1.541
Covariance/Variance/Correlation Matrix UnStructured Tr.sire
0.5941 0.7044 0.2966 0.2032 0.2703
0.6745 1.544 0.1364E-01-0.1224 0.5726
0.2800E-01 0.2076E-02 0.1500E-01 0.1121 -0.4818E-02
0.6238E-01-0.6056E-01 0.5469E-02 0.1586 -0.6331
0.3789E-01 0.1294 -0.1073E-03-0.4586E-01 0.3308E-01
Covariance/Variance/Correlation Matrix UnStructured at(Tr,1).dam
2.161 1.010 0.7663
2.196 2.186 0.8301
0.1577 0.1718 0.1959E-01
Covariance/Variance/Correlation Matrix UnStructured at(Tr,1).lit
3.547 0.5065 -0.1099 -0.4096E-01
1.555 2.657 0.1740 -0.5150
-0.2787E-01 0.3821E-01 0.1815E-01-0.3282
-0.7312E-01-0.7957 -0.4191E-01 0.8984
Wald F statistics
Source of Variation NumDF F-inc
15 Tr.age 5 98.95
16 Tr.brr 15 116.72
17 Tr.sex 5 59.78
19 Tr.age.sex 4 4.90
In the .res file is reported an eigen analysis of these
four variance structures.
Eigen Analysis of UnStructured matrix for Residual
Eigen values 22.458 5.210 3.395 1.160 0.103
Percentage 69.474 16.118 10.502 3.588 0.318
1 0.4970 -0.8663 0.0141 0.0470 0.0027
2 0.8509 0.4765 -0.1316 -0.1746 -0.0327
3 0.0335 0.0230 0.0585 -0.0048 0.9974
4 0.1168 0.0871 0.9843 0.0769 -0.0633
5 0.1187 0.1196 -0.1010 0.9805 0.0039
Eigen Analysis of UnStructured matrix for Tr.sire
Eigen values 1.904 0.304 0.114 0.013 0.010
Percentage 81.199 12.963 4.859 0.535 0.444
1 0.4578 0.7476 0.4695 -0.1052 0.0087
2 0.8860 -0.3646 -0.2766 0.0248 -0.0700
3 0.0077 0.0798 0.0826 0.9438 -0.3098
4 -0.0163 0.5260 -0.8015 0.1116 0.2612
5 0.0710 -0.1587 0.2320 0.2918 0.9115
Eigen Analysis of UnStructured matrix for at(Tr,1).dam
Eigen values 4.382 0.010 -0.025
Percentage 100.352 0.225 -0.577
1 0.7041 -0.2321 0.6711
2 0.7081 0.1585 -0.6881
3 0.0533 0.9597 0.2760
Eigen Analysis of UnStructured matrix for at(Tr,1).lit
Eigen values 4.795 1.827 0.482 0.016
Percentage 67.345 25.664 6.769 0.221
1 0.7752 0.5928 0.2178 0.0133
2 0.6159 -0.6328 -0.4691 -0.0106
3 0.0016 -0.0340 0.0255 0.9991
4 -0.1403 0.4969 -0.8555 0.0390
The REML estimates of all the variance matrices except for
the dam components are
positive definite. Heritabilities for each trait can be calculated using the .pin file
facility of ASReml. The heritability is given by
h2 = σ2A/σ2P
where σ2P is the phenotypic variance and is given by
σ2P= σ2s+ σ2d+ σ2l+ σ2e
recalling that
σ2s = 0.25 σ2A
σ2d = 0.25 σ2A + σ2m
In the half-sib analysis we only use the estimate of additive genetic
variance from the sire variance component. The ASReml .pin
file is presented below along with the output from the following
command
asreml -p mt3
F phenWYG 9:14 + 24:29 + 39:44 + 45:50 # defines 55:60
F phenD 15:18 + 30:33 + 51:54 # defines 61:64
F phenF 19:23 + 34:38 # defines 65:69
F Direct 24:38 * 4. # defines 70:84
F Maternal 39:44 - 24:29 # defines 85:90
H WWTh2 70 55
H YWTh2 72 57
H GFWh2 75 60
H FDMh2 79 64
H FATh2 84 69
R GenCor 24:38
R MatCor 85:90
55 phenWYG 9 15.76 0.3130
56 phenWYG 10 11.76 0.3749
57 phenWYG 11 23.92 0.6313
. . . . .
70 Direct 24 2.376 0.6458
71 Direct 25 2.698 0.8487
72 Direct 26 6.174 1.585
73 Direct 27 0.1120 0.7330E-01
. . . . .
85 Maternal 39 1.567 0.3788
86 Maternal 40 1.521 0.4368
87 Maternal 41 0.6419 0.7797
. . . . .
WWTh2 = Direct 2 70/phenWYG 55= 0.1507 0.0396
YWTh2 = Direct 2 72/phenWYG 57= 0.2581 0.0624
GFWh2 = Direct 2 75/phenWYG 60= 0.3084 0.0716
FDMh2 = Direct 3 79/phenD 18 64= 0.1350 0.0717
FATh2 = Direct 3 84/phenF 23 69= 0.0841 0.0402
GenCor 2 1 = Tr.si 25/SQR[Tr.si 24*Tr.si 26]= 0.7044 0.1025
GenCor 3 1 = Tr.si 27/SQR[Tr.si 24*Tr.si 29]= 0.2966 0.1720
GenCor 3 2 = Tr.si 28/SQR[Tr.si 26*Tr.si 29]= 0.0136 0.1810
GenCor 4 1 = Tr.si 30/SQR[Tr.si 24*Tr.si 33]= 0.2028 0.3513
GenCor 4 2 = Tr.si 31/SQR[Tr.si 26*Tr.si 33]= -0.1227 0.3247
GenCor 4 3 = Tr.si 32/SQR[Tr.si 29*Tr.si 33]= 0.1115 0.3868
GenCor 5 1 = Tr.si 34/SQR[Tr.si 24*Tr.si 38]= 0.2703 0.2724
GenCor 5 2 = Tr.si 35/SQR[Tr.si 26*Tr.si 38]= 0.5726 0.2022
GenCor 5 3 = Tr.si 36/SQR[Tr.si 29*Tr.si 38]= -0.0048 0.2653
GenCor 5 4 = Tr.si 37/SQR[Tr.si 33*Tr.si 38]= -0.6333 0.3775
MatCor 2 1 = Mater 86/SQR[Mater 85*Mater 87]= 1.5168 0.7131
MatCor 3 1 = Mater 88/SQR[Mater 85*Mater 90]= 1.5285 1.1561
MatCor 3 2 = Mater 89/SQR[Mater 87*Mater 90]= 3.1251 2.7985
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