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Pedigree-induced correlation pedigreemm http://r-forge.r-project.org/projects/pedigreemm/ www.r-project.org Ana Ines Vazquez University of Wisconsin. install.packages(“pedigreemm”) library(pedigreemm). pedigreemm : Pedigree-based mixed-effects models. Uses: - PowerPoint PPT Presentation
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Pedigree-induced correlation
pedigreemm http://r-forge.r-project.org/projects/pedigreemm/
www.r-project.org
Ana Ines VazquezUniversity of Wisconsin
install.packages(“pedigreemm”)
library(pedigreemm)
pedigreemm: Pedigree-based mixed-effects models
Uses:
• Sire, Animal model with repeated measures. • Multiple random (nested or cross classified) or fixed effects.• Random regression.• Generalized linear models (Poisson, binomial, etc).
Genetic model
Phenotype, Genetic effects, Model residual
ijiij eup
eZuXβy
RZZGV
VXββy
R0
0G
0
0
e
u
,
,
Np
Np
Mixed Model
Henderson, 1963
yVXXVXβ
VXββy
11 1ˆ
,~
BLUE
N
Xβyyyu,uVG,βy,u 1cov, VEE
XβyGZVu 1 BLUPˆ
Example: Sire linear model
Example:
Phenotypic measures:
Fixed effect (gender and herds):
Sire effects:
eZuXβy
2,171,172,21,22,11,1 ,,...,,,, yyyyyyy
321 ,,,, hhhfmβ
1721 ,...,, sssu
Data
sire gender herd y
1 m 0 257
1 m 0 304
2 m 0 271
2 m 0 340
3 m 0 445
3 m 0 413
4 f 0 425
4 f 0 378
5 f 0 278
5 f 0 278
6 f 0 341
6 f 0 367
7 f 0 244
7 f 0 249
. . . .
. . . .
17 f 3 238
17 f 3 298
, Z=
s1 s2 s3 s4 s17
1 0 0 0 . 0
1 0 0 0 . 0
0 1 0 0 . 0
0 1 0 0 . 0
0 0 1 0 . 0
0 0 1 0 . 0
0 0 0 1 . 0
0 0 0 1 . 0
0 0 0 0 . 0
0 0 0 0 . 0
0 0 0 0 . 0
0 0 0 0 . 0
0 0 0 0 . 0
0 0 0 0 . 0
. . . . . .
0 0 0 0 . 0
0 0 0 0 . 1
0 0 0 0 . 1
X=
Gender, herd
1 0 0 0 0
1 0 0 0 0
1 0 0 0 0
1 0 0 0 0
1 0 0 0 0
1 0 0 0 0
0 1 0 0 0
0 1 0 0 0
0 1 0 0 0
0 1 0 0 0
0 1 0 0 0
0 1 0 0 0
0 1 0 0 0
0 1 0 0 0
. . . . .
0 1 0 1 0
0 1 0 0 1
0 1 0 0 1
Sire
The random effects (sires) are not independent between them.
• They are related, then covariance between two of them is not cero. • The covariance = the relationship between animals times
which can be measured.
2AV AGu
eZuXβy
2,~ uN A0u
2A
Sire-pedigree
2,~ uN A0u
A: Relationships between sires
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
1 1 0.5 0 0 0 0 0 0 0.5 0 0.5 0 0.5 0 0 0.25 0
2 0.5 1 0 0 0 0 0 0.5 0 0.5 0 0 0 0.25 0.5 0.5 0.25
3 0 0 1 0.5 0 0 0 0 0.25 0 0 0.5 0 0.5 0 0 0.5
4 0 0 0.5 1 0 0 0 0 0.5 0 0 0.25 0 0.25 0 0 0.25
5 0 0 0 0 1 0 0 0 0 0.5 0 0 0 0 0 0 0
6 0 0 0 0 0 1 0 0 0 0 0.5 0 0 0 0 0 0
7 0 0 0 0 0 0 1 0 0 0 0 0 0.5 0 0 0.25 0
8 0 0.5 0 0 0 0 0 1 0 0.25 0 0 0 0.5 0.25 0.25 0.13
9 0.5 0 0.25 0.5 0 0 0 0 1 0 0.25 0.13 0.25 0.13 0 0.13 0.13
10 0 0.5 0 0 0.5 0 0 0.25 0 1 0 0 0 0.13 0.25 0.25 0.13
11 0.5 0 0 0 0 0.5 0 0 0.25 0 1 0 0.25 0 0 0.13 0
12 0 0 0.5 0.25 0 0 0 0 0.13 0 0 1 0 0.25 0 0 0.25
13 0.5 0 0 0 0 0 0.5 0 0.25 0 0.25 0 1 0 0 0.5 0
14 0 0.25 0.5 0.25 0 0 0 0.5 0.13 0.13 0 0.25 0 1 0.13 0.13 0.31
15 0 0.5 0 0 0 0 0 0.25 0 0.25 0 0 0 0.13 1 0.25 0.5
16 0.25 0.5 0 0 0 0 0.25 0.25 0.13 0.25 0.13 0 0.5 0.13 0.25 1 0.13
17 0 0.25 0.5 0.25 0 0 0 0.13 0.13 0.13 0 0.25 0 0.31 0.5 0.13 1
Example… u estimatesid
Phenotype (average)
u w/o Pedigree
u w/ Pedigree
1 280 -41 -29
2 305 -22 -11
3 429 69 66
4 402 60 68
5 278 -31 -26
6 354 24 26
7 247 -54 -46
8 315 -5 -11
9 424 10 19
10 276 5 -2
11 257 -9 -7
12 394 -12 3
13 399 2 -9
14 237 -13 -1
15 270 1 5
16 276 16 7
17 268 -1 21
L: [1,] [2,] [3,] [4,] [5,] [6,] [7,] [8,] [9,] [10,] [11,] [12,] [13,] [14,] [15,] [16,] [17,]
[1,] 1 . . . . . . . . . . . . . . . .
[2,] 0.5 0.87 . . . . . . . . . . . . . . .
[3,] . . 1 . . . . . . . . . . . . . .
[4,] . . 0.5 0.87 . . . . . . . . . . . . .
[5,] . . . . 1 . . . . . . . . . . . .
[6,] . . . . . 1 . . . . . . . . . . .
[7,] . . . . . . 1 . . . . . . . . . .
[8,] 0.25 0.43 . . . . . 0.87 . . . . . . . . .
[9,] 0.5 . 0.25 0.43 . . . . 0.71 . . . . . . . .
[10,] 0.25 0.43 . . 0.5 . . . . 0.71 . . . . . . .
[11,] 0.5 . . . . 0.5 . . . . 0.71 . . . . . .
[12,] . . 0.5 . . . . . . . . 0.87 . . . . .
[13,] 0.5 . . . . . 0.5 . . . . . 0.71 . . . .
[14,] 0.13 0.22 0.5 . . . . 0.43 . . . . . 0.71 . . .
[15,] 0.25 0.43 . . . . . . . . . . . . 0.87 . .
[16,] 0.5 0.43 . . . . 0.25 . . . . . 0.35 . . 0.71 .
[17,] 0.13 0.22 0.5 . . . . . . . . . . . 0.43 . 0.71
u*=L-1u then u_est = Lu*
Non-linear model(Logistic regression)
ZuXβl
uzβx
n
iii
ii
lll
p
pl
,...,,
1ln
21
To sum up…
• Sire, Animal model with repeated measures • Multiple random or fixed effects.• Random regression.• Generalized linear models (Poisson, binomial, etc).
