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Fixed effect model for SNP effects

Model

In this section, the author tries to estimate individual SNP effect as a fixed effect based on 8 reference animals that have both genotype and phenotype (fat DYD). Only 3 SNP markers are considered in this small example. We also consider the regular additive genetic (polygenic) effects. The model is \[ y_{i} = \mu + \sum_{k=1}^{3}z_{ik} g_{k} + u_{i} + e_{i} \] where \(y_i\) is an observation for animal \(i\), \(\mu\) is the general mean, \(z_{ik}\) is \(k\)-th weighted marker genotype for the animal i.e. the \((i,k)\) element in the \(\mathbf{Z}\) matrix (see VanRaden, 2008), \(g_k\) is the \(k\)-th fixed SNP effect, \(u_i\) is the additive genetic (polygenic) effect, and \(e_i\) is the residual effect. We can consider more animals in pedigree. The variance components are \(\sigma_u^2= 35.241\) and \(\sigma_e^2 = 245.0\).

Files

In this model, the elements of \(\mathbf{Z}\) are used as covariates so they should be saved in the data file. The data file contains the first 3 columns of \(\mathbf{Z}\); see p.181 in the textbook. Also, the weight used in this analysis is actually the inverse of EDC so the values should be calculated and stored in the data file.

 13  0  0  1 558  9.0  0.00179211   1.357 -0.357  0.286
...

The data file (data_mr11a.txt) has 10 columns.

1. Animal ID
2. Sire ID
3. Dam ID
4. General mean
5. EDC
6. Phenotype (Fat DYD)
7. Weight = inverse of EDC
8. Covariate for SNP 1
9. Covariate for SNP 2
10. Covariate for SNP 3

The pedigree file includes all 26 animals. Animal 1 to 12 have missing parents.

The parameter file for the weighted analysis is shown below.

DATAFILE
data_mr11a.txt
NUMBER_OF_TRAITS
1
NUMBER_OF_EFFECTS
5
OBSERVATION(S)
6
WEIGHT(S)
7
EFFECTS:
 4  1 cross   # general mean
 8  1 cov     # SNP effect 1
 9  1 cov     # SNP effect 2
10  1 cov     # SNP effect 3
 1 26 cross   # additive genetic ( polygenic ) effect
RANDOM_RESIDUAL VALUES
245.0
RANDOM_GROUP
5
RANDOM_TYPE
add_animal
FILE
pedigree_mr11a.txt
(CO)VARIANCES
35.241
OPTION solv_method FSPAK

If you conduct the unweighted analysis, remove 7 from the WEIGHT(S) section.

Solutions

In the weighted analysis, the solutions are the same as the textbook (p.181). The estimate of the general mean is different but I believe this is a typo in the textbook.

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