Information Technology Reference
In-Depth Information
1.0
35
0.8
30
25
0.6
20
0.4
15
10
0.2
5
0.0
5
10
15
20
25
30
35
Locus
Fig. 1.
Simulated heatmap of activation probabilities for main effect and epistatic effects. Activa-
tion probabilities along the diagonal correspond to main effects and off diagonal correspond to
epistatic effects.
determined which needed to be reflected in the analysis. For the
i
th
observation and
locus
l
j
this information can be coded into
X
ij
as:
⎧
⎨
1
,
allele
l
j
is from parent A
−
X
ij
=
1
,
allele
l
j
is from parent B
0
,
allele
l
j
is undetermined
(1)
⎩
Here the
X
ij
correspond to the main effects. For the epistatic effects (two-way interac-
tion) this produces the interaction between loci
l
j
and
l
k
as:
⎧
⎨
1
,
alleles
l
j
and
l
k
from same parent
−
X
ij
X
ik
=
1
,
alleles
l
j
and
l
k
from different parents
0
,
allele
l
j
or
l
k
is undetermined
(2)
⎩
Using a traditional first order model with a two-way multiplicative interaction terms the
model is defined as:
p
β
j
X
ij
I
P
c
(
l
j
)+
k<j
y
i
=
μ
+
β
jk
X
ij
X
ik
I
P
c
(
l
j
)
I
P
c
(
l
k
)+
i
.
(3)
j
=1
N
(0
,σ
c
)
,
P
c
is the set of loci
l
j
in model
M
c
,and
I
P
c
where
i
∼
is an indicator
function that takes the value 1 if
l
j
∈
P
c
and 0 otherwise. Here
β
j
corresponds to the
main effect of locus
l
j
and
β
jk
is the epistatic effect between loci
l
j
and
l
k
.