Skip to main content

Table 1 Matrices for J i = 3 offspring

From: Analysis of binary traits: testing association in the presence of linkage

T

Z matrixb

Ï€ subscriptsc

ø

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

0

1

0

1

0

0

1

1

2

1

1

0

0

1

1

0

0

1

0

1

1, 2

1

0

0

0

1

0

0

0

0

0

1

3

1

1

1

1

0

0

0

0

1

1

0

1, 3

1

0

0

0

0

0

0

0

0

1

0

2, 3

1

1

0

0

0

0

0

0

1

0

0

1, 2, 3

1

0

0

0

0

0

0

0

0

0

0

  1. aAll ordered combinations of 1, 2, 3. Each row in T corresponds in choosing a set off offspring (j = 1, 2, 3) and setting their trait.
  2. Y ij = 1. is the probability of offspring set T being affected.
  3. bThe matrix for which π* = Zπ. The inverse of Z is used to calculate π, given π*.
  4. cThe subscripts for matrix π. For example, row two corresponds to the outcome Yi 1= 0, Yi 1= 1, and Yi 3= 1.