Table 4 Final model describing explanatory variables and random effects of log transformed MilA ELISA antibody units (AU). The marginal R² was 59% and conditional R² was 65%

 Animal

 Residuals

Estimate

SE

P-value

 Intercept

5.77

0.22

<  0.001

 Age days (linear)

12.91

3.53

<  0.001

 Age days (quadratic)

−8.25

2.18

<  0.001

 Herd 1

0

–

 Herd 2

0.61

0.25

0.015

 Herd 3

−0.83

0.25

0.001

 Herd 4

0.32

0.26

0.231

 Age days (linear)*Herd 1

0

–

 Age days (linear)*Herd 2

−11.90

3.89

0.003

 Age days (linear)*Herd 3

10.79

4.35

0.014

 Age days (linear)*Herd 4

−15.88

4.84

0.001

 Age days (quadratic)*Herd 1

0

–

 Age days (quadratic)*Herd 2

4.13

2.64

0.118

 Age days (quadratic)*Herd 3

14.71

3.29

<  0.001

 Age days (quadratic)*Herd 4

−2.19

3.40

0.520