This document describes modelling state transitions in dairy cows based on their somatic cell count (SCC). It begins with background on milk recording data collection, including SCC which indicates mastitis levels. States are defined as Low, High, Dry. A multinomial logit model is used to model the transition between states based on previous states. The model is coded in WinBUGS. Validation data from 100 herds is used to test the model.

1. Modelling
State
Transitions
Aur´lien
e
Madouasse
Background
Modelling State Transitions
Milk Recording
Data Example of a Multinomial Logit Model Applied to Somatic
Somatic Cell
Count Cell Count in Dairy Cows
State
Transition
State Definition
State
Transitions
Data
Aur´lien Madouasse
e
A Simple
Model
Model
WinBUGS code
Results 19th April 2010
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

2. Outline
Modelling
State 1 Background
Transitions Milk Recording
Aur´lien
e Data
Madouasse Somatic Cell Count
Background 2 State Transition
Milk Recording State Definition
Data
Somatic Cell State Transitions
Count Data
State
Transition 3 A Simple Model
State Definition Model
State
Transitions WinBUGS code
Data Results
A Simple
Model 4 Adding Complexity
Model SCC Variation
WinBUGS code
Results Model
Adding
WinBUGS code
Complexity Results
SCC Variation
Model 5 Discussion
WinBUGS code
Results

3. Outline
Modelling
State 1 Background
Transitions Milk Recording
Aur´lien
e Data
Madouasse Somatic Cell Count
Background 2 State Transition
Milk Recording State Definition
Data
Somatic Cell State Transitions
Count Data
State
Transition 3 A Simple Model
State Definition Model
State
Transitions WinBUGS code
Data Results
A Simple
Model 4 Adding Complexity
Model SCC Variation
WinBUGS code
Results Model
Adding
WinBUGS code
Complexity Results
SCC Variation
Model 5 Discussion
WinBUGS code
Results

4. What is Milk Recording?
Modelling
State
Transitions
Aur´lien
e
Madouasse
Milk recording is the regular collection of a milk sample
Background from all lactating cows of a dairy herd
Milk Recording
Data What is measured:
Somatic Cell
Count
Milk yield
State
Transition
% butterfat, % protein, % lactose
State Definition Somatic cell count
State
Transitions
Data Information collected
A Simple Date of birth
Model
Model Date of calving
WinBUGS code
Results
Parity
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

5. What is Milk Recording?
Modelling
State
Transitions
Aur´lien
e
Madouasse
Background Farmers pay for milk recording, in order to:
Milk Recording
Data Adapt management
Somatic Cell
Count Identify cows likely to have mastitis
State
Transition
Identify the best producers
State Definition
State
The information is also used for
Transitions
Data Genetic evaluation
A Simple Epidemiologic studies
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

6. Data
Initial Dataset
Modelling
State
Transitions
Aur´lien
e
Madouasse
Background
The National Milk Records: main provider of milk
Milk Recording
Data
recording in England and Wales
Somatic Cell
Count All the data collected by the NMR between January 2004
State and December 2006 were purchased:
Transition
State Definition 19,893,093 recordings
State
Transitions 1,247,427 cows
Data
5,714 herds
A Simple
Model
Model
⇒ Big!!!
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

7. Data
Data Selection
Modelling
State
Transitions Aim: Obtain a homogeneous dataset and discard unreliable
Aur´lien
e
Madouasse
data
Herds recording:
Background
Milk Recording For the 3 complete years
Data
Somatic Cell On a monthly basis
Count
State
At least 80 % of Holstein-Friesian cows
Transition
State Definition
Milk samples collected on 2 consecutive milkings
State
Transitions
Data
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

8. Data
Data Selection
Modelling
State
Transitions Aim: Obtain a homogeneous dataset and discard unreliable
Aur´lien
e
Madouasse
data
Herds recording:
Background
Milk Recording For the 3 complete years
Data
Somatic Cell On a monthly basis
Count
State
At least 80 % of Holstein-Friesian cows
Transition
State Definition
Milk samples collected on 2 consecutive milkings
State
Transitions
Data
A Simple
Final dataset
Model
Model
8,211,988 recordings
WinBUGS code 483,747 cows
Results
Adding
2,128 herds
Complexity
SCC Variation ⇒ Reasonably big!!!
Model
WinBUGS code
Results

9. Somatic Cell Count
Relation to mastitis
Modelling
State
Transitions
Aur´lien
e
Madouasse
Background
Milk Recording
Data
Somatic Cell
Mastitis
Count
One of the biggest health problems in dairy herds
State
Transition Can be clinical or subclinical
State Definition
State
Causes an increase in milk somatic cell count (SCC)
Transitions
Data
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

10. Somatic Cell Count
Relation to mastitis
Modelling
State
Transitions
Aur´lien
e Individual Somatic Cell Count
Madouasse
Threshold of 200,000 cells/mL used to categorise cows as
Background Infected/Uninfected
Milk Recording
Data
Somatic Cell
Count
Bulk Milk Somatic Cell Count
State Reflects herd mastitis prevalence
Transition
State Definition
Penalty on milk price when it is too high
State
Transitions
Data
Aims of the study
A Simple
Model
Model
Can we model the transition between Low/High SCC from
WinBUGS code
Results
individual cow information?
Adding
Complexity
Can we predict BMSCC from the predicted transitions?
SCC Variation
Model
WinBUGS code
Results

11. Outline
Modelling
State 1 Background
Transitions Milk Recording
Aur´lien
e Data
Madouasse Somatic Cell Count
Background 2 State Transition
Milk Recording State Definition
Data
Somatic Cell State Transitions
Count Data
State
Transition 3 A Simple Model
State Definition Model
State
Transitions WinBUGS code
Data Results
A Simple
Model 4 Adding Complexity
Model SCC Variation
WinBUGS code
Results Model
Adding
WinBUGS code
Complexity Results
SCC Variation
Model 5 Discussion
WinBUGS code
Results

12. State transition
Definition of the States
Modelling
State
Transitions
Aur´lien
e
Madouasse
Background
Milk Recording
Data
Somatic Cell
Count
State
Transition
State Definition
First
Low/High
Low/High
Low/High
Low/High
Low/High
Low/High
Low/High
Low/High
Low/High
Low/High
Low/High
Low/High
Last
Dry
Dry
State
Transitions
Data
A Simple
Model
Low Low Low
Model
WinBUGS code
First Dry Last
Results
High High High
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

13. State transition
Transition Matrix
Modelling
State
Transitions
Aur´lien
e
Madouasse
Background
Milk Recording
Current
Data
Somatic Cell
Low High Dry Last
Count
Low π11 π12 π13 π14
Previous
State
Transition High π21 π22 π23 π24
State Definition
State Dry π31 π32 π33 π34
Transitions
Data First π41 π42 π43 π44
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

14. State transition
Transition Matrix
Modelling
State
Transitions
Aur´lien
e
Madouasse
Background
Milk Recording
Current
Data
Somatic Cell
Low High Dry Last
Count
Low π11 π12 π13 π14
Previous
State
Transition High π21 π22 π23 π24
State Definition
State Dry π31 π32 π33 0
Transitions
Data First π41 π42 0 0
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

15. Data
Data Used for the Study
Modelling
State
Transitions
Aur´lien
e
Madouasse
Background Training data
Milk Recording
Data
100 randomly selected herds
Somatic Cell
Count
Dataset 1: 6 consecutive test-days used for parameter
State estimation (70,382 lines)
Transition Dataset 2: 7th test-day for validation (11,895 lines)
State Definition
State
Transitions Validation data (Dataset 3: 14,669 lines)
Data
100 randomly selected herds
A Simple
Model 1 test-day per herd
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

16. Outline
Modelling
State 1 Background
Transitions Milk Recording
Aur´lien
e Data
Madouasse Somatic Cell Count
Background 2 State Transition
Milk Recording State Definition
Data
Somatic Cell State Transitions
Count Data
State
Transition 3 A Simple Model
State Definition Model
State
Transitions WinBUGS code
Data Results
A Simple
Model 4 Adding Complexity
Model SCC Variation
WinBUGS code
Results Model
Adding
WinBUGS code
Complexity Results
SCC Variation
Model 5 Discussion
WinBUGS code
Results

17. State transition
Model
Modelling
State
Transitions
Aur´lien
e
Madouasse
Background
Milk Recording
Data
Somatic Cell
Count Stateij ∼ Multinomial(πij ) State i
State
Transition
Cow-recording j
State Definition
State
Transitions
Data
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

18. State transition
Model
Modelling
State
Transitions
Aur´lien
e
Madouasse
Background
Milk Recording
Data
Somatic Cell
Count Stateij ∼ Multinomial(πij ) State i
4
State
π Cow-recording j
Transition
State Definition
ij
ln( π1j ) = I [Statei(j−1) ]αii
i
State
i =1
Previous State i
Transitions
Data
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

19. State transition
WinBUGS code
Modelling
State
Transitions
Aur´lien
e
Madouasse
model {
Background
Milk Recording
Data
Somatic Cell
Count
State
Transition
State Definition
State
Transitions
Data
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

20. State transition
WinBUGS code
Modelling
State
Transitions
Aur´lien
e
Madouasse
model {
Background
Milk Recording
Data
Somatic Cell for(i in 1:N) {
Count
State
Transition
State Definition
State
Transitions
Data
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

21. State transition
WinBUGS code
Modelling
State
Transitions
Aur´lien
e
Madouasse
model {
Background
Milk Recording
Data
Somatic Cell for(i in 1:N) {
Count
State
Transition resp[i,1:4] ~ dmulti(pi[i,1:4],1)
State Definition
State
Transitions
Data
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

22. State transition
WinBUGS code
Modelling
State
Transitions
Aur´lien
e
Madouasse
model {
Background
Milk Recording
Data
Somatic Cell for(i in 1:N) {
Count
State
Transition resp[i,1:4] ~ dmulti(pi[i,1:4],1)
State Definition
State
Transitions
Data for(m in 1:4){
A Simple
Model
pi[i,m] <- p[i,m]/sum(p[i,])
Model
WinBUGS code
}
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

23. State transition
WinBUGS code
Modelling
State
Transitions p[i,1] <- 1
Aur´lien
e
Madouasse
# Code for 2
Background
log(p[i,2]) <- beta[1, i] + beta[2, i] + beta[3, i] + beta[4, i]
Milk Recording
Data
Somatic Cell beta[1, i] <- pstate[i, 1] * theta[1]
Count
beta[2, i] <- pstate[i, 2] * theta[2]
State
Transition
beta[3, i] <- pstate[i, 3] * theta[3]
State Definition beta[4, i] <- pstate[i, 4] * theta[4]
State
Transitions
Data
# Code for 3
A Simple log(p[i,3]) <- beta[5, i]+beta[6, i]+ beta[7, i] + beta[8, i]
Model
Model
WinBUGS code
Results
beta[5, i] <- pstate[i, 1] * theta[5]
Adding
beta[6, i] <- pstate[i, 2] * theta[6]
Complexity beta[7, i] <- pstate[i, 3] * theta[7]
SCC Variation
Model
beta[8, i] <- pstate[i, 4] * gamma
WinBUGS code
Results

24. State transition
WinBUGS code
Modelling
State
Transitions # Code for 4
Aur´lien
e log(p[i,4]) <- beta[9, i]+ beta[10, i] + beta[11, i] +
Madouasse
beta[12, i]
Background
Milk Recording beta[9, i] <- pstate[i, 1] * theta[8]
Data
Somatic Cell beta[10, i] <- pstate[i, 2] * theta[9]
Count
beta[11, i] <- pstate[i, 3] * gamma
State
Transition
beta[12, i] <- pstate[i, 4] * gamma
State Definition }
State
Transitions
Data
# Priors for fixed effects
A Simple
Model
for(k in 1:9) {
Model theta[k] ~ dnorm(0, .001)
WinBUGS code
Results
}
Adding
Complexity gamma <- -2000
SCC Variation
Model }
WinBUGS code
Results

25. State transition
Results
Modelling
State
Transitions
Aur´lien
e
Madouasse
Background
Milk Recording
Data
Somatic Cell
Count
State
Transition
State Definition
State
Transitions
Data
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

26. State transition
Results
Modelling
State
Transitions
Aur´lien
e
Madouasse
Background
Milk Recording
Data
Somatic Cell
p1 = 1
Count
log (p2 ) = Ipst1 ∗ θ1 + Ipst2 ∗ θ2 + Ipst3 ∗ θ3 + Ipst4 ∗ θ4
State
Transition log (p3 ) = Ipst1 ∗ θ5 + Ipst2 ∗ θ6 + Ipst3 ∗ θ7 + Ipst4 ∗ γ
State Definition
State log (p4 ) = Ipst1 ∗ θ8 + Ipst2 ∗ θ9 + Ipste3 ∗ γ + Ipst4 ∗ γ
Transitions
Data
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

27. State transition
Results
Modelling
State
Transitions
Aur´lien
e
Madouasse Median Ci2.5 Ci97.5
Background theta[1] -2.04 -2.06 -2.00
Milk Recording
Data
theta[2] 0.80 0.76 0.83
Somatic Cell
Count theta[3] -1.27 -1.35 -1.19
State theta[4] -1.52 -1.68 -1.36
Transition
State Definition theta[5] -2.71 -2.75 -2.67
State
Transitions
Data
theta[6] -0.79 -0.84 -0.73
A Simple theta[7] 0.81 0.77 0.86
Model
Model
theta[8] -3.95 -4.02 -3.88
WinBUGS code
Results
theta[9] -1.55 -1.63 -1.48
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

28. State transition
Results
Modelling
State
Transitions
p1 = 1
Aur´lien
e
Madouasse log (p2 ) = Ipst1 ∗−2.04+Ipst2 ∗0.80+Ipst3 ∗−1.27+Ipst4 ∗−1.52
Background
log (p3 ) = Ipst1 ∗−2.71+Ipst2 ∗−0.79+Ipst3 ∗0.81+Ipst4 ∗−2000
Milk Recording
Data
log (p4 ) = Ipst1 ∗ −3.95 + Ipst2 ∗ −1.55 + Ipst3 ∗ γ + Ipst4 ∗ −2000
Somatic Cell
Count
State
Transition
State Definition
State
Transitions
Data
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

29. State transition
Results
Modelling
State
Transitions
Aur´lien
e
Madouasse p1 = 1
Background
log (p2 ) = −2.04
Milk Recording log (p3 ) = −2.71
Data
Somatic Cell
Count
log (p4 ) = −3.95
State
Transition
State Definition
State
Transitions
Data
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

30. State transition
Results
Modelling
State
Transitions
Aur´lien
e
Madouasse p1 = 1
Background
log (p2 ) = −2.04
Milk Recording log (p3 ) = −2.71
Data
Somatic Cell
Count
log (p4 ) = −3.95
State
Transition
State Definition
State
Transitions
Data
Σ p = p1 + p2 + p3 + p4
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

31. State transition
Results
Modelling
State
Transitions
Aur´lien
e
Madouasse p1 = 1
Background
log (p2 ) = −2.04
Milk Recording log (p3 ) = −2.71
Data
Somatic Cell
Count
log (p4 ) = −3.95
State
Transition
State Definition
State
Transitions
Data
Σp = 1 + e −2.04 + e −2.71 + e −3.95
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

32. State transition
Results
Modelling
State
Transitions
Aur´lien
e
Madouasse p1 = 1
Background
log (p2 ) = −2.04
Milk Recording log (p3 ) = −2.71
Data
Somatic Cell
Count
log (p4 ) = −3.95
State
Transition
State Definition
State
Transitions
Data
Σp = 1 + 0.13 + 0.07 + 0.02
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

33. State transition
Results
Modelling
State
Transitions
Aur´lien
e
Madouasse p1 = 1
Background
log (p2 ) = −2.04
Milk Recording log (p3 ) = −2.71
Data
Somatic Cell
Count
log (p4 ) = −3.95
State
Transition
State Definition
State
Transitions
Data
Σp = 1.22
A Simple
Model
Model
WinBUGS code
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

34. State transition
Results
Modelling
State
Transitions
Aur´lien
e
Madouasse
p1 = 1
log (p2 ) = −2.04
Background
Milk Recording log (p3 ) = −2.71
Data
Somatic Cell log (p4 ) = −3.95
Count
State
Transition
State Definition
State
Transitions
Σp = 1.22
Data
A Simple
Model
Model p1 p2 p3 p4
WinBUGS code π1 = Σp π2 = Σp π3 = Σp π4 = Σp
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

35. State transition
Results
Modelling
State
Transitions
Aur´lien
e
Madouasse
p1 = 1
log (p2 ) = −2.04
Background
Milk Recording
log (p3 ) = −2.71
Data
Somatic Cell log (p4 ) = −3.95
Count
State
Transition
State Definition
State
Transitions
Σp = 1.22
Data
A Simple
Model
Model 1 e −2.04 e −2.71 e −3.95
WinBUGS code π1 = 1.22 π2 = 1.22 π3 = 1.22 π4 = 1.22
Results
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

36. State transition
Results
Modelling
State
Transitions
Aur´lien
e
Madouasse p1 = 1
Background
log (p2 ) = −2.04
Milk Recording log (p3 ) = −2.71
Data
Somatic Cell
Count
log (p4 ) = −3.95
State
Transition
State Definition
State
Transitions
Data
Σp = 1.22
A Simple
Model
Model
WinBUGS code
Results π1 = 0.82 π2 = 0.11 π3 = 0.05 π4 = 0.02
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results

37. State transition
Results
Modelling
State
Transitions
State Probability of transition
Aur´lien
e
Previous
Current
Madouasse Credibility
Interval
Background n Observed Median 2.5 % 97.5 %
Milk Recording Low Low 37,259 0.822 0.822 0.819 0.825
Data
Somatic Cell
Low High 4,870 0.107 0.107 0.105 0.110
Count Low dry 2,487 0.055 0.055 0.053 0.057
State Low culled 720 0.016 0.016 0.015 0.017
Transition High Low 3,770 0.258 0.257 0.251 0.264
State Definition
State High High 8,349 0.570 0.570 0.563 0.579
Transitions High dry 1,718 0.117 0.117 0.113 0.123
Data
High culled 798 0.055 0.054 0.051 0.058
A Simple
Model
dry Low 2,647 0.283 0.283 0.274 0.292
Model dry High 745 0.080 0.079 0.075 0.085
WinBUGS code dry dry 5,967 0.638 0.638 0.627 0.646
Results
first Low 863 0.820 0.821 0.797 0.842
Adding first High 189 0.180 0.179 0.158 0.203
Complexity
SCC Variation
Model
WinBUGS code
Results

38. Outline
Modelling
State 1 Background
Transitions Milk Recording
Aur´lien
e Data
Madouasse Somatic Cell Count
Background 2 State Transition
Milk Recording State Definition
Data
Somatic Cell State Transitions
Count Data
State
Transition 3 A Simple Model
State Definition Model
State
Transitions WinBUGS code
Data Results
A Simple
Model 4 Adding Complexity
Model SCC Variation
WinBUGS code
Results Model
Adding
WinBUGS code
Complexity Results
SCC Variation
Model 5 Discussion
WinBUGS code
Results

39. Somatic Cell Count
Factors of variation
Modelling
State
Transitions
Aur´lien
e
Madouasse
300
q
q q qq
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Background q qq q
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250
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Milk Recording qqq
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Somatic Cell qqq qqq qq
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SCC varies with:
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Count qqq
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State qqq q
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Stage of lactation
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qq q
qqq
qqqqq
qqq
qq
q
q qq q
q qqq
qqq
q q
q qq
qqq
q
q q
q
qq
q q
q
qqq qq q
qqqq
q qqq
qqq q
qq qq
q qq q q q q
qq q q q qq
q
q
q q
Parity
q qqq
q qqq
q q qqqqq qq q
qqq
qqq q qq
q q q q q
qq q qq
qqqqqq
q q
qq qqq q
q q qqq
q q qqq
qq
q q qqqqq q
State Definition q
q
qqq
q qqqq q
q qqq
qq q
qqq
qqq q
qqqqqq
q
q q qqqq q
qqqq
qqqqq
q
qq q
q
qq
qqqq
qqqq
qq qq
q
qq q
q
qqqqq
q
q
q q qqqqq
qqq
q qq
qq
qqqq
qqqq
q
q q
qq q
qqqq q qq q qq
qqqqq
qq qqqq qqq qq
q
qq qqq q
qqq qq
qqqqq
qq q qq q qqq q qqq
100
State qqq
qq q
q q
q q
q
qq
qqqq
q qqqq
q
qq
qqqqqq
qq q
q q
q qqqq
q q
q qqqq
q qqqqq
qq
q q
q
qq qq q
qq q
qqq q
q q
q
qqqqqq
q q
qqqqq
q q
qq q q
q
qqq
qqqqqq
q q
qq
qqq q
qq q
q qq
qq qq
qqq q
qqqq
qqq
q
q
q q q qq
q
q
q
q
q
q
q q q qq
qqqq q q qqqq qqqq
qqq q qq q q qqq qqqq
q qqqq q
Transitions qq q
q q qq
qq qqq
qq
q
qqq q q qqqqqq
qqqqqqqq qqqq
q qq qq qqq
qqqqqq
qqqq q q
qq q q
q
q
q qq
qqq q
qqqq
qq qqq q
qq
qq qq
qqqqq
q qqqqq
q qq q
q qq
q qq q q q
q q
q q
q qq
q qqq
q qq
q qqqqq q
qqq q
qqqqq
qq
qqqqq q
qq q
q
q q
qqq qq
qq
q qqqq q q
q qqqqqq q
q qqq q
qqq
qq qqqqq
qq
qq
qqqq q qq q q
q q
q qqq qqq qqq q
qq qq qq
q q
q
qq
qq
qq
q q q q q
qqqq q qqqqq qqqqq
qq
q qqqqqq q
q q q q q
qq q q q qqq qq
qqq q qq q q qq
q q
qqqqqqqq
qq qqqqq qqqqq qqqqq q
qq q qqqqq
qqqq q q
Data q
q
qqqq
q
q
qq
qqq
qqqqq
q qq
qqq q qqq qqqqqqqqq
q q qqqqqqqq qqq
q q qq qq
qqqq
q
q qqqqqq
qqqq q q
q qq
qq q
q
q
q qqq
qqqqq
q qqq
qq qq
qq
qqqqq
q qq
qq q q
q qqq q
qqqq
q
qqqqqqq
qqq q
qq
qqqq
q qqqqqqqq
qq q
qqq qq
qqq
qq qq
qqqqq
qqqqq
q q qqqqqqqqq q
q q qq qqq q
q qq
qqqqqqqq qq
q qqqqqqqqqq q q
qqq qq
qq q
qqqqqq
q qqqqq qq
qqqqqqqqqqq
qqq
qqqqq
q qqq q
qq qq q q qq
q q q
qq qq qqqqq q
qqq q
qqqq q q qqqqqqqqqqqqq qqq q q
q qqqqqqqqqq
qqqqq
qqq q qq qq qqqqqq qqqqqqqqqqqqqqqqqqqqq
qq qqq
qqqq qqqqq q q qqqqqqq
qqqqqqq qqqqqqq
q qqq
qqq qqqqqqqqq qqqqq qq q
qqqq q qqqq q q
q
q qqqq
q qqqq qqq qqqqqq q qqq q
qqqqqqqqqqq
qq q q
50
q qqqqqq qqqqqqqq
q qqqqqqqqqqqqqqqqqqqqq
q qqqq q qqq qqqqqq
q
qqqqqqqqqqqqqqqqqqqq q
q qqqq
qqqqqq qqqqqqqqqq q
qq qqqqqq q
qq qqqqqqqqqqqq
qqqq qq q
qqq q
A Simple q q
Model
Model
0
WinBUGS code
0 100 200 300 400
Results
Days in Milk
Adding
Complexity
SCC Variation
Model
WinBUGS code
Results