Exact(60)
Let x ij symbolize the individual effect of cow i in herd j.
Let y ij be the outcome of cow i in herd j and x ij an independent variable measured at cow level.
The probability of developing mastitis for cow i can be expressed as (9) π i j k (H D ) = P f i (t + 1 ) (H D ) = 1 f i t (H D ) = 0 and was the same for cow i throughout the entire lactation, i.e. for all values of t, (t = 1,..., T i-1).
The t:th SCC value (in order within a lactation) for cow i, daughter of sire j, and member of herd k is denoted y ijkt, t = 1,..., T i where T i is the number of measurements for cow i within the same lactation.
The binary response h ijkt states whether the t:th order SCC value for cow i is below (H) or above (D) the boundary stated in (1) and is formally expressed as (6) h i j k t = 1 if y i j k t > B (τ t ) 0 if y i j k t ≤ B (τ t ) where τ t is the time since calving for the t:th order response of cow i.
The probability of moving from a healthy to a diseased state for cow i is denoted π i H D and the probability of moving from a diseased to a healthy state, π i D H. The transition probabilities for cow i may be summarized in a transition matrix Tr i, (2) T r i = π i H D 1 - π i H D 1 - π i D H π i D H which gives the probabilities of changing states or remaining in the current state.
The transition probability π ijk is the discrete equivalent of the continuous time hazard function and is defined as the probability that a transition occurs at some time between any two measurements for cow i, daughter of sire j, and member of herd k.
The following model was used: The model was for observed value of cow i at day t: y it = μ + c i + α t + ε it Where μ = overall mean, ci= random effect of the cow, αt = effect of sampling day t, εit = random error.
For case 1, the T-penalty for mating ij (cow i mated to sire j) is defined by T i j = D i j − (D i j ) min σ (D i j ) where the minimum and the standard deviation were obtained by considering the whole mating set (number of matings = number of sires * number of females).
For example, a sequence of h ijk = [0010001110100], containing 13 measurements and three cases of classified mastitis (one which lasted over three measurements) for cow i, generated f i j k H D = 0100110 and f i j k D H = 10011, together with two time indicators ν i j k H D = 1212311 and ν i j k (D H ) = 11231.
"Is that a cow?" I ask again.
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