Example of Mixed Model Analysis using the EM Algorithm The first example is an evaluation of the breeding value of a set of five sires in raising pigs, taken from Snedecor and Cochran (1967).(The data is reported in Appendix 4.)The experiment was designed so that each sire is mated to a random group of dams,each mating producing a litter of pigs whose characteristics are criterion.The model to be estimated is k=μ+ai+Bi+eik, (4) where a;is a constant associated with the i-th sire effect,Bij is a random effect associated with the i-th sire and j-th dam,k is a random term.The three different initial values for (o,o1)are(1,1),(10,10)and (.038,.0375);the last initial value corresponds to the estimates from the SAS ANOVA procedure. Table 1:Average Daily Gain of Two Pigs of Each Litter (in pounds) Sire Dam Gain Sire Dam Gain 1 2.77 3 2.72 2 y 2.38 3 2 2.74 1 2 2.58 4 义 2.87 1 2 2.94 4 义 2.46 2 1 2.28 4 2 2.31 2 1 2.22 4 2 2.24 2 2 3.01 5 义 2.74 2 2 2.61 5 1 2.56 3 1 2.36 5 2 2.50 1 2.71 5 2 2.48 20Example of Mixed Model Analysis using the EM Algorithm The first example is an evaluation of the breeding value of a set of five sires in raising pigs, taken from Snedecor and Cochran (1967). (The data is reported in Appendix 4.) The experiment was designed so that each sire is mated to a random group of dams, each mating producing a litter of pigs whose characteristics are criterion. The model to be estimated is yijk = µ + αi + βij + ijk, (4) where αi is a constant associated with the i-th sire effect, βij is a random effect associated with the i-th sire and j-th dam, ijk is a random term. The three different initial values for (σ 2 0 , σ 2 1 ) are (1, 1), (10, 10) and (.038, .0375); the last initial value corresponds to the estimates from the SAS ANOVA procedure. Table 1: Average Daily Gain of Two Pigs of Each Litter (in pounds) Sire Dam Gain Sire Dam Gain 1 1 2.77 3 2 2.72 1 1 2.38 3 2 2.74 1 2 2.58 4 1 2.87 1 2 2.94 4 1 2.46 2 1 2.28 4 2 2.31 2 1 2.22 4 2 2.24 2 2 3.01 5 1 2.74 2 2 2.61 5 1 2.56 3 1 2.36 5 2 2.50 3 1 2.71 5 2 2.48 20