ASReml-S reference manual - VSN International

Table B.1: Details of the available variance modelsB Available variance models 124functionnamedescriptionalgebraicformnumber of parameterscorr hom hetvariance varianceCorrelation modelsid() identity C ii= 1, C ij= 0, i ≠ j 0 1 ωar1() 1 st orderautoregressiveC ii= 1, C i+1,i= φ 1C ij= φ 1C i−1,j, i > j + 1|φ 1| < 11 2 1 + ωar2() 2 nd orderautoregressivear3() 3 rd orderautoregressivesar()symmetricautoregressiveC ii= 1,C i+1,i= φ 1/(1 − φ 2)C ij= φ 1C i−1,j+φ 2C i−2,j, i > j +1|φ 1± φ 2| < 1,|φ 1| < 1, |φ 2| < 1C ii= 1, Ω = 1 − φ 2− φ 3(φ 1+ φ 3),C i+1,i= (φ 1+ φ 2φ 3)/Ω,C i+2,i= (φ 1(φ 1+ φ 3) + φ 2(1 − φ 2))/Ω,C ij= φ 1C i−1,j+ φ 2C i−2,j+ φ 3C i−3,j, i > j + 2|φ 1| < (1 − φ 2), |φ 2| < 1, |φ 3| < 1C ii= 1,C i+1,i= φ 1/(1 + φ 2 1 /4)C ij= φ 1C i−1,j− φ 2 1 /4 C i−2,j ,i > j + 1|φ 1| < 12 3 2 + ω3 4 3 + ω1 2 1 + ωsar2()constrainedautoregressive 3used forcompetitionas for AR3 usingφ 1= γ 1+ 2γ 2,φ 2= −γ 2(2γ 1+ γ 2),φ 3= γ 1γ 2 , 22 3 2 + ωma1() 1 st ordermoving averagema2() 2 nd ordermoving averageC ii= 1,C i+1,i= −θ 1/(1 + θ 2 ) 1C ji= 0, j > i + 2|θ 1| < 1C ii= 1,C i+1,i= −θ 1(1 − θ 2)/(1 + θ 2 + 1 θ2)2C i+2,i= −θ 2/(1 + θ 2 + 1 θ2)2C ji= 0, j > i + 2θ 2± θ 1< 1|θ 1| < 1, |θ 2| < 11 2 1 + ω2 3 2 + ω