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1 5 9 13 18 23 28 33 38 43 48 53 58 63 68 73 78 83 88 93 98 103 1 3 5 7 9 11 14 17 20 23 26 29 32 35 38 41 44 47 50 Distância (cm)

Indivíduos 1 4 7 10 14 18 22 26 30 34 38 42 46 50 54 58 62 66 70 74 78 82 86 90 94 98 102 1 3 5 7 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 Marcadores

30 50 70 30 50 70 BW 30 50 70 30 50 70 BW1 BW2 30 50 70 30 50 70 BW3 BW4 30 50 70 30 50 70 30 50 70 30 50 70

1 2 3 4 5 1 2 3 4 5

y j1 = β 01 + β 1 x j + δ 1z j + y j2 = β 02 + β 2 x j + δ 2z j +...... y jm = β 0m + β mx j + δ mz j + t (β l1 x jl + δ l1 z jl ) + ε j1 l t (β l2 x jl + δ l2 z jl ) + ε j2 l t (β lm x jl + δ lm z jl ) + ε jm y jk = k j β 0k = k β k = k x j = δ k = k z j = x jl, z jl = ε jk = k j l

e jk Cov(e jk, e jl ) = σ kl = ρ kl σ k σ l, e jk 0 V V = σ 2 1 σ 12... σ 1m σ 21 σ 2 2... σ 2m............ σ m1 σ m2... σ 2 m

H 0 : β 1 = 0, δ 1 = 0, β 2 = 0, δ 2 = 0 H 1 : H 0 : β 1 = β 2 = β, δ 1 = δ 2 = δ H 1 : β 1 β 2, δ 1 δ 2 QT L E

H 0 : β 1 = 0, δ 1 = 0, β 2 = 0, δ 2 = 0 H 1 : H 10 : β 1 = 0, δ 1 = 0, β 2 0, δ 2 0 H 11 : β 1 0, δ 1 0, β 2 0, δ 2 0 H 20 : β 1 0, δ 1 0, β 2 = 0, δ 2 = 0 H 21 : β 1 0, δ 1 0, β 2 0, δ 2 0 H 0 : p(1) = p(2) H 1 : p(1) p(2)

P ij = µ + E j + G i + GE ij = µ + E j + (G + GE) ij = µ + E j + ε ij = µ j + ε ij

j j var(ε ij ) cov(ε ij, ε ij ) σg 2 0 σg 2 + σ2 GE σg 2 σg 2 j 0 σg 2 + σ2 GE j σg 2 σg 2 j θσ Gj σ Gj σg 2 j σ Gjj

x i y ij = µ + E j + G i + GE ij = µ + E j + βx i + G i + GE ij = µ + E j + βx i + (G + GE) ij = (µ + E j ) + βx i + ε ij = µ j + βx i + ε ij

x i β j y ij = µ + E j + G i + GE ij = µ + E j + βx i + G i + β j x i + GE ij = µ + E j + βx i + β j x i + (G i + GE ij ) = µ + E j + βx i + β j x i + ε ij = (µ + E j ) + β j x i + ε ij = µ j + β j x i + ε ij

y isjkr = µ + L j + H k + LH jk + G ijk + ε isjkr G ijk = { gijk c ijk i = 1,..., n g i = n g + 1,..., n g + n c = (g 111,..., g IJK ) I ε isjkr = t s + t sjk + b sjkr + η isjkr η isjkr N(0, σ 2 )

n P AR = L H M M Het = L J J H K K Het

y isjkr = µ + L j + H k + LH jk + x piw α pjkw + x qiw α qjkw + x pqiw δ pqjkw + G ijk + ε isjkr y isjkr = µ + L j + H k + LH jk + x piw α pw + x qiw α qw + x pqiw δ pqw + G ijk + ε isjkr

α qjk α p α q α qk α pjk α qk α pj α pk α qk α pjk α pk α pj α pk α qjk

m p y ti = µ t + β tr x ir + w trl x ir x il + e ti r=1 r<l i i = 1,..., n t t = 1,..., T x ir 1 2 1 2 β tr r t µ t p w trl e ti

i = (y 1i, y 2i,..., y T i ) i = (e 1i, e 2i,..., e T i ) 0 Σ e i MV N T (, Σ e ) β r = (β 1r,..., β T r ) b = (w 1rl, w 2rl,..., w T rl ) µ = (µ 1, µ 2,..., µ T ) T S θ Σ e s 2 m

L i (θ i, i, λ) = 2 m j=1 p ij ϕ( i µ + [.,j], Σ e ) n L(θ,, λ) = L i (θ i, i, λ) i=1 λ

H 0 (β 1m, β 2m,..., β T m ) = (0, 0,..., 0) H 1 (β 1m, β 2m,..., β T m ) (0, 0,..., 0) α c = α T

λ 1 λ 2 λ 3 ( ) ( ) ( ) y1i µ1 β11 β = + 12 β i1 ( ) 13 x x y 2i µ 2 β 21 β 22 β i2 e1i + 23 e x 2i i3 λ 3 ( ) ( ) ( ) x i1 ( ) y1i µ1 β11 β = + 12 β 13 0 x i2 y 2i µ 2 β 21 β 22 0 β 24 x i3 + e1i e 2i x i4