26REML

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Unformatted text preview: 2 (Iowa State University) Statistics 511 16 / 31 For the normal theory Gauss-Markov linear model, y = Xβ + , ∼ N (0, σ 2 I), the REML estimator of σ 2 is σ2 = ˆ y (I − PX )y , n−r the unbiased estimator that we used previously. Copyright c 2012 (Iowa State University) Statistics 511 17 / 31 For linear mixed effects models, the REML estimators of variance components produce the same estimates as the unbiased ANOVA-based estimators formed by taking appropriate linear combinations of mean squares when the latter are positive and data are balanced. Copyright c 2012 (Iowa State University) Statistics 511 18 / 31 In any case, once a REML estimate of γ (and thus Σ) has been obtained, the BLUE of an estimable Cβ can be approximated by ˆˆ ˆ −1 ˆ −1 Cβ Σ = C(X Σ X)− X Σ y, ˆ ˆ where Σ is Σ with γ (the REML estimate of γ ) in place of γ . Copyright c 2012 (Iowa State University) Statistics 511 19 / 31 A A B B A B B A 2 0 A A B B B A B A 2 1 d=read.delim( "http://www.public.iastate.edu/~dnett/S511/SeedlingDryWeight2.txt" ) d 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Genotype Tray Seedling SeedlingWeight A 1 1 8 A 1 2 9 A 1 3 11 A 1 4 12 A 1 5 10 A 2 1 17 A 2 2 17 A 2 3 16 A 2 4 15 A 2 5 19 A 2 6 18 A 2 7 18 A 2 8 18 A 2 9 24 A 3 1 12 A 3 2 12 A 3 3 16 2 2 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 A A A A A A A A A A A A B B B B B B B B B 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 4 5 6 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 1 2 3 15 15 14 17 20 20 19 19 18 20 19 19 9 12 13 16 14 14 10 10 9 2 3...
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This document was uploaded on 03/27/2014.

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