Approximate confidence bounds for ratios of variance components in two-way unbalanced crossed models with interactions |
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| Authors: | MK Kazempour Franklin A Graybill |
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| Institution: | 1. Department of statistics , University of Central Florida , Orlando, FL, 32816;2. Department of statistics , Colorado State University , Ft. Collins, CO, 80523 |
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| Abstract: | Consider the general unbalanced two-factor crossed components-of-variance model with interaction given by Yijk: = μ+Ai: +Bj: + Cij: +Eijk: (i = 1,2, … a; j = 1,…,b; k = 1,…,.nij:=0) Ai:,Bj:, Cij: and Eijk: are independent unobservable random variables. Also Ai:sim; N(0,σ2 A),Bj: ～ N(0,σ2 B), Cij:～N(0,s2 C:) and Eijk:～N(0,s2 E:). In this paper approximate confidence bounds are obtained for ρA: = ρ2 A/2 and ρB: = ρ2 B:/ρ2 (where σ2 = σ2 A:+ σ2 B+σ2 Cσ2 E) for special cases of the above model. The balanced incomplete block model is studied as a special case. |
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| Keywords: | unbalanced models confidence bounds missing cells |
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