Approximate confidence bounds for ratios of variance components in two-way unbalanced crossed models with interactions

Abstract

Consider the general unbalanced two-factor crossed components-of-variance model with interaction given by Y_ijk: = μ+A_i: +B_j: + C_ij: +E_ijk: (i = 1,2, … a; j = 1,…,b; k = 1,…,.n_ij:=0) A_i:,B_j:, C_ij: and E_ijk: are independent unobservable random variables. Also A_i:sim; N(0,σ² _A),B_j: ∼ N(0,σ² _B), C_ij:∼N(0,s² _C:) and E_ijk:∼N(0,s² _E:). In this paper approximate confidence bounds are obtained for ρ_A: = ρ² _A/² and ρ_B: = 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.

Keywords:

• unbalanced models
• confidence bounds
• missing cells