An Unbalanced Two‐way Model With Random Effects Having Unequal Variances

Consider the model y ijk =u ± a i ± b i ± c ij ± e ijk i=1, 2,…, t; j=1, 2,…b; k=1, 2,…,n ij where μ is a constant and a i , b i , c ij are distributed independently and normally with zero means and variances Δ 2 Δ2/bd ij and δ 2 respectively. It is assumed that d i 's, and d ij 's are known (positive) constants (for all i and j ). In this paper procedures for estimating the variance components (Δ 2 , Δ 2 b and Δ 2 a ) and for testing the hypothesis H oc :Δ 2 c /Δ 2 = y 3 and H oa :Δ 2 b /Δ 2 = y 4 (where y 2 , y 3 , and y 4 , are specified constants) are presented. A generalization for the mixed model case is discussed in the last section.