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An Unbalanced Two‐way Model With Random Effects Having Unequal Variances
Author(s) -
Hussein M.,
Milliken G. A.
Publication year - 1978
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710200302
Subject(s) - mathematics , combinatorics , generalization , constant (computer programming) , zero (linguistics) , variance (accounting) , statistics , mathematical analysis , linguistics , philosophy , accounting , computer science , business , programming language
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.