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An Unbalanced Nested Model with Random Effects Having Unequal Variances
Author(s) -
Hussein Mohamed,
Milliken George 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.4710200403
Subject(s) - mathematics , combinatorics , constant (computer programming) , zero (linguistics) , variance (accounting) , statistics , mixed model , philosophy , linguistics , accounting , computer science , business , programming language
Consider the model Y ijk =μ + a i + b ij + e ijk (i=1, 2,…, t; j=1,2,…, B i ; k=1,2…,n ij ), where μ is a constant and a 1 ,b ij and e ijk are distributed independently and normally with zero means and variances σ 2 a d ij and σ 2 , respectively, where it is assumed that the d i 's and d ij 's are known. In this paper procedures for estimating the variance components (σ 2 , σ 2 a and σ 2 b ) and for testing the hypothesis σ 2 b = 0 and σ 2 a = 0 are presented. In the last section the mixed model y ijk , where x ijkkm are known constants and β m 's are unknown fixed effects ( m = 1, 2,…, p ), is transformed to a fixed effect model with equal variances so that least squares theory can be used to draw inferences about the β m 's.