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An Unbalanced Nested Model with Random Effects Having Unequal Variances
Authors:Mohamed Hussein  George A. Milliken
Abstract:Consider the model Yijk=μ + ai + bij + eijk (i=1, 2,…, t; j=1,2,…, Bi; k=1,2…,nij), where μ is a constant and a1,bij and eijk are distributed independently and normally with zero means and variances σ2adij and σ2, respectively, where it is assumed that the di's and dij's are known. In this paper procedures for estimating the variance components (σ2, σ2a and σ2b) and for testing the hypothesis σ2b = 0 and σ2a = 0 are presented. In the last section the mixed model yijk, where xijkkm are known constants and βm'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 βm's.
Keywords:Fitting  constants method  variance components  mixed model  transformation  estimations  hypothesis testing
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