An Unbalanced Mixed Model with Random Effects Having Unequal Variances

✍ Scribed by Dr. M. Hussein; Dr. G. A. Milliken

• Publisher: John Wiley and Sons
• Year: 1979
• Tongue: English
• Weight: 369 KB
• Volume: 21
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710210203

✦ Synopsis

P k -i

Consider the mixed model yi, = p + 2 q f & k +at + eii (i = 1,2. . . . , I, j = 1,2,. . . , nit, k = 1.2, . . . , p ) .

where q , k '8 are known constants, Pk'8 are unknown parameters and ai, eij are random variables independently nnd normally distributed with zero means and vnriances u& and u2 respectively, where it is assumed that the d i ' s are k c o m (I& >O). This paper presents procedures for estimating the variance components u,2, u*, for testing the hypothesis u,2=0, and for making transformations to random variables with uncorrelated crrors and constant variances in order t o estimate as wcll as to test hypothcsis concerning the j?k' 8 in the model.