By Hardeo Sahai
Systematic remedy of the generally hired crossed and nested category types utilized in research of variance designs with a close and thorough dialogue of definite random results types no longer generally present in texts on the introductory or intermediate point. it is also numerical examples to investigate information from a large choice of disciplines in addition to any labored examples containing computing device outputs from common software program programs akin to SAS, SPSS, and BMDP for every numerical instance.
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Extra info for Analysis of Variance for Random Models, Volume 2: Unbalanced Data: Theory, Methods, Applications, and Data Analysis
1. As pointed out by Harville (1969a), however, there are several drawbacks of the Hartley and Rao procedure. Some of them are as follow: (i) Though it produces a solution to the likelihood equations, over the constrained parameter space, there is no guarantee that the solution is an absolute maximum of the likelihood function over that space. (ii) While it is true that the procedure yields a sequence estimator with the usual asymptotic properties of maximum likelihood estimators, it is hard to justify the choice of an estimator on the basis of its being a part of a “good’’ sequence.
1992, Chapter 8). Utmost caution should be exercised in using these algorithms for problems that are fairly large and highly unbalanced. As Klotz and Putter (1970) have noted, the behavior of likelihood as a function of variance components is generally complex even for a relatively simple model. For example, the likelihood equation may have multiple roots or the ML estimate may lie at the boundary rather than a solution of any of these roots. In fact, J. N. K. Rao (1977) has commented that none of the existing algorithms guarantee a solution, which is indeed ML or REML.
The procedure involves evaluating sums of squares analogous to those used for the analysis of variance for balanced data. These are then equated to their respective expected values and solved for variance components. 1) following closely the developments given in Searle (1971b, pp. 431–434). In subsequent chapters, we discuss the application of the method for special cases. 2) and P Var(Y ) = Xθ Var(βθ )Xθ + σe2 IN . θ=A Now, let y. (Ai ) and n(Ai ) denote the total value and the number of observations in the ith level of the factor A.
Analysis of Variance for Random Models, Volume 2: Unbalanced Data: Theory, Methods, Applications, and Data Analysis by Hardeo Sahai