By Hardeo Sahai
Systematic therapy of the widely 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 typically present in texts on the introductory or intermediate point. additionally it is numerical examples to research facts from a large choice of disciplines in addition to any labored examples containing desktop outputs from common software program applications reminiscent of SAS, SPSS, and BMDP for every numerical instance.
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Additional info for Analysis of Variance for Random Models, Volume 2: Unbalanced Data: Theory, Methods, Applications, and Data Analysis
In the modiﬁed procedure, instead of using symmetric sums of products, symmetric sums of squares of differences are used. Forthofer and Koch (1974) have extended the SSP method of the estimation of variance components to the general mixed model. Here, we illustrate the SSP method for the degenerate or one-stage design. In subsequent chapters, we consider the application of the method for speciﬁc experimental situations. To illustrate the SSP method for the degenerate or one-stage design, let the observations yi s (i = 1, 2, .
The resulting estimators are unbiased and consistent, and they are identical to the analysis of variance estimators for balanced data. However, for certain unbalanced experiments, the estimates obtained in this manner have an undesirable property that they may change in value if the same constant is added to all the observations, and their variances are functions of the general mean µ. This difﬁculty is overcome by Koch (1968), who suggested a modiﬁcation of the above method to obtain estimators of the variance components, which are invariant under changes in location of the data.
Numerical results indicate that these algorithms improve on the method of successive approximation and the Newton–Raphson algorithm and are superior to other widely used algorithms like Fisher’s scoring and the EM algorithm. Robinson (1984, 1987) discussed a modiﬁcation of an algorithm proposed by Thompson (1977a) which is similar to Fisher’s scoring technique. Robinson (1984, 1987) noted that his algorithm compares favorably with the Newton– Raphson algorithm outlined by Dempster et al. (1984).
Analysis of Variance for Random Models, Volume 2: Unbalanced Data: Theory, Methods, Applications, and Data Analysis by Hardeo Sahai