Testing fixed effects in mixed linear models Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/f4752k442

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  • This dissertation is concerned with hypothesis testing for fixed effects in mixed linear models. Our primary emphasis is on mixed models when the class of covariance matrices has what we call a rich linear structure. Such models include mixed ANOVA models and regression models with heteroscedastic variances. For the majority of our results we have also assumed that the covariance structure is commutative. We show how to uniquely partition a chi-squared sum of squares into two independent parts, one related to the fixed effects and the other involving only error contrasts. Based on this partition and the commutativity of the covariance structure, we can decompose our model into a number of independent models. When we assume that the model has Zyskind structure, that is, that all estimable linear parameteric functions have BLUEs (best linear unbiased estimators), then this gives full partitions of both the expectation space and the error space. For a model with Zyskind structure, a convenient minimal sufficient statistics is obtained. The problem of testing a linear hypothesis about the fixed effects, when the model is commutative and has Zyskind structure, is shown to be invariant under a certain group of transformations. The maximal invariant statistic is derived, generalizing a result of Seifert (1979). The ANOVA test is seen to be uniformly most powerful invariant unbiased. A uniformly most powerful test within the class of Bartlettr Scheffe tests is considered.
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