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For data following a balanced mixed Anova model, the standard Anova method typically leads to exact F tests of the usual hypotheses about fixed effects. However, for most unbalanced designs with most hypotheses, the Anova method does not produce exact tests, and approximate methods are needed. One approach to approximate inference about fixed effects in mixed linear models is the method of Kenward and Roger (1997), which is available in SAS and widely used. In this thesis, we strengthen the theoretical foundations of the method by clarifying and weakening the assumptions, and by determining the orders of the approximations used in the derivation. We present two modifications of the K-R method which are comparable in performance but simpler in derivation and computation. It is known that the K-R method reproduces exact F tests in two special cases, namely for Hotelling and for Anova F ratios in fixed-effects models. We show that the K-R and proposed methods reproduce exact F tests in three more general models which include the two special cases, plus tests in all fixed effects linear models, many balanced mixed Anova models, and all multivariate regressions models. In addition, we present some theorems on the K-R, proposed, and Satterthwaite methods, investigating conditions under which they are identical. Also, we show the 2T
difficulties in developing a K-R type method using the conventional, rather than adjusted, estimator of the variance-covariance matrix of the fixed-effects estimator. A simulation study is conducted to assess the performance of the K-R, proposed, Satterthwaite, and Containment methods for three kinds of block designs. The K-R and proposed methods perform quite similarly and they outperform other approaches in most cases. |
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