Structures and properties of repeated measurement designs
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In this study the structure and properties of repeated measurement (RM) designs are investigated from different points of view, such as (i) balancedness or partial balancedness, (ii) construction versus estimation, (iii) underlying linear models, (iv) factorial treatment structure. In studying balanced repeated measurement designs for the first order residual effects model it becomes apparent that one has to distinguish between balancedness with respect to construction and balancedness with respect to estimation. These two concepts do not necessarily imply each other as they do, for example, for the balanced incomplete block design. Such designs are referred to as BRMl and BRMlE designs, respectively. It is shown that they are imbedded in a much larger class of RM designs. This class is based on generalized partially balanced incomplete block designs and hence referred to as GPBRMl designs. The properties of GPBRMl designs can be investigated by means of association matrices. For the construction of these designs the concept of asymmetrically repeated differences is introduced as a generalization of symmetrically repeated differences used for constructing certain PBIB designs. Another generalization of RM designs concerns the underlying linear model. In particular, the situation is considered where in addition to first order residual effects the model also contains second order residual effects. This leads to BRM2 and BRM2E designs. Extension to kᵗʰ order residual effect models are mentioned briefly. Modifications of existing RM designs can be achieved if the treatments have a factorial structure and if certain, usually higher order, interactions can be considered negligible. In particular, it is shown how this can lead to a substantial reduction in the number of periods and/or subjects for a RM design.
- Doctoral Dissertations