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This thesis develops a general strategy for factorial linear model analysis for experimental and observational studies. It satisfactorily deals with a number of issues that have previously caused problems in such analyses. The strategy developed here is an iterative, four-stage, model comparison procedure as described in Brien (1989); it is a generalization of the approach of Nelder (1965a,b). The approach is applicable to studies characterized as being structure-balanced, multitiered and based on Tjur structures unless the structure involves variation factors when it must be a regular Tjur structure. It covers a wide range of experiments including multiple-error, change-over, two-phase, superimposed and unbalanced experiments. Examples illustrating this are presented. Inference from the approach is based on linear expectation and v...
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This paper gives a general method for constructing quasi-Latin square, quasi-Latin rectangle and extended quasi-Latin rectangle designs for symmetric factorial experiments. Two further methods are given for parameter values satisfying certain conditions. The construction of designs for a range of numbers of rows and columns is discussed so that the different construction techniques are covered. For some row and column combinations, different designs are compared. The construction of designs with rows and columns that are nested or contiguous is also discussed.
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