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 variation models and employs an analysis of variance.
The sources included in the analysis of variance table is based on the division of the
factors, on the basis of the randomization employed in the study, into sets called tiers.
The factors are also subdivided into expectation factors and variation factors. From
this subdivision models appropriate to the study can be formulated and the expected
mean squares based on these models obtained. The terms in the expectation model
may be nonorthogonal and the terms in the variation model may exhibit a certain
kind of nonorthogonal variation structure. Rules are derived for obtaining the sums
of squares, degrees of freedom and expected mean squares for the class of studies
covered.
The models used in the approach make it clear that the expected mean squares
depend on the subdivision into expectation and variation factors. The approach
clarifes the appropriate mean square comparisons for model selection. The analysis
of variance table produced with the approach has the advantage that it will reflect
all the relevant physical features of the study. A consequence of this is that studies,
in which the randomization is such that their confounding patterns differ, will have
different analysis of variance tables.Thesis (Ph.D.)--University of Adelaide, Dept. of Plant Science, 1992
