Structured orthogonal families of one and two strata prime basis factorial models

The models in structured families correspond to the treatments of a fixed effects base design <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\pi $$</EquationSource> </InlineEquation>. Then the action of factors in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\pi $$</EquationSource> </InlineEquation>, on the fixed effects parameters of the models, is studied. Analyzing such a families enables the study of the action of nesting factors on the effects and interactions of nested factors. When <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\pi $$</EquationSource> </InlineEquation> has an orthogonal structure, the family of models is said to be orthogonal. The models in the family can have one, two or more strata. Models with more than one stratum are obtained through nesting of one stratum models. A general treatment of the case in which the base design has orthogonal structure is presented and a special emphasis is given to the families of prime basis factorials models. These last models are, as it is well known, widely used in fertilization trials. Copyright Springer-Verlag Berlin Heidelberg 2014