ABSTRACT
It is difficult to argue with the claim that normal linear models-which include linear regression, analysis of variance (ANOVA), mixed-effect models, etc-are the most widely used models in applied statistics. For this reason, we think it is important to discuss these models in some detail. Of particular interest here is, first, some general auxiliary variable dimension reduction strategies. In the examples considered here, this corresponds to specifying a lower-dimensional association for the sufficient statistics. Once all the general dimension reduction has been carried out, the question becomes whether a further dimension reduction can be carried out due to the fact that only some feature of the unknown parameter is of interest. For this we will apply various marginalization techniques as discussed in Chapter 7 to further reduce the auxiliary variable dimension.
