ABSTRACT
Chapter 5 shows how to estimate and test the parameters of any complete hierarchical log-linear frequency model. As far as the mechanics of calculation are concerned, that chapter contains most of what one needs to know. But deciding how to apply the procedures is often more confusing than the procedures themselves. When there are many factors, the number of possible models is large: excluding constant-frequency models, there are 2 models for two factors ([A][B] and [AB]), 9 for three factors (recall Figure 3.4), 114 for four factors, and the number increases rapidly in larger tables. By the time 10 factors are involved, the number of models is enormous—there are 115,974 hypotheses of complete independence and 3,475,978 of complete or conditional independence, including those that postulate equal frequencies over some of the factors (Good, 1975). These only touch the full set of possible models. An idea of the vastness of the number of 10-factor models is gained when one realizes that there are 45 pairwise combinations of factors, hence 245 = 35,184,372,088,832 models involving only pairwise associations. Obviously, a strategy is needed to cope with this plethora.
