3 Building and Fitting Models

As long as we study random samples of unrelated individuals, our understanding of what causes the differences we see will be limited. The total population variation is simply an aggregate of all the various components of variance. One practical approach to the analysis of variation is to obtain several measures of it, each known to reflect a different proportion of genetic and environmental components of the differences. Then, if we have a model for how the effects of genes and environment contribute differentially to each distinct measure of variation, we can solve to obtain estimates of the separate components. Figure 1.6

Figure 1.6: Diagram of the interrelationship between theory, model and empirical observation.

shows the principal stages in this process. There are two aspects: theory and data. The model is a formal, in our case mathematical, statement which mediates between the logic of the theory and the reality of the data. Once a model is formulated consistently, the predictions implied for different sets of data can be derived by a series of elementary mathematical operations. Model building is the task of translating the ideas of theory into mathematical form. A large part of this book is devoted to a discussion of model building. Inspection of the model, sometimes aided by computer simulation (see Chapters 7 and ), may suggest appropriate study designs which can be used to generate critical data to test some or all parts of a current model. The statistical processes of model fitting allow us to compare the predictions of a particular model with the actual observations about a given population. If the model fails, then we are forced to revise all or some of our theory. If, on the other hand, the model fits then we cannot know it is ``right" in some ultimate sense. However, we might now wish to base new testable conjectures on the theory in order to enlarge the scope of observations it can encompass.