Next: 4 The Elements of
Up: 1 The Scope of
Previous: 3 Within Family Differences
Index
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.
Next: 4 The Elements of
Up: 1 The Scope of
Previous: 3 Within Family Differences
Index
Jeff Lessem
20020321