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Path analysis was invented by the geneticist Sewall Wright (1921a,
1934, 1960, 1968), and has been widely applied to problems
in
genetics and the behavioral sciences. It is a technique which allows
us to represent, in diagrammatic form, linear `structural'
models and hence derive predictions for
the variances and covariances (the *covariance
structure*) of our variables under that
model. The books by Kenny (1979), Li (1975), or Wright (1968) supply
good introductory treatments of path analysis, and general
descriptions of structural equation modeling can be found in Bollen
(1989) and Loehlin (1987). In this chapter we provide only the basic
background necessary to understand models used in the genetic analyses
presented in this text.
A path diagram is a useful heuristic tool to graphically display
causal and correlational relations or the paths between variables.
Used correctly, it is one of several mathematically complete
descriptions of a linear model, which include less visually immediate
forms such as (i) structural equations and (ii) expected covariances
derived in terms of the parameters of the model. Since all three
forms are mathematically complete, it is possible to translate from
one to another for such purposes as applying it to data, increasing
understanding of the model, verifying its identification, or
presenting results.
The advantage of the path method is that it goes beyond measuring the
degree of association by the correlation coefficient or determining
the best prediction by the regression coefficient. Instead, the user
makes explicit hypotheses about relationships between the variables
which are quantified by path coefficients. Better still, the model's
predictions may be statistically compared with the observed data, as
we shall go on to discuss in Chapters
and . Path models are in fact extremely general,
subsuming a large number of multivariate methods, including (but not
limited to) multiple regression, principle component or factor
analysis, canonical correlation, discriminant analysis and
multivariate analysis of variance and covariance. Therefore those
that take exception to `path analysis' in its broadest sense, should
be aware that they dismiss a vast array of multivariate statistical
methods.
We begin by considering the conventions used to draw and read a path
diagram, and explain the difference between correlational paths and
causal paths
(Section 5.2). In
Sections 5.3 and 5.4 we briefly describe
assumptions of the method and tracing rules for path diagrams. Then,
to illustrate their use, we present simple linear regression models
familiar to most readers (Section 5.5). We define these
both as path diagrams and as structural equations -- some individuals
handle path diagrams more easily, others respond better to equations!
We also apply the method to two basic representations of a simple
genetic model for covariation in twins (Section 5.6),
with special reference to the identity between the matrix
specification of a model and its graphical representation. Finally we
discuss identification of models and parameters in
Section 5.7.

** Next:** 2 Conventions Used in
** Up:** 5 Path Analysis and
** Previous:** 5 Path Analysis and
** Index**
Jeff Lessem
2002-03-21