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#

2 Phenotypic Factor Analysis

Factor analysis is one of the most widely used multivariate methods.
The general idea is to explain variation within and covariation
between a large number of observed variables with a smaller number of
latent factors. Here we give a brief outline of the method -- those
seeking more thorough treatments are referred to e.g., Gorsuch (1983),
Harman (1976), Lawley and Maxwell (1971).
Typically the free parameters of
primary interest in factor models are the *factor
loadings* and *factor
correlations*. Factor loadings
indicate the degree of relationship between a latent factor and an
observed variable, while factor correlations represent the
relationships between the hypothesized latent factors. An observed
variable that is a good indicator of a latent factor is said to ``load
highly'' on that factor. For example, in intelligence research, where
factor theory has its origins (Spearman, 1904), it may be noted that a
vocabulary test loads highly on a hypothesized (latent) verbal ability
factor, but loads to a much lesser extent on a latent spatial ability
factor; i.e., the vocabulary test relates strongly to verbal ability,
but less so to spatial ability. Normally a factor loading is
identical to a path coefficient of the type described in
Chapter 5.
In this section we describe factor analytic models and present some
illustrative applications to observed measurements without reference
to genetic and environmental causality. We turn to genetic factor
models in Section 10.3.

**Subsections**

** Next:** 1 Exploratory and Confirmatory
** Up:** 10 Multivariate Analysis
** Previous:** 1 Introduction
** Index**
Jeff Lessem
2002-03-21