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.