A multivariate method in which the basic data consist of the observed values of the p characteristics of each of n individuals. The method, introduced in 1931 by Thurstone, aims to explain the p×p variance–covariance matrix for these data in terms of the relationships between a much smaller number (q) of unobserved variables (latent variables) called factors. The underlying proposition is that the jth observed value, x_j, is the sum of a linear combination of the factors f₁, f₂,…, f_q and an error term, ε_j,:

The multipliers λ_j1, λ_j2,…, λ_jq are called factor loadings.

Unlike principal components analysis, which it resembles, the methodology makes many assumptions (for example, that factors exist and that there are exactly q of them). Its use has therefore attracted considerable criticism. Its popularity might be thought to be based on the ability of the method to produce the result desired by the researcher!