Factor analysis

Factor analysis is a family of statistical methods for explaining correlations among observed variables with a smaller set of unobserved dimensions, or factors. It can make a large data set more interpretable, but only when the variables, sample and model are suitable.

When to use it

Use factor analysis when many measured variables may reflect a smaller number of underlying constructs. It is especially useful when developing a questionnaire, validating a scale or simplifying a set of correlated attributes.

For example, customer-research data may contain many ratings about a product. Factor analysis can test whether groups of ratings move together in ways consistent with broader dimensions such as convenience, perceived quality or value.

The method helps answer questions such as:

• Which measured attributes cluster together?
• What latent dimensions may organise customer attitudes?
• Can a long instrument be reduced without discarding essential information?
• Are proposed measures of loyalty, engagement or turnover-related attitudes empirically distinct?

It reveals covariance structure; it does not, by itself, identify causal relationships.

Origins

Factor analysis began in psychometrics. Charles Spearman’s early twentieth-century work examined correlations among test scores and proposed a common latent ability. Later researchers, notably L. L. Thurstone, developed methods for multiple factors and rotation. The approach subsequently spread into behavioural and social science, marketing, product research and operations. Its central idea is that several observed variables may display similar response patterns because they relate to an underlying construct that is not measured directly.