Factor analysis

A family of statistical methods for identifying the underlying latent factors that explain correlations among observed items.

Factor analysis is a family of statistical methods used to identify the underlying ("latent") factors that explain patterns of correlations among observed variables. In assessment, it's used to discover how many distinct constructs an item set is really measuring — and which items belong to each one.

Exploratory factor analysis (EFA) is used when researchers don't have a strong prior structure in mind: the method finds the factors that best account for the correlations. Confirmatory factor analysis (CFA) tests a specific predicted structure: "Do these 12 items form three subscales as theorized?" CFA model fit indices are standard fare in modern assessment validation papers.

Subscale — A group of items within a larger assessment that measures one specific facet of the overall construct.
Construct validity — Evidence that an assessment actually measures the abstract concept (construct) it claims to measure.
Item response theory (IRT) — A modern measurement framework that models how a person's trait level relates to their probability of each item response.
Measurement invariance — Evidence that an assessment measures the same construct in the same way across groups, so scores can be fairly compared.

Factor analysis

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