Factor analysis

Factor analysis is a statistical model that explains correlations among observed variables through a smaller set of latent factors and variable-specific errors. It estimates which shared dimensions may underlie the measurements.

Common factor model: A latent-variable model that explains covariation among observed variables with shared factors and variable-specific error. It states the core structure factor analysis estimates.
Correlation matrix: A square table containing pairwise correlations among a set of variables. Factor analysis models patterns in the correlations among observed variables.
Principal component analysis: A dimension-reduction method that constructs components as weighted combinations of observed variables. Unlike factor analysis, it represents total observed variance rather than modeling shared variance and errors.
Psychometrics: The field concerned with measuring psychological attributes through tests and statistical models. Factor analysis is widely used to examine psychological scales and tests.
Charles Spearman: An English psychologist who developed early statistical methods for studying general intelligence. His two-factor account helped establish factor analysis as a way to model mental abilities.
Factor loading: A model coefficient describing the relationship between an observed variable and a latent factor. Loadings show which variables define each factor and how strongly.
Latent variable: A variable that is not directly observed but is inferred from measured indicators. Factors are latent variables inferred from shared patterns in measurements.
Confirmatory factor analysis: A factor-analysis approach that tests a prespecified structure of relations between variables and factors. Exploratory analysis searches for structure; confirmatory analysis evaluates a specified one.
Questionnaire: A structured set of questions used to collect respondents’ answers about attributes, experiences, or opinions. Patterns across questionnaire items can reveal shared underlying dimensions.
General intelligence: A proposed broad cognitive ability underlying performance across diverse intellectual tasks. Spearman used factor analysis to argue that test correlations reflected a common ability.

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