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# Factor Analysis

Factor Analysis (.pdf)

Factor analysis is a statistical technique, the aim of which is to simplify a complex data set by representing the set of variables in terms of a smaller number of underlying (hypothetical or unobservable) variables, known as factors or latent variables. The origins of factor analysis can be traced back to Pearson (1901) and Spearman (1904), the term was first introduced by Thurstone (1931) and a good text on the subject is Gorsuch (1983). The technique is a branch of multivariate analysis and may also be descibed as unsupervised learning and an excerise in modelling. The observed variables are modelled as linear combinations of the factors, plus “error” terms.

Steps in performing factor analysis:

1. Collect data.
2. Generate a variance-covariance matrix of the observed variables.
3. Select the number of factors.
4. Extract your initial set of factors.
5. Perform factor rotation to a terminal solution.
6. Interpret the factor structure.
7. Construct factor scores to use in further analyses.

The methodology relies on the (often unjustified) assumption that n factors exist.