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Factor Analysis

Statistical Theory and Methods

  1. Jan Graffelman

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vaf001.pub2

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Graffelman, J. 2013. Factor Analysis . Encyclopedia of Environmetrics. 2.

Author Information

  1. Universitat Politécnica de Catalunya, Barcelona, Spain

Publication History

  1. Published Online: 15 JAN 2013


Factor analysis is a multivariate statistical method for data reduction that originated in psychometrics and has found applications in many branches of science. The method aims to describe the correlation structure between a large set of observed variables in terms of a few underlying latent variables called factors. Factor analysis employs a specific model, where observed variables are modelled as linear combinations of common factors plus a specific error term. This model can be estimated by using principal components, by using the iterative principal factor method, or by maximum likelihood. After estimation, factors may be rotated in order to improve their interpretation. An example of the application of factor analysis to a set of pollutants in an environmental monitoring study is discussed.


  • latent variable;
  • factor loading;
  • communality;
  • specificity;
  • factor rotation;
  • principal component;
  • mamaximum likelihood;
  • structural equation model