Factor analysis

Christopher Chatfield and Alexander J. Collins
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Christopher Chatfield: Bath University, School of Mathematics
Alexander J. Collins: Bath University, School of Mathematics

Chapter Chapter Five in Introduction to Multivariate Analysis, 1980, pp 82-89 from Springer

Abstract: Abstract Factor analysis (abbreviated to FA) has somewhat similar aims to principal component analysis (PCA) in that it is a variable-directed technique which is appropriate when the variables arise ‘on an equal footing’. The idea is to derive new variables called factors which will hopefully give us a better understanding of the data. But whereas PCA produces an orthogonal transformation of the variables which depends on no underlying model, FA is based on a proper statistical model and is more concerned with explaining the covariance structure of the variables than with explaining the variances. Any variance which is unexplained by the common factors can be described by residual ‘error’ terms. Despite several basic differences, it is an unfortunate fact that FA and PCA are often confused by non-statisticians.

Keywords: Principal Component Analysis; Factor Loading; Common Factor; Multivariate Normal Distribution; Sample Covariance Matrix (search for similar items in EconPapers)
Date: 1980
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DOI: 10.1007/978-1-4899-3184-9_5

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