Factor Analysis attempts to identify underlying variables, or factors, that explain the pattern of correlations within a set of observed variables. Factor analysis can be used in data compression to identify a small number of latent variables that explain most of the variance observed in a much larger number of manifest variables. Factor analysis is a linear modeling framework: any observed variable is a linear combination of the hidden factors.
Factor analysis has the same goals as principal component analysis (PCA). The latter is often viewed as part of the former. However, in its narrow sense, factor analysis is somewhat different from PCA. PCA attempts to explain the variables with factors in a completely non-parametric fashion. No assumptions about the structure of random errors are made before the analysis (except for them being uncorrelated). Before the analysis, we express no opinion regarding how the variance of the random error of one observed variable relates to that of another observed variable. On the other hand, factor analysis makes these assumptions. As the result, it leads to solving a slightly different linear algebra problem compared to PCA. In practice, the insights from PCA and factor analysis can be very close.
FACTOR ANALYSIS REFERENCES
Bartholomew, D. J., Steele, F., Galbraith, J., & Moustaki, I. (2008). Analysis of Multivariate Social Science Data (2 ed.). New York: Chapman & Hall / Crc.
Child, Dennis (1973). The Essentials of Factor Analysis. London: Holt, Rinehart & Winston.
Thompson, B. (2004). Exploratory and confirmatory factor analysis: Understanding concepts and applications. Washington, DC: American Psychological Association.
Gorsuch, R. L. (1974). Factor analysis. Toronto: W.B. Saunders.
Bartholomew, D.J. (1987). Latent variable models and factor analysis. London: Charles Griffin.
Jackson, J. E. (1991). A user's guide to principal components. New York: Wiley.
Kline, P. (1994). An Easy Guide to Factor Analysis. New York: Routledge.
Harmon, H. H. (1967). Modern factor analysis. (2nd ed.). Chicago: University of Chicago Press.
Thurstone, L. L. (1947). Multiple factor analysis. Chicago: University of Chicago Press.
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