Factor analysis is a method of the family of multivariate statistics, which is designed to describe variability among observed variables by means of latent variables (unobserved). To reduce the number of variables, the method calculates these latent variables as linear combinations of the observed variables. Created by Charles Spearman, this method is used in psychology, social sciences, and more generally in any discipline facing large amounts of data.
Factor analysis often gives similar results to the Principal Component Analysis (PCA). However, both methods are formally different (the variance-covariance matrices analyzed are different). There is a debate about the advantages and disadvantages of both methods.
It should also not be confused with the correspondence analysis (AFC). This method developed by Jean-Paul Benzecri also aims to analyze large arrays of homogeneous data. For this it uses the chi-square metric: each row of a table is affected by a mass, which is the sum marginal. The table studied is the table of the table rows profile, which can be represented in the same space at the same time the two clouds of points associated with the rows and columns of the data table.
Confirmatory factor analysis can be considered somehow a step that follows an exploratory factor analysis. It aims, as its name says, to confirm the model under consideration. This is a special case of structural equation modeling.
Factor analysis, which originated in psychometrics, is now widely used not only in psychology, neuroscience, sociology, political science, in economics, statistics, and other sciences. The basic idea of factor analysis were laid English psychologist and anthropologist, the founder of eugenics F. Galton (1822-1911), who made a great contribution to the study of individual differences. However, Galton was not the only scientist, who has greatly contributed to the development of factor analysis – many others followed him. The development and implementation of factor analysis in psychology involved such scholars as Charles Spearman (1904, 1927, 1946), L. Thurstone (1935, 1947, 1951) and R. Cattell (1946, 1947, 1951). It is also impossible not to mention the English mathematician and philosopher K. Pearson, who largely developed the ideas of F. Galton. As well as an American mathematician H. Hotelling, who developed a modern version of the principal component. Noteworthy is the English psychologist G. Eysenck, who used widely used factor analysis to develop a psychological theory of personality. Mathematically, factor analysis was developed Hotelling Harman Kaiser, Thurstone, Tucker, etc. Today, the factor analysis is included in all packages of statistical data – R, SAS, SPSS, Statistica, etc.
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