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## Factor Analysis

With principal components analysis we were fundamentally interested in the variables and their contributions. Factor analysis aims to provide usable numerical values for quantities such as intelligence or social status that are not directly measurable. The idea is to use correlations between observable variables in terms of underlying ‘factors'. Note that ‘factors' in factor analysis are not the same as the categorical explanatory variables we have been calling factors throughout the rest of this book.

Compared with PCA, the variables themselves are of relatively little interest in factor analysis; it is an understanding of the hypothesized underlying factors that is the main aim. The idea is that the correlations amongst the variables are explained by the common factors. The function factanal performs maximum likelihood factor analysis on a covariance matrix or data matrix. The pgd dataframe is introduced on p. 732. You need to specify the number of factors you want to estimate – we begin with 8:

`factanal(pgd, 8) Call: factanal(x = pgd, factors = 8) Uniquenesses: AC AE AM AO AP AR AS AU BH BM 0.638 0.086 0.641 0.796 0.197 0.938 0.374 0.005 0.852 0.266 CC CF CM CN CX CY DC DG ER FM 0.056 0.574 0.786 0.579 0.549 0.733 0.837 0.408 0.072 0.956 FP FR GV HI HL HP HS HR KA LA 0.371 0.815 0.971 0.827 0.921 0.218 0.332 0.915 0.319 0.305 LC LH LM LO LP OR PL PP PS PT 0.349 0.333 0.927 0.121 0.403 0.005 0.286 0.606 0.336 0.401 QR RA RB RC SG SM SO TF TG TO 0.913 0.491 0.005 ...`

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