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Unformatted text preview: Factor Analysis Jaime Frade December 5, 2007 Part I 9.4: Factor Rotation 1 Review: 1.1 Covariance Structure for the Orthogonal Factor Model 1. Cov( X ) = LL t + Var( X i ) = l 2 i 1 + + l 2 im + (1) Cov( X i ) = l i 1 l k 1 + + l im l km + 2. Cov( X , F ) = L or Cov( X i , F i ) = l ij It has been shown (98) pg 487 , that all factor loadings obtained from the initial loadings by an orthogonal transformation have the same ability to reproduce the covariance (or correlation) matrix. An orthogonal transformation is a rotation or reflection of the coordinate axis. Factor analysis is a generic term for a family of statistical techniques concerned with the reduction of a set of observable variables in terms of a small number of latent factors. It has been developed primarily for analyzing relationships among a number of measurable entities (such as survey items or test scores). The underlying assumption of factor analysis is that there exists a number of unobserved latent variables (or factors) that account for the correlations among observed variables, such that if the latent variables are partialled out or held constant, the partial correlations among observed variables all become zero. In other words, the latent factors determine the values of the observed variables. The primary purpose of factor analysis is data reduction and summarization 2 Definition: Factor Rotation: An orthogonal transformation of the factor loadings , as well as the implied orthogonal transformation of the factors . Let T m m be an orthogonal matrix, ( TT t = T t T = I m m ). If b L is the p m matrix of estimated factor loading obtained by any method (PCP, ML, etc.) then b L * = b LT, where TT t = T t T = I (2) is the p m matrix of rotated loadings. b L * is an orthogonal transformation of the factor loading matrix. The estimated covariance (or correlation) matrix remains unchanged. b L b L t + b = b LTT t b L t + b = b L * ( b L * ) t + b (3) indicates that the residual matrix remains unchanged....
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This note was uploaded on 12/16/2011 for the course STAT 5705 taught by Professor Staff during the Fall '09 term at FSU.
 Fall '09
 staff
 Covariance, Variance

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