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Factor analysis
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===Differences in procedure and results=== The differences between PCA and factor analysis (FA) are further illustrated by Suhr (2009):<ref name=Suhr /> * PCA results in principal components that account for a maximal amount of variance for observed variables; FA accounts for ''common'' variance in the data. * PCA inserts ones on the diagonals of the correlation matrix; FA adjusts the diagonals of the correlation matrix with the unique factors. * PCA minimizes the sum of squared perpendicular distance to the component axis; FA estimates factors that influence responses on observed variables. * The component scores in PCA represent a linear combination of the observed variables weighted by [[Eigenvalues and eigenvectors|eigenvectors]]; the observed variables in FA are linear combinations of the underlying and unique factors. * In PCA, the components yielded are uninterpretable, i.e. they do not represent underlying ‘constructs’; in FA, the underlying constructs can be labelled and readily interpreted, given an accurate model specification.
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