Factor Analysis

by G. David Garson

FACTOR ANALYSIS Factor analysis is used to uncover the latent structure (dimensions) of a set of variables. It reduces attribute space from a larger number of variables to a smaller number of factors and as such is a "non-dependent" procedure (that is, it does not assume a dependent variable is specified). Illustrated with numerous how-to figures, output tables, and examples for SPSS, SAS, and Stata. New in the 2013 50% additional coverage; now covers categorical (nonlinear) categorical principal components analysis as well as principal components and principal factor analysis for continuous variables; thorough restructuring for better readability; new coverage for Stata as well as SPSS and SAS; coverage of factor loading plots; expanded discussion of rotation methods; hyperlinking of FAQs to key words in text; numerous other updates. FACTOR ANALYSISTable of Contents Overview8Data10Key Concepts and Terms10Exploratory factor analysis (EFA)10Exploratory vs. confirmatory factor analysis (CFA)10Factor Analytic Data Modes11R-mode factor analysis11Q-mode factor analysis11Other rarer modes of factor analysis12Types of factor extraction13Principal components analysis (PCA)13Principal factor analysis (PFA)14PCA and PFA compared14Other Extraction Methods16Types of factor rotation17Rotation methods17No rotation18Varimax rotation19Quartimax rotation20Equamax rotation21Direct oblimin (oblique) rotation22Promax rotation23Other rotation methods24Summary24Factor analysis in SPSS24Data setup24The "Factor" dialog24Descriptives and Options25Extraction26Rotation27Factor Scores28Statistical output in SPSS29Factor loadings29Plot of factor loadings (factor space plot)31Factor, component, pattern, and structure matrices33Communality34Uniqueness36Eigenvalues36Extraction sums of squared loadings37Trace37Factor scores38Bartlett scores39Saving factor scores40Criteria for number of factors to model40Parallel analysis42Other Criteria43Using reproduced correlation residuals to validate the choice of number of factors43Summary44Factor analysis in SAS44SAS interface44SAS syntax45Rotation methods in SAS47Statistical output in SAS48Factor loadings in SAS output48SAS output for communalities48SAS output for eigenvalues48SAS scree plot output49SAS factor loadings plots51Factor analysis in Stata52Stata interface52Importing data into Stata53Stata syntax55Statistical output in Stata58Stata output for eigenvalues58Factor loadings in Stata output59Stata output for communalities59Stata scree plot output59Stata loading plots60Categorical principal components analysis (CATPCA)62Overview62SPSS categorical principal components analysis63Data considerations63CATPCA user interface in SPSS63The “Optimal Scaling” dialog63The main CATPCA dialog64The “Discretize” button dialog66The “Missing” button dialog67The “Options” button dialog68The “Output” button dialog70The “Save” button dialog72The “Object” button dialog72The “Category” button dialog73The “Loading” bu

142 pages, Kindle Edition

First published January 19, 2013