What is the purpose of FATOR ROTATION in factor analysis?

Question

What is the purpose of FATOR ROTATION in factor analysis?

Answer 1

Principal Components Analysis - SPSS

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In principal components analysis (PCA) and factor analysis (FA) one wishes to extract from a set of p variables a reduced set of m components or factors that accounts for most of the variance in the p variables.  In other words, we wish to reduce a set of p variables to a set of m underlying superordinate dimensions.

Goals of PCA and FA

One may do a PCA or FA simply to reduce a set of p variables to m components or factors prior to further analyses on those m factors.  For example, Ossenkopp and Mazmanian (Physiology and Behavior, 34:  935-941) had 19 behavioral and physiological variables from which they wished to predict a single criterion variable, physiological response to four hours of cold-restraint. They first subjected the 19 predictor variables to a FA.  They extracted five factors, which were labeled Exploration, General Activity, Metabolic Rate, Behavioral Reactivity, and Autonomic Reactivity.  They then computed for each subject scores on each of the five factors.  That is, each subject’s set of scores on 19 variables was reduced to a set of scores on 5 factors.  These five factors were then used as predictors (of the single criterion) in a stepwise multiple regression.

One may use FA to discover and summarize the pattern of intercorrelations among variables.  This is often called Exploratory FA.  One simply wishes to group together (into factors) variables that are highly correlated with one another, presumably because they all are influenced by the same underlying dimension (factor).  One may also then operationalize (invent a way to measure) the underlying dimension by a linear combination of the variables that contributed most heavily to the factor.

If one has a theory regarding what basic dimensions underlie an observed event, e may engage in Confirmatory Factor Analysis.  For example, if I believe that performance on standardized tests of academic aptitude represents the joint operation