Extracting Factors: The Algebraic Picture

Abstract

Typically, the factor analyst takes a careful choice of variables in the area of behavior in which he is out to test a theory or to explore structure, e.g., primary ability variables; marker variables for a supposed extravert temperament; measures which psychologists have thought to be indicators of strength of motivation; or representatives of an hypothesized learning gain pattern. As he looks at the square matrix of all correlations among, say, thirty such variables, he wants to know how many distinct independent influences—presumably decidedly fewer than thirty—can be considered responsible for the observed covariations in this domain of behavior.