Fixing the Number of Factors: The Scientific Model

Abstract

Before proceeding to the art of rotation, which gives the unique resolution ultimately needed as the solution to a factorial investigation, we need to return to base and tidy up some by-passed technical details of the factor extraction process itself. One may hope that the reader has, through the combined algebraic and geometrical approaches, got the conception of a factor as a common source and direction of variance contributing to the observed covariation of several psychological measures. He has, further, become acquainted with the computational process of extracting a series of successively smaller factor variances from the R matrix. The general outline has thus been given for the extraction process but there still remains thorny practical technique details about how we decide the number of factors, how we guess (or, to use a better term “estimate”) the communalities, like those inserted in Table 2.1 and how we finally get to the most accurate form of the unrotated factor matrix. Also we need to note the slight distinctions between the factors from weighted and unweighted summation methods.