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Multiple-factor analysis : its purpose and meaning

University of British Columbia

The purpose of the present study was that of presenting the fundamental theorems and techniques of Thurstone's Multiple-Factor Analysis in a manner that would be understandable to the non-mathematically trained student of psychology. The work was introduced by a discussion of Spearman's "Theory of Two Factors" which is so-called since the method analyses each test into a general factor "g" and a specific factor. It was found that such a factorization could be performed if the correlation matrix exhibited hierarchical order. The tetrad difference equation and a standard error formula were next discussed as tests of this order. Finally, mention was made of a few of the problems which investigators have attempted to solve by means of the method. Upon turning attention to the multiple-factor theory, an initial chapter was devoted to the presentation of the relationship between such theory and scientific method in general. This facilitated a discussion of some of the major limitations and values of the technique. It was found that the methods could best be designated as classificatory. Furthermore, it was discovered that factor analysis was not only applicable to a diversity of problems in psychology but also to those of other sciences. Following this more general discussion, consideration was given to the derivation of the fundamental equations. It was proven that if the original scores are converted to standard form the sum of the squares of the factor loadings for any test is equal to unity. It was also shown that each factor loading for statistically independent factors is the square root of the variance that is attributable to that factor. The fundamental theorem of factor analysis, which proves that any reduced correlation matrix can be factorized, was then discussed since it is basic to the entire theory. The centroid method of factoring a reduced correlation matrix was next developed. A method was thus obtained by which the correlation matrix could be analysed into a common factor matrix. However, since Thurstone does not consider these to be psychologically meaningful factors it was found that a rotation of reference frame must then be carried out. Consideration was given to the problem of rotating axes and a method examined which enables one to rotate axes in a two-dimensional plot. This method was found to be such that it could be generalized to an r dimensional factor pattern. It had the advantage of furnishing a graphic record of the relationships among the tests. However, it had a disadvantage in that many diagrams must be plotted if the number of dimensions is large. Upon examining the problem of attaching psychological meaning to the factors, it was noted that subjectivity must play a large part and so no rote rules could be furnished as a solution to this problem. For this reason several examples of interpretations were presented in order to enable the reader to obtain a clearer insight into the logical steps employed. Finally, the limitations of this study were considered and a brief discussion of the possible future development of factor analysis was presented.

Text

2012-03-14

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http://hdl.handle.net/2429/41414

Psychology

University of British Columbia

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