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Übersicht

The Vectors of Mind is an exposition of Thurstone's method for multiple factor analysis, first presented in a paper of that name in 1931. Thurstone's presentation in the book relies heavily upon matrix algebra, mathematical methods that were not widely known by either psychologists or statisticians of that era, and the book provides an introduction to those methods. He presented a paper of the same name in 1933 that introduced several new concepts of factor analysis, including communalities, factor loadings, and matrix rank. This book, published in 1935, then introduced several other of Thurstone's factor analysis concepts, including uniqueness, rotation, oblique factors, and simple structure. It also provided a definition of test reliability in terms of factor loadings. It is a technical book that provides full mathematical details, along with worked examples.

Historical Context

In 1904 Charles Spearman published a paper that largely founded the field of psychometrics and included an early and relatively crude form of factor analysis that attempted to determine if a single factor model was appropriate. There was little subsequent work on factor analysis until Thurstone published a paper in 1931 called Multiple Factor Analysis, which expanded Spearman's single-factor analysis to include more than one factor. In 1932, Hotelling presented a more accurate method of extracting factors, now called principal components analysis. Thurstone rejected Hotelling's approach because it set the commonalities to 1.0, which Thurstone realized introduced distortions to the results. Hotelling's method was also limited by the fact that it required too much calculation to be useable with more than about ten variables until electronic computers became available in the 1950's. A year after Hotelling's paper, Thurstone presented a more efficient way of extracting factors, called the centroid method, which allowed the factor analysis of a far larger number of variables. Later that year he gave his presidential address to the American Psychological Association wherein he presented the results of several factor analyses, including a factor analysis of 60 adjectives describing personality traits, showing how they could be reduced to five personality traits. He also presented analyses of 37 mental health symptoms, of attitudes towards 12 controversial social issues, and of 9 IQ tests. In those analyses, Thurstone had made use of tetrachoric correlation coefficients, a mathematically sophisticated method that requires arduous calculations. In 1933, and two colleagues at the University of Chicago published a set of computing diagrams that great reduce the calculations needed for those coefficients. His 1933 presidential address was published in early 1934 with the title Vectors of the Mind. It lacked methodological and mathematical details, which is the subject of the 1935 book of the same name. The book and the preceding articles had a large influence of the methods of psychological study, and on psychometrics in particular. A 2004 conference called "Factor Analysis at 100" produced two papers that examined Thurstone's role in the development of factor analysis. Factor analysis remains an important method in psychological research, and has since been used in other fields of study. It is now considered part of a family of methods for analyzing the covariance structure of variables, which includes principal components analysis, exploratory factor analysis, confirmatory factor analysis, and structural equations modeling.