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Übersicht

The Vectors of Mind is an exposition of Thurstone's method for multiple factor analysis, which was first presented in a paper in 1931 but further developed before the complete method was presented in this book. It relies heavily upon matrix algebra and gives a technical presentation of mathematical methods and worked examples. His paper of the same name, published a year before the book, had introduced several fundamental concepts of factor analysis, including communality, factor loadings, and matrix rank. The book introduced concepts of uniqueness, rotation, oblique factors, and simple structure. It also defined test reliability in terms of factor loadings. Fast electronic computers were not even imagined in 1935, and Thurstone's presents the centroid method of factor extraction which requires calculations that, while arduous, can be completed by hand. All the methods necessary to conduct a factor analysis with multiple factors, including both orthogonal and oblique rotation.

Synopsis

Preface. Thurstone explains that this is an extended and more formal presentation of his Multiple Factor Analysis paper of 1931, and gives an overview of the book's chapters. He notes that he only recently learned of matrix theory and presumes that other psychologists had similar limitations to their training. He therefore finds it imperative to present matrix theory, particularly as existing textbooks on the topic are inadequate. He wrote the introduction for those who have had a conventional undergraduate instruction in analytic geometry and the calculus, for real numbers only. He is indebted to various professors in the mathematics department of the University of Chicago for helping him to develop his ideas about factor analysis. He voices appreciation to his computer, Miss Leone Chesire, who also edited his manuscripts and wrote the appendix on the calculation of the centroid method. He foresees a bright future for factor analysis, imagining that the computational methods will be further simplified. He views factor analysis as an important technique for the early stages of science and speculates that the laws of classical mechanics might have been revealed by a factor analysis, if they were not already known, by analyzing a great many attributes of objects that are dropped or thrown from an elevated point, with the time of fall factor uncorrelated with the weight factor. He cites some related work by Sewell Wright on path coefficients and Truman L. Kelley on multiple factors, but notes those approaches are quite different from his own approach. He sees his work as an extension of professor Spearman's work, and in no way in conflict with that.

Mathematical Introduction In a 43 page introduction, Thurstone gives a brief presentations of matrices, determinants, matrix multiplication, diagonal matrices, the inverse, the characteristic equation, summation notation, linear dependence, geometric interpretations, orthogonal transformations, and oblique transformations.

Chapter I. The Factor Problem. Thurstone begins with comments on the nature of science, arguing that natural phenomena are only comprehensible through constructs that are man-made inventions. A scientific law is not part of nature; it is but man's way of understanding nature. Examples are provided of such man-made constructs from physics. He responds to skepticism from the practitioners of "rigorous science" that human behavior can ever be brought into the fold of such rigorous science by pointing out that there is considerable individuality in physical events that are described by scientific laws, such as the fact that every explosion is unique, even though governed by rigorous scientific laws. Human abilities are the cause of individual differences in the "completion of a task". The science of psychology will succeed in reducing a large number of psychological abilities down to primary reference traits. Formal definitions of some terms relevant to a psychological study of traits are provided: trait, ability, test, score, linear independence, statistical independence, experimental independence, reference abilities, primary abilities, and unitary ability. These conceptions constitute a theory of measurement.

Historical Context

In 1904 Charles Spearman published a paper that largely founded the field of psychometrics and included a crude form of factor analysis that attempted to determine if a single factor model was appropriate. There was limited 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, which he called principal components analysis. Thurstone rejected Hotelling's approach because it set the commonalities to 1.0, and Thurstone realized that will introduce distortions to the factor loadings when variables include unique components. Hotelling's method was also limited by the fact that it required too much calculation to be useable with more than about ten variables. 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 method for estimating continuous variable correlations with dichotomous variables. Tetrachorics require extensive calculations but in early 1933, he and two colleagues at the University of Chicago published a set of computing diagrams that greatly 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 of his technique, which is then the subject of this book. A 2004 conference called Factor Analysis at 100 produced a book with two chapters that document the historical importance Thurstone's contributions to factor analysis. Thurstone's approach to factor analysis remains an important method in psychological research and it has since been used in numerous 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 equation modeling.