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== Historical Context == |
== Historical Context == |
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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.<ref>{{Cite journal|last=Spearson|first=Charles|date=1904|title=General intelligence objectively determined and measured|url=|journal=American Journal of Psychology|volume=15|pages=201-293|via=}}</ref> There was little subsequent work on factor analysis until Thurstone published a paper in 1931 called ''Multiple Factor Analysis'',<ref name=":0" /> 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.<ref>{{Cite journal|last=Hotelling|first=H.|date=|title=Analysis of a complex of statistical variables into principal components.|url=|journal=Journal of Educational Psychology|volume=24|pages=417-441, 498-520.|via=}}</ref> Thurstone rejected Hotelling's approach because it set the commonalities to 1.0, and Thurstone realized that 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.<ref>{{Cite book|last=Harman|first=Harry|title=Modern Factor Analysis, Third Edition Revised|publisher=The University of Chicago Press|year=1976|isbn=0-226-31652-1|location=Chicago, Illinois|pages=5}}</ref> A year after Hotelling's paper, Thurstone presented a more efficient way of extracting factors, called the centroid method,<ref>{{Cite book|last=Mulaik|first=Stanley|title=Foundations of Factor Analysis, Second Edition|publisher=CRC Press|year=2010|isbn=978-1-4200-9961-4|location=Boca Raton, Florida|pages=147-151}}</ref> 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.<ref name=":1" /> 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.<ref>{{Cite book|last=Chesire|first=Leone|title=Computing Diagrams for the Tetrachoric Correlation Coefficient|last2=Saffir|first2=Milton|last3=Thurstone|first3=L.L.|publisher=The University of Chicago Bookstore|year=1933|isbn=|location=Chicago, Illinois|pages=}}</ref> 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 this book. 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 |
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.<ref>{{Cite journal|last=Spearson|first=Charles|date=1904|title=General intelligence objectively determined and measured|url=|journal=American Journal of Psychology|volume=15|pages=201-293|via=}}</ref> There was little subsequent work on factor analysis until Thurstone published a paper in 1931 called ''Multiple Factor Analysis'',<ref name=":0" /> 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.<ref>{{Cite journal|last=Hotelling|first=H.|date=|title=Analysis of a complex of statistical variables into principal components.|url=|journal=Journal of Educational Psychology|volume=24|pages=417-441, 498-520.|via=}}</ref> Thurstone rejected Hotelling's approach because it set the commonalities to 1.0, and Thurstone realized that 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.<ref>{{Cite book|last=Harman|first=Harry|title=Modern Factor Analysis, Third Edition Revised|publisher=The University of Chicago Press|year=1976|isbn=0-226-31652-1|location=Chicago, Illinois|pages=5}}</ref> A year after Hotelling's paper, Thurstone presented a more efficient way of extracting factors, called the centroid method,<ref>{{Cite book|last=Mulaik|first=Stanley|title=Foundations of Factor Analysis, Second Edition|publisher=CRC Press|year=2010|isbn=978-1-4200-9961-4|location=Boca Raton, Florida|pages=147-151}}</ref> 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.<ref name=":1" /> 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.<ref>{{Cite book|last=Chesire|first=Leone|title=Computing Diagrams for the Tetrachoric Correlation Coefficient|last2=Saffir|first2=Milton|last3=Thurstone|first3=L.L.|publisher=The University of Chicago Bookstore|year=1933|isbn=|location=Chicago, Illinois|pages=}}</ref> 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 this book. 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 a book with two chapters that examined Thurstone's role in the development of factor analysis.<ref name=":2">{{Cite book|last=Bock|first=Darrell|title=Factor Analysis at 100. Historical Developments and Future Directions|publisher=Lawrence Erlbaum Associates|year=2007|isbn=978-0-8058-5347-6|editor-last=Cudeck|editor-first=Robert|location=Mahwah, New Jersey|pages=|chapter=Rethinking Thurstone|editor-last2=MacCallum|editor-first2=Robert C.}}</ref><ref name=":2" />Factor analysis remains an important method in psychological research, and<ref name=":2" /> 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. |
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== See also == |
== See also == |
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Revision as of 22:23, 4 July 2020
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[1] but further developed before a complete method for conducting a multiple factor analysis, complete with rotation, was presented in this book. The book relies heavily upon matrix algebra and the book begins with an introduction to those methods. His paper of the same name, published a year before the book,[2] introduced several fundamental concepts of factor analysis, including communalities, factor loadings, and matrix rank. The book then gave a more complete description of the method and introduced concepts of uniqueness, rotation, oblique factors, and simple structure. It also provided a definition of test reliability in terms of factor loadings. This is a technical book that provides full mathematical details, along with worked examples. Fast electronic computers were not even imagined in 1935, and Thurstone's method used calculations that, while arduous, could be computed by hand. In particular, he developed the centroid method of factor extraction, with which he was able to complete a factor analysis of 60 variables. The book is the reference point for many variations of factor analysis that were developed over the next 50 years.
Synopsis
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.[3] There was little subsequent work on factor analysis until Thurstone published a paper in 1931 called Multiple Factor Analysis,[1] 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.[4] Thurstone rejected Hotelling's approach because it set the commonalities to 1.0, and Thurstone realized that 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.[5] A year after Hotelling's paper, Thurstone presented a more efficient way of extracting factors, called the centroid method,[6] 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.[2] 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.[7] 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 this book. 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 a book with two chapters that examined Thurstone's role in the development of factor analysis.[8][8]Factor analysis remains an important method in psychological research, and[8] 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.
See also
References
- ^ a b Thurstone, Louis (1931). "Multiple factor analysis". Psychological Review. 38: 406–427.
- ^ a b Thurstone, Louis (1934). "The Vectors of Mind". The Psychological Review. 41: 1–32.
- ^ Spearson, Charles (1904). "General intelligence objectively determined and measured". American Journal of Psychology. 15: 201–293.
- ^ Hotelling, H. "Analysis of a complex of statistical variables into principal components". Journal of Educational Psychology. 24: 417–441, 498-520.
- ^ Harman, Harry (1976). Modern Factor Analysis, Third Edition Revised. Chicago, Illinois: The University of Chicago Press. p. 5. ISBN 0-226-31652-1.
- ^ Mulaik, Stanley (2010). Foundations of Factor Analysis, Second Edition. Boca Raton, Florida: CRC Press. pp. 147–151. ISBN 978-1-4200-9961-4.
- ^ Chesire, Leone; Saffir, Milton; Thurstone, L.L. (1933). Computing Diagrams for the Tetrachoric Correlation Coefficient. Chicago, Illinois: The University of Chicago Bookstore.
- ^ a b c Bock, Darrell (2007). "Rethinking Thurstone". In Cudeck, Robert; MacCallum, Robert C. (eds.). Factor Analysis at 100. Historical Developments and Future Directions. Mahwah, New Jersey: Lawrence Erlbaum Associates. ISBN 978-0-8058-5347-6.