Summary
This paper illustrates uses of vectors and matrices in psychometric problems with special emphasis on generalized inverse and projection matrices. As examples of recommended uses of vectors, the idea of covariance ratio is first introduced, which is useful in determining the weights for high school subjects taken at the university entrance examinations. Secondly, results on the range of a correlation coefficient are summarized and generalized by extensive uses of generalized inverse and projection matrices. Thirdly, previous results showing that multiple correlation and canonical correlations can be computed from a singular correlation matrix, are explained and by extending these results, some new results are introduced, and the relationships on multiple, canonical and partial canonical correlations among some sets of residual variables are discussed. Our emphasis given in this paper is that uses of vectors and matrices allow one to understand the complex problems in psychometrics quite easily without making use of complicated algebra.
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Yanai, H. (2003). Vectors and Matrices in Psychometrics with Special Emphasis on Generalized Inverse and Projection Matrices. In: Yanai, H., Okada, A., Shigemasu, K., Kano, Y., Meulman, J.J. (eds) New Developments in Psychometrics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-66996-8_2
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DOI: https://doi.org/10.1007/978-4-431-66996-8_2
Publisher Name: Springer, Tokyo
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