The algorithm for determining differences in cognitive abilities and personality characteristics between track and field athletes and basketball players

Veroljub Stanković, Evagelia Boli, Dragan Popovic, Nicolae Ochiana, Milos Popovic, Vladimir Savic, Jasna Popovic

Abstract


The resulting solution is very easy to convert into a form obtained under the canonical model of discriminant analysis. The matrix of discriminant coefficients can be defined as a matrix of partial regression coefficients that is obtained by solving the problem ZW = K + E | trag(EtE) = minimum. As K = ZR-1/2X, it is clear that E = 0 and W = R-1/2X. Therefore, vectors wk from W are proportional to the coordinates of the vectors of discriminant functions in the tilted coordinate system formed by vectors from Z with cosines of the angles between the coordinate axes equal to the elements of correlation matrix R. Since discriminant analysis can also be interpreted as a special case of component analysis with principal components transformed by a permissive singular transformation so as to maximize distances between centroids of subsets Ep , or canonical correlations ρk (Cooley & Lohnes, 1971), the custom is to identify the content of discriminant functions on the basis of structural vectors fk from the matrix F = ZtK = RW = R1/2X = (fk) = (Rwk), which is analogous to the identification of the content of canonical variables obtained by Hotelling`s method of biorthogonal canonical correlation analysis because it is possible to show by easy calculation that F is a factor matrix of matrix R In this metric, the cross structure of discriminant functions will be U = Zt-1 = ZtPZWρ-1 = as, of course, WtZtPZW = ρ2, and it is clear that U is a factor matrix of the matrix ZtPZ, or intergroup covariance matrix defined in the space with standard metric.

Keywords: /canonical/discriminant analysis/coefficients /model/regression


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References


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