Some new results on correlation-preserving factor scores prediction methods

Jos M.F. ten Berge, Wim P. Krijnen, Tom Wansbeek, Alexander Shapiro

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Anderson and Rubin and McDonald have proposed a correlation-preserving method of factor scores prediction which minimizes the trace of a residual covariance matrix for variables. Green has proposed a correlation-preserving method which minimizes the trace of a residual covariance matrix for factors. Krijnen, Wansbeek and Ten Berge have proposed minimizing the determinant rather than the trace of the latter covariance matrix, and offered an iterative procedure to that effect. In the present paper it is shown that the iterative procedure can be replaced by a closed-form solution. When all unique variances are strictly positive, this solution is the same as McDonald's. The solution coincides with Green's solution in certain special cases, for instance, when the factors are orthogonal.
Original languageEnglish
Pages (from-to)311-318
JournalLinear algebra and its applications
Volume289
Issue number1-3
DOIs
Publication statusPublished - 1999

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