To What Extent Can Communalities Reduce Rank?  

Oleh:

Guttman, Louis

Jenis: Article from Journal - e-Journal
Dalam koleksi: Psychometrika: A Journal of Quantitative Psychology vol. 23 no. 4 (Dec. 1958), page 297-308.
Topik: Mental Test Data; Best Possible General Upper Bound: n --1; Relatice Algebraic Incidence; Psychological Considerations; Simplex As a Counter Example; Further Structural Psychological Possibilities
Fulltext: Vol 23 No. 4 Dec 1958 p.297-308.pdf (703.11KB)

Isi artikel

The question is raised as to whether the null hypothesis concerning the number of common factors underlying a given set of correlations should be that this number is small. Psychological and algebraic evidence indicate that a more appropriate null hypothesis is that the number is relatively large, and that smallness should be but an alternative hypothesis. The question is also raised as to why approximation procedures should be aimed primarily at the observed correlation matrixR and not at, say,R -1. What may be best forR may be worst forR -1, and conversely, yetR -1 is directly involved in problems of multiple and partial regressions. It is shown that a widely accepted inequality for the possible rank to whichR can be reduced, when modified by communalities, is indeed false.

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