An Analytical Solution for Approximating Simple Structure in Factor Analysis  

Oleh:

Carroll, John B.

Jenis: Article from Journal - e-Journal
Dalam koleksi: Psychometrika: A Journal of Quantitative Psychology vol. 18 no. 1 (Mar. 1953), page 23-38.
Topik: Analytical Solution; Approximating Simple Structure
Fulltext: Vol 18 No.1 March 1953 p.23-38.pdf (663.52KB)

Isi artikel

It is proposed that a satisfactory criterion for an approximation to simple structure is the minimization of the sums of cross-products (across factors) ofsquares of factor loadings. This criterion is completely analytical and yields a unique solution; it requires no plotting, nor any decisions as to the clustering of variables into subgroups. The equations involved appear to be capable only of iterative solution; for more than three or four factors the computations become extremely laborious but may be feasible for high-speed electronic equipment. Either orthogonal or oblique solutions may be achieved. For illustrations, the Johnson-Reynolds study of “flow” and “selection” factors and the Thurstone box problem are reanalyzed. The presence of factorially complex tests produces a type of hyperplanar fit which the investigator may desire to adjust by graphical rotations; the smaller the number of such tests, the closer the criterion comes to approximating simple structure.

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