Determination of the Number of Independent Parameters of a Score Matrix from the Examination of Rank Orders  

Oleh:

Bennett, Joseph F.

Jenis: Article from Journal - e-Journal
Dalam koleksi: Psychometrika: A Journal of Quantitative Psychology vol. 21 no. 4 (Dec. 1956), page 383-393.
Topik: Number of Linear Rankings; Algebraic Properties of the Permissible Rankings; Box Problem
Fulltext: Vol 21 No.4 Des 1956 p.383-393.pdf (482.9KB)

Isi artikel

Two ordinal consequences are drawn from the linear multiple-factor analysis model. First, the numberR(s, d) of distinct ways in whichs subjects can be ranked by linear functions ofd factors is limited by the recursive expressionR(s, d)=R(s-1,d)+(s-1)R(s-1,d-1). Second, every setS ofd+2 subjects can be separated into two subsetsS* andS - S* such that no linear function ofd variables can rank allS* over allS - S*, and vice versa. When these results are applied to the hypothetical data of Thurstone's “box problem,” three independent parameters are found. Relations to Thurstone's suggestion for a non-correlational factor analysis are discussed.

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