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

Joseph F. Bennett

doi:10.1007/bf02296304

journal article Dec 01, 1956

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

Joseph F. Bennett

Psychometrika Vol. 21 No. 4 pp. 383-393 · Cambridge University Press (CUP)

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Abstract

Two ordinal consequences are drawn from the linear multiple-factor analysis model. First, the number R(s, d) of distinct ways in which s subjects can be ranked by linear functions of d factors is limited by the recursive expression R(s, d) = R(s−, d)+(s−1) R(s−, d−1). Second, every set S of d+2 subjects can be separated into two subsets S* and S − S* such that no linear function of d variables can rank all S* over all S − 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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References

3

[1]

1. Bennett, J. F. A method for determing the dimensionality of a set of rank orders. Unpublished Ph.D. dissertation, University of Michigan, 1951.

[2]

Psychological scaling without a unit of measurement.

Clyde H. Coombs

Psychological Review 10.1037/h0060984

[3]

Thurstone (1947)

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References

Details

Published: Dec 01, 1956
Vol/Issue: 21(4)
Pages: 383-393
License: View

Authors

J

Joseph F. Bennett

Lincoln Laboratories, Massachusetts Institute of Technology

Cite This Article

Joseph F. Bennett (1956). Determination of the Number of Independent Parameters of a Score Matrix from the Examination of Rank Orders. Psychometrika, 21(4), 383-393. https://doi.org/10.1007/bf02296304

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

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