Determination of the number of independent parameters of a score matrix from the examination of rank orders |
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Authors: | Joseph F Bennett |
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Institution: | (1) Massachusetts Institute of Technology, USA |
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Abstract: | 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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