Midpoint Sequences, Intransitive J Scales and Scale Values in Unidimensional Unfolding
Using combinatorial techniques, a number of procedures has been developed to find the best qualitative and quantitative J scales in unidimensional unfolding. On the basis of these procedures a computer program, UNFOLD, has been written. The criterion for a ‘best’ J scale is derived from nonparametric statistics: the minimization of the total number of inversions between the J scale and subjects’ rankings. In defining a quantitative J scale as a ’midpoint sequence’ some useful results are attained: 1) a transitivity check of a quantitative J scale can be done on the basis of the midpoint sequence; 2) scale values for individuals and stimuli can be found using the midpoint sequence and linear programming techniques. The procedures are illustrated on the Coombs’ (1964) Grade Expectations data.
Keywordsunidimensional unfolding combinatorics backtracking branch-and-bound-methods linear programming
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