Midpoint Sequences, Intransitive J Scales and Scale Values in Unidimensional Unfolding

  • Rian A. W. van Blokland-Vogelesang
Part of the Recent Research in Psychology book series (PSYCHOLOGY)


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.


unidimensional unfolding combinatorics backtracking branch-and-bound-methods linear programming 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Rian A. W. van Blokland-Vogelesang
    • 1
  1. 1.Department of PsychologyFree UniversityAmsterdamThe Netherlands

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