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Multidimensional Fechnerian Scaling: Basics.
MedLine Citation:
PMID:  11583528     Owner:  NLM     Status:  Publisher    
Fechnerian scaling is a theory of how a certain (Fechnerian) metric can be computed in a continuous stimulus space of arbitrary dimensionality from the shapes of psychometric (discrimination probability) functions taken in small vicinities of stimuli at which these functions reach their minima. This theory is rigorously derived in this paper from three assumptions about psychometric functions: (1) that they are continuous and have single minima around which they increase in all directions; (2) that any two stimulus differences from these minimum points that correspond to equal rises in discrimination probabilities are comeasurable in the small (i.e., asymptotically proportional), with a continuous coefficient of proportionality; and (3) that oppositely directed stimulus differences from a minimum point that correspond to equal rises in discrimination probabilities are equal in the small. A Fechnerian metric derived from these assumptions is an internal (or generalized Finsler) metric whose indicatrices are asymptotically similar to the horizontal cross-sections of the psychometric functions made just above their minima. Copyright 2001 Academic Press.
Ehtibar N. Dzhafarov; Hans Colonius
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Publication Detail:
Journal Detail:
Title:  Journal of mathematical psychology     Volume:  45     ISSN:  -     ISO Abbreviation:  J Math Psychol     Publication Date:  2001 Oct 
Date Detail:
Created Date:  2001-Oct-3     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  2985082R     Medline TA:  J Math Psychol     Country:  -    
Other Details:
Languages:  ENG     Pagination:  670-719     Citation Subset:  -    
Purdue University
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