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On the functional forms in a psychophysical law of similarity under a subtractive representation

Dr. Christopher Doble
McGraw-Hill Education/ALEKS Corporation
Dr. Yung-Fong Hsu
National Taiwan University ~ Psychology

Writing ξ_{s}(x) for the stimulus intensity judged greater (louder, heavier, brighter) than stimulus intensity x with criterion s, Iverson (2006) proposed a law of similarity ξ_{s}(λx) = γ(λ,s)ξ_{η(λ,s)}(x) to model the dependence of ξ_{s}(x) on x. This model, which has η(λ,s) and γ(λ,s) as parameters, is quite general and may be applied in a number of situations in psychophysics. Iverson (2006) analyzed this model assuming the representation s = u(ξ_{s}(x)) − u(x) and derived the possible functional forms for the scale u. In the present work, we extend the analysis to the more general s = u(ξ_{s}(x)) − w(x) and derive the forms for the scales u and w. We avoid the assumption of differentiability and replace it with an assumption either of non-constancy or of dependence on only one input variable. We find that for some solutions, w has the same form as u, reflective of the context for which u = w, while for other solutions, w takes a different form than u. Comparisons are made to Iverson (2006) and to other work.



functional equations
psychophysical modeling


Measurement Theory
Model Analysis and Comparison
Theory development
Experimental follow-up? Last updated 3 years ago

Nice work on functional equations! Are there empirical counterparts (experimental projects) that would allow to select between these different classes of hypotheses and their attending solutions?

Dr. Eric Cosyn 1 comment
Cite this as:

Doble, C., & Hsu, Y.-F. (2020, July). On the functional forms in a psychophysical law of similarity under a subtractive representation. Paper presented at Virtual MathPsych/ICCM 2020. Via