TY - JOUR

T1 - Finite and infinite state confusion models

AU - van Santen, Jan P.H.

AU - Bamber, Donald

N1 - Funding Information:
The first author’s present address is: Department of Psychology, New York University. The paper was completed while the first author was supported by grant AFOSR-80-0279 of the United States Airforce. The second author was supported by the Veterans Administration. We express gratitude to Jim Johnston, Jim Townsend, and John van Praag for helpful comments, and in particular to Dave Noreen for a thorough review and for suggesting a shorter proof of Theorem I. Address reprint requests to Jan P. H. van Santen, Department of Psychology, New York University, 6 Washington Place, New York. N.Y. 10003.

PY - 1981/10

Y1 - 1981/10

N2 - A confusion model is defined as a model that decomposes response probabilities in stimulus identification experiments into perceptual parameters and response parameters. Historically, confusion models fall into two groups. Models in Group I, which includes Townsend's (Perception and Psychophysics, 1971, 9, 40-50) overlap model, were developed on the basis of the notion that stimulus identification is mediated by a finite number of internal states. We call the general class of models that have this processing interpretation finite state confusion models. Models in Group II, which includes Luce's (R. O. Luce et al., Eds., Handbook of Mathematical Psychology (Vol. I), New York: Wiley, 1963) biased choice model, were not developed on the basis of an explicit processing interpretation. It is shown here that models in Group II are not finite state confusion models. We prove in addition that except for Falmagne's (Journal of Mathematical Psychology, 1972, 9, 206-224) simply biased model models in Group II belong to a certain class of infinite state confusion models, namely, models asserting that stimulus identification is mediated by a continuous space of vectors representing detector activation levels.

AB - A confusion model is defined as a model that decomposes response probabilities in stimulus identification experiments into perceptual parameters and response parameters. Historically, confusion models fall into two groups. Models in Group I, which includes Townsend's (Perception and Psychophysics, 1971, 9, 40-50) overlap model, were developed on the basis of the notion that stimulus identification is mediated by a finite number of internal states. We call the general class of models that have this processing interpretation finite state confusion models. Models in Group II, which includes Luce's (R. O. Luce et al., Eds., Handbook of Mathematical Psychology (Vol. I), New York: Wiley, 1963) biased choice model, were not developed on the basis of an explicit processing interpretation. It is shown here that models in Group II are not finite state confusion models. We prove in addition that except for Falmagne's (Journal of Mathematical Psychology, 1972, 9, 206-224) simply biased model models in Group II belong to a certain class of infinite state confusion models, namely, models asserting that stimulus identification is mediated by a continuous space of vectors representing detector activation levels.

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U2 - 10.1016/0022-2496(81)90038-9

DO - 10.1016/0022-2496(81)90038-9

M3 - Article

AN - SCOPUS:0007104450

SN - 0022-2496

VL - 24

SP - 101

EP - 111

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

IS - 2

ER -