### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 101-111 |

Number of pages | 11 |

Journal | Journal of Mathematical Psychology |

Volume | 24 |

Issue number | 2 |

DOIs | |

State | Published - 1981 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Applied Mathematics
- Experimental and Cognitive Psychology

### Cite this

*Journal of Mathematical Psychology*,

*24*(2), 101-111. https://doi.org/10.1016/0022-2496(81)90038-9

**Finite and infinite state confusion models.** / Van Santen, Jan; Bamber, Donald.

Research output: Contribution to journal › Article

*Journal of Mathematical Psychology*, vol. 24, no. 2, pp. 101-111. https://doi.org/10.1016/0022-2496(81)90038-9

}

TY - JOUR

T1 - Finite and infinite state confusion models

AU - Van Santen, Jan

AU - Bamber, Donald

PY - 1981

Y1 - 1981

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.

UR - http://www.scopus.com/inward/record.url?scp=0007104450&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0007104450&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:0007104450

VL - 24

SP - 101

EP - 111

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

SN - 0022-2496

IS - 2

ER -