Random-Walk and Accumulator Models of Psychophysical Discrimination: A Critical Evaluation

Abstract

The accumulator model proposed by Vickers and the modified random-walk model proposed by Link and Heath are compared in their ability to account for confidence judgments in line-length discrimination tasks. The random-walk model proves to be a viable alternative to the accumulator model, and is able to account for the relationship between mean response time and confidence. The parameter estimation techniques available for the random-walk model are considered advantageous when compared with the accumulator model, because the predictions from the latter have been obtained with the use of computer simulation.

Two-stage dynamic signal detection: A theory of choice, decision time, and confidence.

“…For the remainder of this article, this function in combination with a DSD model describing choice and decision time is called Pierce's model. Link (2003) and Heath (1984) showed that Pierce's model gave a good account of mean confidence ratings. In terms of passing the empirical hurdles, Pierce's model passes several of them and in fact identifies two new hurdles that any model of confidence should explain.…”

“…Although innovative and thought provoking for its time, the law is descriptive at best. Link (1992Link ( , 2003 and Heath (1984), however, reformulated Equation 9 into the process parameters of the DSD model. If we assume no bias on the part of the judge, then substituting the DSD choice probabilities (see Appendix A Equation A1) into Equation 9 yields…”

“…In words, Pierce's hypothesis implies confidence is a multiplicative function of the quantity of the information needed to make a decision ( ; or the distance traveled by the diffusion process) and the quality of the information (␦; or the rate of evidence accumulation in the diffusion process) accumulated in DSD (for a more general derivation allowing for response bias, see Heath, 1984). For the remainder of this article, this function in combination with a DSD model describing choice and decision time is called Pierce's model.…”

“…This assumption is true for signal detection models of confidence (e.g., Budescu, Wallsten, & Au, 1997;Macmillan & Creelman, 2005;Suantak, Bolger, & Ferrell, 1996) as well as a majority of sequential sampling models of confidence (e.g., Heath, 1984;Link, 2003;Merkle & Van Zandt, 2006;Moreno-Bote, in press;Van Zandt, 2000b;Vickers, 1979Vickers, , 2001. We take a different course.…”

Realism of confidence in sensory discrimination

“…Understandably, this difference in the data on the realism of confidence in sensory discrimination has been manifested in a clear divergence in theoretical direction. We have advocated the investigation and development of broad classes of decision and confidence models, such as those rooted in signal detection theory (Ferrell, 1994(Ferrell, , 1995Ferrell & McGoey, 1980), in stochastic-latency mechanisms, such as accumulator processes (see, e.g., Audley, 1960;Baranski & Petrusic, 1991, 1996, 1998Petrusic & Baranski, 1997;Vickers, 1979;Vickers & Packer, 1982;Vickers, Smith, Burt, & Brown, 1985) and random walks (e.g., Heath, 1985;Link, 1992), or in very general judgmental error mechanisms . The Uppsala group, on the other hand, has advocated and developed distinct models of judgment and confidence in the cognitive (knowledge) domain (Bjorkman, 1994;Juslin, 1993Juslin, , 1994Juslin et aI., 1997), as opposed to the sensory domain (Bjorkman et al, 1993;Winman & Juslin, 1993).…”