Purely relative models cannot provide a general account of absolute identification

Abstract

Unidimensional absolute identification-identifying a presented stimulus from an ordered set-is a common component of everyday tasks. Laboratory investigations have mostly usedAbsolute identification requires participants to identify which stimulus has been presented from a prespecified set. In general, people are unable to accurately identify more than about 8-10 stimuli that vary on a single psychological dimension, which is surprising when comparative judgments with the same stimuli (i.e., judging whether one stimulus is less than, equal to, or greater than another stimulus) are completely accurate. For over 20 years, theories of absolute identification have been divided along a continuum from purely absolute accounts to purely relative accounts (for reviews, see Brown, Marley, Donkin, & Heathcote, 2008;Stewart, Brown, & Chater, 2005). Absolute models assume some form of memory for the magnitude of each stimulus in the set-a set of long-term referents that represent the stimuli. Relative models make a more parsimonious assumption by representing the stimuli with a limited set of partial information. Usually, relative models assume that the only long-term memory is for a single scale factor related to the spacing of the stimuli-that is, to the magnitude differences between adjacent stimuli. The relative approach has proven successful in magnitude estimation tasks (e.g., Luce & Green, 1974;Marley, 1976), and the superficial similarity between the tasks suggests that the same approach may work in absolute identification.The theoretical debate has progressed mainly by pairwise comparison of particular absolute and relative models-for example, Marley and Cook (1984) Here, we present a classwise comparison based on key differences in the way absolute and relative models map from the stimulus to the response space. Rather than relying on small differences in quantitative goodness of fit, we identify a qualitative failure of relative models, caused by their core structure. In particular, we show that relative models make very strong and surprising predictions for experiments in which unequally spaced stimuli are used. We then test these predictions with a new experiment that addresses a potential limitation of past research.We focus on absolute identification experiments with unequally spaced stimuli presented with feedback, which means that participants are informed of the correct response after each trial. Feedback is almost always presented in numeric format (e.g., as a digit on a computer screen), and so researchers have used the term numeric feedback (Holland & Lockhead, 1968, p. 412). The numeric nature of feedback is important in our discussion of relative models, especially of the relative judgment model (RJM;Stewart et al., 2005). In fact, we show that relative models-including the RJM-are unable to account for certain aspects of data from experiments with unequally spaced stimuli. Although it is not the model described by Stewart et al., an extended version of the RJM can account very accurately for unequal...

Relative judgement is relatively difficult: Evidence against the role of relative judgement in absolute identification

“…This is probably because the idea of relative judgement appears intuitive and simple. Indeed, Brown et al (2009) note that it is more parsimonious because it assumes that only a limited set of information is represented. However, this line of reasoning is questionable in terms of what we know about memory.…”

“…Brown et al (2009) argued that the RJM needs to contain some absolute knowledge about the spacing between stimuli in the range in order to account for the effects of unequal stimulus spacing. Stewart and Matthews (2009) therefore proposed an augmented RJM to account for unequal spacing effects that contained knowledge of the differences between all stimuli in the stimulus set.…”

Relative judgment and knowledge of the category structure

“…In such a case, as Brown et al (2009) describe, the above-mentioned strategy will not work. There is no simple exchange rate between stimulus differences and response-scale differences, because the size of stimulus difference required for a change in response category varies as a function of the previous stimulus.…”

“…We show that, if redundancy in the category structure representation is exploited, the look-up table representation is equivalent to the Stewart et al (2005) relative judgment model (known by the acronym RJM). Finally, we demonstrate that this model can account for the uneven spacing data from Brown et al (2009).…”

“…Most recently, the SAMBA model has integrated these two accounts (Brown, Marley, Donkin, & Heathcote, 2008). Brown, Marley, Dodds, and Heathcote (2009) discuss how relative judgment might account for data from category structures in which stimuli are unevenly spaced. Figure 1 illustrates the three spacings of stimuli along a single continuum taken from their experiment.…”