For evenly spaced stimuli, a purely relative judgment account of unidimensional categorization performance is trivial: All that is required is knowledge of the size of stimulus difference corresponding to the width of a category. For unevenly spaced stimuli, long-term knowledge of the category structure is required. In the present article, we will argue that such knowledge does not necessitate a direct, absolute mapping between (representations of ) stimulus magnitudes and category labels. We will show that Stewart, Brown, and Chater's (2005) relative judgment model can account for data from absolute identification experiments with uneven stimulus spacing.
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Models of the identification and categorization of simple perceptual stimuli have been divided into two classes. First, there are those models in which there is a direct mapping between stimulus magnitudes or regions of stimulus space and category labels (Ashby & Townsend, 1986; Durlach & Braida, 1969; Kent & Lamberts, 2005; Lacouture & Marley, 2004; Luce, Green, & Weber, 1976; Marley & Cook, 1986; Nosofsky, 1986, 1997; Petrov & Anderson, 2005). Second, there are relative judgment models in which there is no longterm mapping between stimulus magnitudes or regions of stimulus space and category labels. These mappings are assumed to be unavailable or, at least, unused. Instead, in relative judgment models, judgments are made with reference to recently encountered stimuli and category labels (Holland & Lockhead, 1968; Laming, 1984, 1997; Stewart, 2007; Stewart & Brown, 2004; Stewart, Brown, & Chater, 2002, 2005). 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. The experiment was absolute identification, in which stimuli are presented one at a time (with replacement) and participants are required to identify each stimulus with a unique label. Trialbytrial feedback of the correct answer is provided. A relative judgment account for the evenspread condition is quite straightforward. All that is required is knowledge of the exchange rate between stimulus units and response units. Thus, if one has learned that 3 dB equals one response category, then-given the category of the previous stimulus and a perception of the difference between current and previous stimuli-one can determine the category of the current stimulus (see Holland & Lockhead, 1968, for a relative judgment account of this sort).
When stimuli are not evenly spaced along the continuum, as in the lowand highspread conditions, relative judgment is not quite so straightforward. In such a case, as Brown et al. (2009) describe, the abovementioned strategy will not work. There is no simple exchange rate between stimulus differences and responsescale differences, because the size of stimulus difference required for a change in response category varies as a function of the previous stimulus.
In the remainder of this article, we describe a lookup table model of relative judgment. We show that, if redundancy in the category structure representation is exploited, the lookup 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).
A Look-Up Table Model of Relative Judgment
Consider a purely relative judgment model, in which one constructs a lookup table for the current response as a function of (1) the previous feedback linguistic label and (2) the difference between the previous stimulus and the current stimulus. …