Purely Relative Models Cannot Provide a General Account of Absolute Identification

Article excerpt

Unidimensional absolute identification-identifying a presented stimulus from an ordered set-is a common component of everyday tasks. Laboratory investigations have mostly used equally spaced stimuli, and the theoretical debate has focused on the merits of purely relative versus purely absolute models. Absolute models incorporate substantial knowledge of the complete set of stimuli, whereas relative models allow only partial knowledge and assume that each stimulus is compared with recently observed stimuli. We test and refute a general prediction made by relative models, that accuracy is very low for some stimulus sequences when the stimuli are unequally spaced. We conclude that, although relative judgment processes may occur in absolute identification, a model must incorporate long-term referents to explain performance with unequally spaced stimuli. This implies that purely relative models cannot provide a general account of absolute identification.

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Unidimensional absolute identification-identifying a presented stimulus from an ordered set-is a common component of everyday tasks. Laboratory investigations have mostly used equally spaced stimuli, and the theoretical debate has focused on the merits of purely relative versus purely absolute models. Absolute models incorporate substantial knowledge of the complete set of stimuli, whereas relative models allow only partial knowledge and assume that each stimulus is compared with recently observed stimuli. We test and refute a general prediction made by relative models, that accuracy is very low for some stimulus sequences when the stimuli are unequally spaced. We conclude that, although relative judgment processes may occur in absolute identification, a model must incorporate long-term referents to explain performance with unequally spaced stimuli. This implies that purely relative models cannot provide a general account of absolute identification.

The theoretical debate has progressed mainly by pairwise comparison of particular absolute and relative models-for example, Marley and Cook (1984) versus Laming (1984); Petrov and Anderson (2005) versus Stewart et al. (2005); and Stewart et al. (2005) versus Brown et al. (2008). There have been one or two attempts at a more general comparison, but these have proven less diagnostic than was hoped (see, e.g., Brown, Marley, & Lacouture, 2007; Stewart, 2007; Stewart et al., 2005, Experiment 2). 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 unequally spaced designs.1 However, the extension contradicts the core assumptions of the relative account of absolute identification, transforming the relative judgment model into an absolute judgment model, or at least into a hybrid absolute-relative judgment model. …