ANCHOR: A Memory-Based Model of Category Rating

ANCHOR: A Memory-Based Model of Category Rating Alexander A. Petrov ( apetrov@andrew.cmu.edu ) Department of Psychology; Carnegie Mellon University Pittsburgh, PA 15213 USA John R. Anderson ( ja+@cmu.edu ) Department of Psychology; Carnegie Mellon University Pittsburgh, PA 15213 USA Abstract This paper attempts to draw a bridge between psychophys- ics and memory research by proposing a memory-based model of category rating. The model is based on the cogni- tive architecture ACT-R and uses anchors stored in memory that serve as prototypes for the stimuli classified within a response category. The anchors are retrieved by a partial matching mechanism and updated dynamically by an in- cremental learning mechanism. Anchors also have base- level activations that reflect the frequency and recency of the responses. These mechanisms give rise to sequential effects and nonuniform response distributions. A psycho- logical experiment involving category rating of physical length is reported and the predictions of the model are compared against the empirical data. The psychophysical implications of the model are discussed. Introduction Category rating is a widely used method of data collection in experimental psychology. A category-rating situation arises whenever the participants are asked to assign each stimulus to one of several ordered categories such as 1, 2, …, 9 or very dissimilar, …, very similar. Procedures of this kind are common for many studies ranging from psychophysical scaling to similarity judgment to personality inventories. Therefore a detailed analysis of the cognitive mechanisms underlying this task is potentially relevant to a diverse set of situations. S perceptual subsystem M central subsystem R Figure 1: Simplified decomposition of the cate- gory-rating process. The external stimulus S maps to an internal magnitude M which in turn gives rise to the overt response R . A rough decomposition of the process of category rating is presented in Figure 1. (This diagram is by no means complete or accurate; it is provided for expository purposes only.) The perceptual subsystem maps the external stimulus S onto an internal representation M on a psychological con- tinuum. In this paper the internal representation is called magnitude. The magnitude M then serves as a basis for gen- erating an overt response R on the category scale. The latter transformation is the responsibility of the central (or cogni- tive) subsystem. Both subsystems are characterized with internal states that unfold in time and may differ from trial to trial. Thus each box in Figure 1 has underlying dynamics and the whole system is more complex than the open-loop pipeline suggested by the diagram. The present paper focuses on the central subsystem and the computational mechanisms converting subjective magni- tudes into external reports. While the perceptual aspects of the process are certainly important, they are not central to the research reported here. Therefore the research strategy has been to try to minimize the contribution of the perceptual subsystem so that the properties of the central one can show through. This dictated the choice of a modality for which the perceptual transformation is as simple as possible—physical length. The empirical relation between stimulus intensities S and averaged category ratings R tends to follow a power func- tion: R = k . S n (Stevens, 1957). The exponent n is character- istic of the perceptual modality. For physical length, this exponent is very close to 1.0 (Stevens, 1957). In other words, the scale is linear. Thus it seems reasonable to as- sume that the perceptual subsystem delivers veridical repre- sentations of physical length, with little if any systematic distortions (Krantz, 1972). Under this assumption, any pat- terns in the category-rating data for length are largely due to the central subsystem. The psychophysical literature reports several phenomena related to category rating. The most basic finding is that the participants are able to perform this task without major dif- ficulties and provide robust and regular data: the average rat- ing values vary smoothly with stimulus intensity (Stevens, 1957). This is true whether or not feedback is provided (e.g. Ward & Lockhead, 1970). The second major finding is Ste- vens’ power law stated above. In addition to these first-order results, there are several second-order effects as well. The sequential effects are of special interest here because they shed light on the dynamics of the rating process. Nu- merous studies have indicated that the successive trials in a rating experiment are not independent (Ward & Lockhead, 1970; Jesteadt et al., 1977; Petzold, 1981; Schifferstein & Frijters, 1992). The responses, regarded as a time series, show autocorrelational structure. Typically the data are ana- lyzed using multiple regression in which the stimulus S t-1 and the response R t-1 on the preceding trial enter as predic- tors after the contribution of the current stimulus S t has