The dynamics of scaling: a memory-based anchor model of category rating and absolute identification.

A memory-based scaling model—ANCHOR—is proposed and tested. The perceived magnitude of the target stimulus is compared with a set of anchors in memory. Anchor selection is probabilistic and sensitive to similarity, base-level strength, and recency. The winning anchor provides a reference point near the target and thereby converts the global scaling problem into a local comparison. An explicit correction strategy determines the final response. Two incremental learning mechanisms update the locations and base-level activations of the anchors. This gives rise to sequential, context, transfer, practice, and other dynamic effects. The scale unfolds as an adaptive map. A hierarchy of models is tested on a battery of quantitative measures from 2 experiments in absolute identification and category rating. Category rating is a widely used method of data collection in experimental psychology. Ratings come in a wide variety of guises: psychophysical scales, similarity judgments, typicality judgments, confidence ratings, attitude questionnaires, health selfreports, and many others. The participants in all these tasks are asked to rate things using an ordered set of categories such as 1, ..., 7 orstrongly agree, ... , strongly disagree. Most people can do this without effort, and most psychologists tend to take their responses at face value. Ratings are among our primary dependent measures. Yet the field lacks a comprehensive theory of how these responses are produced. There are many partial theories, each within the confines of a particular discipline, and the practitioners in each discipline make conscious efforts to minimize the impact of factors outside their scope. Thus, psychophysicists treat nonperceptual factors such as sequential dependencies and guessing strategies as nuisance biases that must be minimized through randomization, counterbalancing, and averaging (Stevens, 1957). Cognitive psychologists, conversely, tend to ignore low-level perceptual features in their stimuli, experiments, and theories. The problem with this divide-and-conquer approach is that each theory is incomplete. Both peripheral and central mechanisms are engaged in most real-life situations. The overall behavior stems from the joint action and interaction of these various components. Thus, careful study of the isolated components is valuable and necessary, but it must be followed by systemic efforts to put the pieces back together. The pursuit of integration is hardly new. Miller’s (1956) classic article devotes equal amounts of space to short-term memory and absolute identification, a close relative of category rating. Both are subject to capacity limitations, and Miller cast them both in information-processing terms. The research that sprouted from this influential early effort, however, splintered into increasingly divergent traditions. Forty years later, a review of Miller’s impact concludes that “the dominant theories and paradigmatic approaches in these two domains have gone their separate ways, with little, if any, cross talk” (Shiffrin & Nosofsky, 1994, p. 360). Integration was premature in 1956, but perhaps in 2005 the time is ripe. The psychophysics and memory traditions have amassed a rich collection of empirical data and theoretical insights. By pooling knowledge from all these sources, one can hope to achieve unified understanding. We propose a theory bridging the gap between psychophysics and memory. It is based on the ACT–R architecture (Anderson &