The Dynamics of Direct Psychophysical Scaling: A Memory-Based Model

Abstract:

We propose ANCHOR: a memory-based model of category rating and absolute identification. It gives a principled quantitative account of over a dozen empirical phenomena (Petrov & Anderson, 2005, Psychological Review). The stimuli are represented by Thurstonian magnitudes. The focus of the model is on the central mechanisms that map these internal magnitudes onto the overt response scale. ANCHOR's defining claims are that (1) this mapping is memory-based, (2) stabilized by explicit corrections, and (3) dynamic and statistically driven. Specifically, magnitude-response associations -- "anchors" -- stored in memory compete to match the target. Anchor selection is stochastic and depends on the similarity with the target and the base-level activations of the anchors. Explicit correction strategies promote homomorphism and ensure stability even in the absence of feedback. A competitive learning mechanism updates the anchor locations, tracking the density of the stimulus distribution. Another mechanism learns the base-level activations of the anchors, tracking the frequency and recency of responses. Interesting dynamics emerges from the interplay of these two mechanisms under skewed stimulus distributions as competitive learning induces compensation while activation learning induces assimilation. External feedback effectively disables the competitive learning mechanism and thus the direction of the context effect is determined by activation-based assimilation towards recent and/or frequent responses. Without external feedback, in contrast, the dynamics is dominated by competitive learning, reversing the direction of the observable context effect. Two experiments, with and without feedback, confirm ANCHOR's predictions.

Slides (pdf) ANCHOR Project Software