Internal References in Cross-modal Matching: A Global Psychophysical Perspective

Cross-modal matching builds upon our ability to compare intensities across modalities. For example, we can easily match the brightness of a visual stimulus to the loudness of a tone, and vice versa. The regression effect in cross-modal matching relates to the observation that the intensity of whatever stimulus is adjusted exhibits a tendency toward some mean magnitude, which is interpreted as serving as an internal reference. Internal references, however, are not part of classical psychophysical theory in the tradition of Stevens, but form a key ingredient for the theory of global psychophysics initiated by R. Duncan Luce. The present paper extends and generalizes Luce's theory of what he called cross-dimensional magnitude production (Luce et al., 2010, Psychological Review, 117, 1247-1258) to integrate potentially role-dependent internal references (pertaining to the standard, or the adjusted stimulus) as suggested by the regression effect. The attribute cross-dimensional is more comprehensive than cross-modal, because it also includes intra-modal tasks where stimuli differ in an additional dimension (e.g., loudness of tones of different frequency). Reevaluating the available empirical evidence for magnitude production and matching experiments on the basis of these theoretical developments leads to a coherent picture. The results support role-dependence of internal references in cross-dimensional tasks (intra- or cross-modal), but clearly reject it in intra-dimensional tasks. Moreover, predictions derived from the generalized theory provide a close fit of classical data on cross-modal matching. Further directions for empirical as well as theoretical research are highlighted.