Stimulus Sampling Shapes Estimated Perceptual Geometry in Psychophysical Scaling

We used simulations and mathematical analysis to investigate how simultaneous estimation of transducer nonlinearity and perceptual geometry affects bias in maximum likelihood difference scaling (MLDS). Uniform sampling in the stimulus domain disproportionately sampled slowly varying regions and inadequately sampled rapidly varying regions of nonlinear transducers, leading to biased estimates of transducer shape. These biases were substantially reduced when stimuli were sampled uniformly in response space, distributing observations more evenly across the transducer. Likelihood-surface analysis revealed substantial confounding between sampling-induced distortions and effects attributable to changes in perceptual geometry. Uniform stimulus-domain sampling produced a pronounced trade-off between the parameters governing transducer nonlinearity and perceptual geometry, which was substantially reduced under uniform response-space sampling. Although response-space sampling generally improved the local conditioning of the likelihood surface, parameter identifiability remained dependent on its intrinsic geometry and thus on the underlying transducer. These results show that stimulus sampling can influence whether departures from a Riemannian perceptual metric are detected, highlighting the importance of sampling designs that adequately represent perceptual space. More generally, they demonstrate how appropriate sampling can help disentangle the effects of nonlinear transduction from those of nonlinear contributions of perceptual differences to judgments.