Maximum likelihood difference scales represent perceptual magnitudes and predict appearance matches

Abstract

One central problem in perception research is to understand how internal experiences are linked to physical variables. Most commonly, this relationship is measured using the method of adjustment, but this has two shortcomings: The perceptual scales that relate physical and perceptual variables are not measured directly, and the method often requires perceptual comparisons between viewing conditions. To overcome these problems, we measured perceptual scales of surface lightness using maximum likelihood difference scaling, asking observers only to compare the lightness of surfaces presented in the same context. Observers were lightness constant, and the perceptual scales qualitatively and quantitatively predicted perceptual matches obtained in a conventional adjustment experiment. Additionally, we show that a contrast-based model of lightness perception predicted 98% of the variance in the scaling and 88% in the matching data. We suggest that the predictive power was higher for scales because they are closer to the true variables of interest.

Suprathreshold contrast response in normal and anomalous trichromats

“…All statistical analyses were performed using the OpenSource software R [30]. The signal detection model underlying MLDS and the fitting procedure have been previously described [25][26][27]31,32]. In summary, given a set of p stimuli ordered along a physical continuum, triples or non-overlapping quadruples are sampled on each trial.…”

“…In practice, we fit the data using functions from the R package MLDS [26,27]. These functions implement the fitting procedure in terms of a generalized linear model with a binomial family and a probit link function [26,27,[31][32][33]. The obtained scales are unique up to addition of a constant or multiplication by a coefficient.…”

“…The representation of the MLDS response scale in terms of the signal detection parameter d is based on a parameterization that sets the judgment noise equal to unity on the response scale. How this measure of d relates to that obtained from discrimination experiments is an unsettled question [31,32] that perhaps can be answered by comparing the MLDS response estimates directly with those from discrimination experiments.…”

Suprathreshold contrast response in normal and anomalous trichromats

“…In practice, we fit the data using functions from the R package MLDS [26,27]. These functions implement the fitting procedure in terms of a generalized linear model with a binomial family [26,27,[31][32][33]. The obtained scales are unique up to addition of a constant or multiplication by a coefficient.…”

“…The representation of the MLDS response scale in terms of the signal detection parameter d is based on a parameterization that sets the judgment noise equal to unity on the response scale. How this measure of d relates to that obtained from discrimination experiments is an unsettled question [31,32] that perhaps can be answered by comparing MLDS response estimates directly with those from discrimination experiments.…”