From: Maximum likelihood difference scales represent perceptual magnitudes and predict appearance matches Journal of Vision. 2017;17(4):1. doi:10.1167/17.4.1 Figure Legend: Estimation of scales using MLDS with triads. (A) Hypothetical scale relating perceptual experiences Ψ(xi) to stimulus values xi. For an example stimulus triad (x2, x5, x8), observers are asked to compare which pair is more different, (x2, x5) or (x5, x8). The decision model for this example triad is Δ = [Ψ(x8) − Ψ(x5)] − [Ψ(x5) − Ψ(x2)] or Δ = Ψ(x8) − 2Ψ(x5) + Ψ (x2). (B) The weights for each term in the decision model are the covariates in a design matrix, X, in a binomial GLM. Each row in the design matrix X indicates the elements of a triad in one trial. The shaded rows are two repetitions of the same triad, which is the example triad in panel A. The design matrix contains all triads shown in one experiment. (C) Empirical scale that results from solving the GLM and obtaining the coefficients β. The coefficients correspond to the scale values at different levels of the physical variable. Error bars are estimates for the error associated with each coefficient and were obtained using bootstrap. Date of download: 11/12/2017 The Association for Research in Vision and Ophthalmology Copyright © 2017. All rights reserved.