Maximum likelihood estimation of difference scaling functions for suprathreshold judgments

Maximum likelihood estimation (MLE) has been used to produce perceptual scales from binary judgments of triads and quadruples. This method relies on Thurstone's theory of a stochastic perceptual process where the perceived difference of two stimuli is the difference in their perceived strengths. It is possible that the perception of a suprathreshold difference is overestimated when adding smaller differences, a phenomenon referred to as diminishing returns. The current approach to construct a perceptual scale using MLE does not account for this phenomenon. We present a way to model the perception of differences using MLE and Thurstone's theory, adapted to allow the possibility of diminishing returns. This method is validated using Monte Carlo simulated responses to experimental triads and can correctly model diminishing returns, the absence of diminishing returns, and the opposite of diminishing returns both in the cases when a perceptual scale is known and when the true perceived strengths of the stimuli are unknown. Additionally, this method was applied to empirical data sets to determine its feasibility in investigations of perception. Ultimately, it was found that this analysis allows for more accurate modeling of suprathreshold difference judgments, a more complete understanding of the perceptual processes underlying comparisons, and the evaluation of Thurstone's theory of difference judgments.