New Perspectives in Computing the Point of Subjective Equality Using Rasch Models

Abstract

In psychophysics, the point of subject equality (PSE) is any of the points along a stimulus dimension at which a variable stimulus (visual, tactile, auditory, and so on) is judged by an observer to be equal to a standard stimulus. Rasch models have been found to offer a valid solution for computing the PSE when the method of constant stimuli is applied in the version of the method of transitions. The present work provides an overview of the procedures for computing the PSE using Rasch models and proposes some new developments. An adaptive procedure is described that allows for estimating the PSE of an observer without presenting him/her with all stimuli pairs. This procedure can be particularly useful in those situations in which psychophysical conditions of the individuals require that the number of trials is limited. Moreover, it allows for saving time that can be used to scrutinize the results of the experiment or to run other experiments. Also, the possibility of using Rasch-based fit statistics for identifying observers who gave unexpected judgments is explored. They could be individuals who, instead of carefully evaluating the presented stimuli pairs, gave random, inattentive, or careless responses, or gave the same response to many consecutive stimuli pairs. Otherwise, they could be atypical and clinically relevant individuals who deserve further investigation. The aforementioned developments are implemented using procedures and statistics that are well established in the framework of Rasch models. In particular, computerized adaptive testing procedures are used for efficiently estimating the PSE of the observers, whereas infit and outfit mean-squares statistics are used for detecting observers who gave unexpected judgments. Results of the analyses carried out on simulated data sets suggest that the proposed developments can be used in psychophysical experiments.