A limited capacity rehearsal model for psychophysical judgements applied to magnitude estimation

Abstract

A generalization of Marley and Cook's (1984. British Journal of Mathematical and Statistical Psychology 37, 136–151) rehearsal model is applied to the magnitude estimation data of Baird, Green, and Luce (1980. Journal of Experimental Psychology: Human Perception and Performance 6, 277–289) and of Green, Luce, and Smith (1980. Perception and Psychophysics 27, 483–488). The data analyses that are considered are: the mean magnitude estimates and response variances, each as a function of the stimulus intensity; the coefficient of variation of the response and of the response ratio on adjacent trials and the correlation coefficient of the log responses on adjacent trials, each as a function of the difference in the stimulus intensities on the adjacent trials. Several versions of the model are discussed, with each version yielding good fits to different aspects of the data. However, it is clear from the theoretical framework why each version fails on part of the data, and suggestions are given for a future version that might fit all aspects of the data simultaneously. This suggested version, which includes aspects of Ward's (1979. Journal of Experimental Psychology: Human Perception and Performance 5, 444–459) fuzzy judgement approach and of Treisman's (1984. Journal of Experimental Psychology: General 113, 443–463) criterion setting model, can also handle assimilation of the current response to the previous response, which is not obviously implied by the current versions of the model.