Response Threshold Models for Binary Ranking and Sorting

The present paper provides two response models: one for binary ranking and the other for sorting. The former is a behavior of choosing, in a random order, only those comparison stimuli which are judged to be very similar to a standard stimulus, and the latter is that of selecting stimuli which are judged very similar to each other to form them into clusters. The key assumption of these models is that the subject perceives any two stimuli as very similar to each other when their dissimilarity, which varies over time, is below response thresholds that are associated with those stimuli. Maximum likelihood estimation procedures are used for the estimation of parameters of these models. The proposed models are applied, for illustrative purposes, to the similarity data collected by the binary ranking and sorting methods. We discuss some advantages of the binary ranking method to be used for collecting similarity data and a practical limitation of our response model for sorting.