# FECHNERIAN SCALING OF IRT MODELS FOR DICHOTOMOUS DATA

### Abstract

Fechnerian scaling as developed by Dzhafarov and Colonius aims at imposing a metric on a set of objects based on their pairwise dissimilarities, e.g., discrimination probabilities. The objects may be perceptual stimuli or abstract categories. In this paper we apply Fechnerian scaling to a space of uni- and multidimensional logistic models used in item response theory for dichotomous data. The space of models is created by assigning to each ordered pair of models (A,B) a discrimination probability, taken to be the probability with which model B fits, by some statistical criterion, a data set randomly generated by model A at least as well as A fits this data set itself. We then use (metric) multidimensional scaling to (isometrically) embed, for visualization purposes, the set of the item response theory models with pairwise Fechnerian distances in the Euclidean 2D space.