An alternative to Rasch analysis using triadic comparisons and multi-dimensional scaling

Rasch analysis is a principled approach for estimating the magnitude of some shared property of a set of items when a group of people assign ordinal ratings to them. In the general case, Rasch analysis not only estimates person and item measures on the same invariant scale, but also estimates the average thresholds used by the population to define rating categories. However, Rasch analysis fails when there is insufficient variance in the observed responses because it assumes a probabilistic relationship between person measures, item measures and the rating assigned by a person to an item. When only a single person is rating all items, there may be cases where the person assigns the same rating to many items no matter how many times he rates them. We introduce an alternative to Rasch analysis for precisely these situations. Our approach leverages multi-dimensional scaling (MDS) and requires only rank orderings of items and rank orderings of pairs of distances between items to work. Simulations show one variant of this approach - triadic comparisons with non-metric MDS - provides highly accurate estimates of item measures in realistic situations.