Some New and Some Old Results for the Polytomous Rasch Model

Abstract

In the first part, the polytomous Rasch model is discussed as it was presented by Rasch at the Berkeley Symposium in 1960, and published in the Proceedings from the Symposium in 1961. I shall then discuss what was achieved in the next 10 to 15 years as regards estimation and check of the model. As Georg Rasch himself never learned to program a computer, this work was carried out by a handful or so statisticians, who worked on the model. In the next 10 to 15 years much work was done on the polytomous Rasch model in many directions. But I shall skip this period. In the second part, I shall present a quite recent result for the estimates in the polytomous Rasch model, which is extremely simple and require only very few elementary combinations of quantities already computed. In addition it solves the problem of identifying significant points on the graphs suggested by Rasch.