extended · article · 2019

Rasch and Rationality: Scale typologies as applied to Item Response Theory

Rebecca Freund; Mark Wilson

This dissertation consists of three papers on a central topic: the application of scale type theory to the Rasch and 2PL models. Each paper uses a different framework or set of frameworks for defining a typology of scales.In the first paper, I begin the analysis of scale types through the Stevens (1946) typology. I introduce the notion of difference scales using a formalization of this typology. In applying this formalization to the Rasch and 2PL models, I discuss alternate paradigms for conceptualizing the restrictive assumptions of the Rasch model.In the second paper, I apply the Suppes (1958) typology to the two IRT models. The conclusions here echo and reinforce those of the first chapter. In the second half of this paper, I examine other perspectives on connecting scale type theory and the Rasch model, focusing on the case of additive conjoint measurement theory.The first two papers...