A Rasch model and rating system for continuous responses collected in large-scale learning systems

An extension to a rating system for tracking the evolution of parameters over time using continuous variables is introduced. The proposed rating system assumes a distribution for the continuous responses, which is agnostic to the origin of the continuous scores and thus can be used for applications as varied as continuous scores obtained from language testing to scores derived from accuracy and response time from elementary arithmetic learning systems. Large-scale, high-stakes, online, anywhere anytime learning and testing inherently comes with a number of unique problems that require new psychometric solutions. These include (1) the cold start problem, (2) problem of change, and (3) the problem of personalization and adaptation. We outline how our proposed method addresses each of these problems. Three simulations are carried out to demonstrate the utility of the proposed rating system.