Student Monitoring Using Chess Ratings

Abstract

Abstract. The Elo rating system has it origins in chess ability estima- tion. The system is proposed as a means of analyzing data from student monitoring systems. Such data often consists of varying amounts of measurements at varying time points. Applying the Elo rating system to such data has several advantages. There is no need for a growth model, both person ability and item difficulty are estimated simultane- ous, an individual rating is updated immediately after a response and the algorithm requires no computationally intensive calculations. Seve- ral theoretical properties of the Elo rating system are evaluated, such as stationarity of the mean, of the variance and of the distribution. The evaluation of these properties leads to several variants of the system. A logistic, normal ogive and mixture variant are discussed, alongside with an adaptive element. The research concludes with an adaptive mixture variant of the Elo rating system in order to obtain a stationary distribution.