Dynamic Parameter Estimation In Student Monitoring Systems

Data from progress tests often consists of varying numbers 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 simultaneous, an individual rating is updated immediately after a response, and the algorithm requires no computationally intensive calculations. Several theoretical properties of the Elo rating system are evaluated, such as stationarity of the mean, the variance and the distribution. The evaluation of these properties leads to several variants of the system. A logistic, normal ogive, and mixture variant are discussed. Variants using adaptive opponent matching are evaluated as well. The research concludes with an adaptive mixture variant of the Elo rating system in order to obtain a stationary  distribution.