A stochastic growth model applied to repeated tests of academic knowledge

In the course of the medical program at the University of Limburg, students complete a total of 24 progress tests, consisting of items drawn from a constant itembank. A model is presented for the growth of knowledge reflected by these results. The Rasch model is used as a starting point, but both ability and difficulty parameters are taken to be random, and moreover the logistic distribution is replaced by the normal. Both individual and group abilities are estimated and explained through simple linear regression. Application to real data shows that the model fits very well.