The Gain-Loss Model: Bias of the Parameter Estimates

The gain-loss model is a formal model developed within Knowledge Space Theory. It consists of five parameters (initial probabilities of the skills, effects of learning objects on gaining and losing skills, careless error and lucky guess probabilities of the items) that are estimated by maximum likelihood. Three simulation studies show that high values of both initial and final probabilities of an item lead to a systematic overestimation of the lucky guess parameter of that item. A re-parameterization of the model is proposed, in which a joint probability of lucky guess is introduced.