Forgetting,Guessing,and Mastery: The Macready and Dayton Models Revisited and Compared with a Latent Trait Approach

Abstract

Macready and Dayton (1977) introduced two probabilistic models for mastery assessment based on an idealistic all-or-none conception of mastery. Although these models are in statistical respects complete, the question is whether they are a plausible rendering of what happens when an examinee responds to an item. First, a correction is proposed that takes account of the fact that a master who is not able to produce the right answer to an item may guess. The meaning of this correction and its consequences for estimating the model parameters are discussed. Second, Macready and Dayton’s latent class models are confronted with the three-parameter logistic model extended with the conception of mastery as a region on a latent variable. It appears that from a latent trait theoretic point of view, the Macready and Dayton models assume item characteristic curves that have the unrealistic form of a step function with a single step. The implications of the all-or-none conception of mastery for the learning process will be pointed out shortly. Finally, the interpretation of the forgetting parameter of the Macready and Dayton models is discussed and approached form a latent trait theoretic point of view.