Simple estimators for the simple latent class mastery testing model

Latent class models for mastery testing differ from continuum models in that they do not postulate a latent mastery continuum but conceive mastery and non-mastery as two latent classes, each characterized by different probabilities of success. Several researchers use a simple latent class model that is basically a simultaneous application of the binomial error model to both mastery classes. W. A. Reulecke (1977) presents a version of this model that assumes that non-masters guess blindly, with a probability of success equal to the reciprocal of the number of alternatives. Assuming a loss ratio, these models enable the derivation of an optimal cutting score for separating masters from non-masters. To compute this cutting score, the model parameters must be estimated. J. A. Emrick and F. N. Adams (1969) suggest a method that is based on the average inter-item correlation but which, due to its assumptions, is only of restricted applicability. The sample applies to the maximum likelihood method in as much as this involves estimation equations that can be solved iteratively. In this paper, the method of moments is used to obtain "quick and easy" estimates. An endpoint that assumes that the parameters can simply be estimated from the tails of the sample distribution is discussed. A Monte Carlo experiment demonstrates that the method of moments yields excellent estimators and beats the endpoint method uniformly.