Estimating the parameters of Emrick's mastery testing mode

Abstract

Emrick’s model is a latent class or state model for mastery testing that entails a simple rule for separating masters from nonmasters with respect to a homogeneous domain of items. His method for estimating the model parameters has only restricted applicability inasmuch as it assumes a mixing parameter equal to .50 and an a priori known ratio of the two latent success probabilities. The maximum likelihood method is also available but yields an intractable system of estimation equations which can only be solved iteratively. The emphasis in this paper is on estimates to be computed by hand but nonetheless accurate enough for most practical situations. It is shown how the method of moments can be used to obtain such "quick and easy" estimates. In addition, an endpoint method is discussed that assumes that the parameters can be estimated from the tails of the sample distribution. A monte carlo experiment demonstrated that for a great variety of parameter values, test lengths, and sample sizes, the method of moments yields excellent results and is uniformly much better than the endpoint method.