Estimating the parameters of Emrick's mastery testing mode

Emrick’s model is a latent class or state modelfor mastery testing that entails a simple rule forseparating masters from nonmasters with respect toa homogeneous domain of items. His method forestimating the model parameters has only restrictedapplicability inasmuch as it assumes a mixing parameterequal to .50 and an a priori known ratio ofthe two latent success probabilities. The maximumlikelihood method is also available but yields an intractablesystem of estimation equations which canonly be solved iteratively. The emphasis in this paperis on estimates to be computed by hand butnonetheless accurate enough for most practical situations.It is shown how the method of moments canbe used to obtain such "quick and easy" estimates.In addition, an endpoint method is discussed thatassumes that the parameters can be estimated fromthe tails of the sample distribution. A monte carloexperiment demonstrated that for a great variety ofparameter values, test lengths, and sample sizes,the method of moments yields excellent results andis uniformly much better than the endpoint method.