This paper presents a detailed derivation of method of moments estimates used in computer programs for the four-parameter beta compound binomial strong true score model. A procedure is presented to deal with the case in which the usual method of moments estimates do not exist or result in invalid parameter estimates. The results presented regarding the method of moments estimates are used to derive formulas for computing classification consistency indices under the four-parameter beta compound binomial model. The bulk of the document consists of equations. There is a seven-item list of references. (Author/SLD)