A general process for testing the feasibility of applying alternative mathematical or statistical models to the solution of a practical problem is presented and flowcharted. The system is used to compare five models for test equating: (1) anchor test equating using classical test theory; (2) anchor test equating using the one-parameter logistic model; (3) anchor test equating using the three-parameter logistic model; (4) preequating using the one-parameter logistic model; and (5) preequating using the three-parameter logistic model. Sources of estimation instability are identified for the logistic models. Various practical and theoretical problems associated with the general process and test equating are discussed. Investigating the consistency and validity of results obtained from alternative models is a critical feature of the process. Occurrences of inconsistent results are caused by sampling error or bias, estimation procedure error, or violation of the model's assumptions. Validity is investigated by a comparison of model results to observable criteria or by consideration of the patterns of convergence and divergence of results of different models. A model is considered feasible if it shows evidence of consistency and validity. (Author/MH)