Three item response models were evaluated for estimating item parameters and equating test scores. The models, which approximated the traditional three-parameter model, included: (1) the Rasch one-parameter model, operationalized in the BICAL computer program; (2) an approximate three-parameter logistic model based on coarse group data divided into fifths and twentieths, and using the Quantile modification of the LOGIST program; and (3) a modified three-parameter logistic model with fixed a's and c's, using the LOGIST computer program. The data came from a study of the Scholastic Aptitude Test (SAT), which involved the chain equating of a test to itself through five intermediary forms; approximately 2,670 cases were used for each SAT form. Results showed that item calibrations based on twentieths were closer to the true values and to LOGIST estimates than those based on fifths, but the equating results based on twentieths were not more accurate. Method (2) yielded highly accurate score conversions in equating a test to itself, and all three models yielded very accurate equating results. Questions were raised about the adequacy of equating a test to itself as a criterion for evaluating equating results. Further research was recommended before adopting any of the approximate models. Twelve tables and 22 figures are appended. (Author/GDC)