In almost all high-stakes testing programs, test equating is necessary to ensure that test scores across multiple test administrations are equivalent and can be used interchangeably. Test equating becomes even more challenging in mixed-format tests, such as Advanced Placement Program® (AP®) Exams, that contain both multiple-choice and constructed response items. This report examines (1) the performance of various equating methods in terms of first- and second-order equity properties using mixed-format tests; (2) the effect of underlying psychometric models on the assessment of the performance of the equating methods; and (3) the relationship between reliability and equity properties in equating. Three AP Exams (Biology, English Language and Composition, and French Language and Culture) were analyzed with the common-item, nonequivalent-groups design. The 11 equating methods were analyzed, and the results were obtained and compared based upon two different psychometric model frameworks: the two-parameter beta binomial and item-response theory (IRT). In general, the results showed that the performance of various equating methods in terms of equity properties depended on the psychometric model assumed. Furthermore, this report provides empirical evidence that the magnitude of reliability plays a role in achieving the equity properties for the various equating methods. Tables and figures are appended.