Recent theoretical developments in the field of absolute identification have stressed differences between relative and absolute processes, that is, whether stimulus magnitudes are judged relative to a shorter term context provided by recently presented stimuli or a longer term context provided by the entire set of stimuli. The authors developed a model (SAMBA: selective attention, mapping, and ballistic accumulation) that integrates shorter and longer term memory processes and accounts for both the choices made and the associated response time distributions, including sequential effects in each. The model's predictions arise as a consequence of its architecture and require estimation of only a few parameters with values that are consistent across numerous data sets. The authors show that SAMBA provides a quantitative account of benchmark choice phenomena in classical absolute identification experiments and in contemporary data involving both choice and response time. (Contains 19 figures, 3 tables and 11 footnotes.)