A major impediment to identifying the molecular substrates of addiction and developing effective therapeutics has been the lack of animal models that both recapitulate clinical disease presentation and are amenable to genetic manipulation. Intravenous self-administration is the “gold standard” for modeling cocaine and opioid addiction-associated behaviors in animals, but technical limitations have precluded its widespread use in mice, the mammalian species for which the most genetic tools are available. Here, we describe the establishment and demonstrate the utility of multi-stage cocaine and remifentanil paradigms that overcome classic challenges in murine intravenous self-administration. We evaluated self-administration acquisition, maintenance, extinction, and cue-induced reinstatement of drug seeking longitudinally in large cohorts of mice with indwelling catheters. In short daily sessions, mice without prior operant conditioning engaged in drug-associated lever responding that was fixed ratio- and dose-dependent, extinguished by the withholding of drugs, and reinstated by the reintroduction of paired cues. Multivariate statistics, to which this type of longitudinal data is well-suited, revealed that patterns of cocaine and remifentanil taking were similar while those of cocaine and remifentanil seeking were distinct. Individual performance in both drug paradigms was a function of two latent variables we termed incentive motivation and discriminative control. These latent variables identified drug class-specific self-administration phenotypes and were differentially predicted by a priori novelty- and drug-induced locomotor activity in the open field. Application of this behavioral and statistical analysis approach to genetically engineered mice will facilitate the identification of the cell types and neural circuits driving addictive behaviors and their underlying constructs.