Interest in quantifying consistent among-individual variation in primate behavior, also known as personality, has grown rapidly in recent decades. Although behavioral coding is the most frequently utilized method for assessing primate personality, limitations in current statistical practice prevent researchers' from utilizing the full potential of their coding datasets. These limitations include the use of extensive data aggregation, not modeling biologically relevant sources of individual variance during repeatability estimation, not partitioning between-individual (co)variance prior to modeling personality structure, the misuse of principal component analysis, and an over-reliance upon exploratory statistical techniques to compare personality models across populations, species, and data collection methods. In this paper, we propose a statistical framework for primate personality research designed to address these limitations. Our framework synthesizes recently developed mixed-effects modeling approaches for quantifying behavioral variation with an information-theoretic model selection paradigm for confirmatory personality research. After detailing a multi-step analytic procedure for personality assessment and model comparison, we employ this framework to evaluate seven models of personality structure in zoo-housed bonobos (Pan paniscus). We find that differences between sexes, ages, zoos, time of observation, and social group composition contributed to significant behavioral variance. Independently of these factors, however, personality nonetheless accounted for a moderate to high proportion of variance in average behavior across observational periods. A personality structure derived from past rating research receives the strongest support relative to our model set. This model suggests that personality variation across the measured behavioral traits is best described by two correlated but distinct dimensions reflecting individual differences in affiliation and sociability (Agreeableness) as well as activity level, social play, and neophilia toward non-threatening stimuli (Openness). These results underscore the utility of our framework for quantifying personality in primates and facilitating greater integration between the behavioral ecological and comparative psychological approaches to personality research.