Purpose Generalized linear mixed-model (GLMM) and Bayesian methods together provide a framework capable of handling a wide variety of complex data commonly encountered across the communication sciences. Using language sample analysis, we demonstrate the utility of these methods in answering specific questions regarding the differences between discourse patterns of children who have experienced a traumatic brain injury (TBI), as compared to those with typical development. Method Language samples were collected from 55 adolescents ages 13-18 years, five of whom had experienced a TBI. We describe parameters relating to the productivity, syntactic complexity, and lexical diversity of language samples. A Bayesian GLMM is developed for each parameter of interest, relating these parameters to age, sex, prior history (TBI or typical development), and socioeconomic status, as well as the type of discourse sample (compare-contrast, cause-effect, or narrative). Statistical models are thoroughly described. Results Comparing the discourse of adolescents with TBI to those with typical development, substantial differences are detected in productivity and lexical diversity, while differences in syntactic complexity are more moderate. Female adolescents exhibited greater syntactic complexity, while male adolescents exhibited greater productivity and lexical diversity. Generally, our models suggest more advanced discourse among adolescents who are older or who have indicators of higher socioeconomic status. Differences relating to lecture type were also detected. Conclusions Bayesian and GLMM methods yield more informative and intuitive results than traditional statistical analyses, with a greater degree of confidence in model assumptions. We recommend that these methods be used more widely in language sample analysis. Supplemental Material https://doi.org/10.23641/asha.14226959.