Hierarchical Linear Modeling

4 units · Undergraduate upper division (100-199)

Lecture, three hours. Requisites: courses 100B (or Mathematics 170S), 101A, 101B. Introduction to hierarchical linear modeling (HLM) with emphasis on theoretical foundations and applied analysis of multilevel data. Topics include formulation and interpretation of random-intercept and random-slope models, intraclass correlation, variance partitioning, centering strategies, cross-level interactions, and design considerations such as sample size at each level and construction of appropriate multilevel data structures. Applications to science, technology, engineering, and mathematics fields—including laboratory experiments nested within technicians, repeated measurements nested within experimental units, or engineering teams nested within projects—are highlighted, with brief extensions to education, psychology, sociology, and medicine. Focus is placed on conceptual understanding, theoretical grounding, hands-on programming skills in R, and accurate interpretation and communication of multilevel findings within context to both statistical and non-statistical audiences. P/NP or letter grading.