<p>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.</p>

Statistics

College of Letters and Science

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Statistics and Data Science

STATS 153 - Hierarchical Linear Modeling

Hierarchical Linear Modeling

Develop a strong theoretical understanding of hierarchical linear modeling, including nested data structures, variance partitioning, intraclass correlation, fixed and random effects, random intercept and random slope models, cross-level interactions, centering strategies, and shrinkage (empirical Bayes estimation).

Communicate multilevel model results effectively to non-statistical audiences by translating model parameters, variance components, and cross-level effects into accurate and accessible language.

Design, specify, and fit multilevel models appropriate to real-world applications by identifying units of analysis, levels of nesting, relevant predictors, and suitable model structures.

General Catalog

Hierarchical Linear Modeling

STATS 153

4 units