Motivating example Random Effects Other topics References HLM Short Course Introduction.pdf

Motivating example Random Effects Other topics References HLM Short Course: Introduction Lane Burgette Department of Statistics University of Wisconsin-Madison /~burgette March 5, 2008 Motivating example Random Effects Other topics References Note These slides will ignore pretty much all the math. See, e.g., Pinheiro and Bates (2000) for the details. Motivating example Random Effects Other topics References Hierarchical structures Hierarchical linear models (HLM) (or mixed models for statisticians) are a tool for analyzing data when we have a nested structure For example: • Students within schools • Residents within neighborhoods • Multiple observations per person Motivating example Random Effects Other topics References Example • Interested in modeling academic performance for students • If we ignore nesting of students within classrooms, we have two options • Either model with a school-level error, or student-level error • Both methods are problematic Motivating example Random Effects Other topics References School-level analysis • Possible to model average performance, with school-level error • How do we weight observations if within-school sample sizes vary? • Cannot include student-level predictors • Lose information about student-level variation – may be of intere