STEM / applied
Mixed models · Graduate · Math
Learning objectives from the Mixed models syllabus, grouped by unit. Click an objective for study materials.
Topics typically covered
Click a topic for the full text and related unit practice.
Graduate Mixed models — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable).
Linear mixed models
- Hierarchical data — Hierarchical data
- Random effects motivation — Random effects motivation
- LMM specification — LMM specification
- Interpretation — Interpretation
- Estimation: REML and ML — Estimation: REML and ML
- BLUPs and shrinkage — BLUPs and shrinkage
- Crossed and nested random effects — Crossed and nested random effects
Generalized LMMs
- GLMMs for binary and count outcomes — GLMMs for binary and count outcomes
- Laplace approximation — Laplace approximation
- Quadrature — Quadrature
- Convergence issues — Convergence issues
- Identifiability — Identifiability
- Ordinal mixed models (introduction) — Ordinal mixed models (introduction)
- Bayesian mixed models (overview) — Bayesian mixed models (overview)
Extensions
- Multilevel models for longitudinal data — Multilevel models for longitudinal data
- Random slopes for treatment effect heterogeneity — Random slopes for treatment effect heterogeneity
- ICC and variance partitioning — ICC and variance partitioning
- Simulation-based power for mixed models — Simulation-based power for mixed models
Learning objectives
Click an objective for study materials.
Linear mixed models
- Hierarchical data — Hierarchical data
- Random effects motivation — Random effects motivation
- LMM specification — LMM specification
- Interpretation — Interpretation
- Estimation: REML and ML — Estimation: REML and ML
- BLUPs and shrinkage — BLUPs and shrinkage
- Crossed and nested random effects — Crossed and nested random effects
Generalized LMMs
- GLMMs for binary and count outcomes — GLMMs for binary and count outcomes
- Laplace approximation — Laplace approximation
- Quadrature — Quadrature
- Convergence issues — Convergence issues
- Identifiability — Identifiability
- Ordinal mixed models (introduction) — Ordinal mixed models (introduction)
- Bayesian mixed models (overview) — Bayesian mixed models (overview)
Extensions
- Multilevel models for longitudinal data — Multilevel models for longitudinal data
- Random slopes for treatment effect heterogeneity — Random slopes for treatment effect heterogeneity
- ICC and variance partitioning — ICC and variance partitioning
- Simulation-based power for mixed models — Simulation-based power for mixed models
Definitions and structure
- Hierarchical data — Hierarchical data
- Random effects motivation — Random effects motivation
- LMM specification — LMM specification
- Interpretation — Interpretation
- Estimation: REML and ML — Estimation: REML and ML
Proofs and reasoning
- BLUPs and shrinkage — BLUPs and shrinkage
- Crossed and nested random effects — Crossed and nested random effects
- GLMMs for binary and count outcomes — GLMMs for binary and count outcomes
- Laplace approximation — Laplace approximation
- Quadrature — Quadrature
Abstraction and generalization
- Convergence issues — Convergence issues
- Identifiability — Identifiability
- Ordinal mixed models (introduction) — Ordinal mixed models (introduction)
- Bayesian mixed models (overview) — Bayesian mixed models (overview)
- Multilevel models for longitudinal data — Multilevel models for longitudinal data
Modeling and computation
- Apply hierarchical data in engineering contexts — Apply hierarchical data in engineering contexts
- Apply random effects motivation in engineering contexts — Apply random effects motivation in engineering contexts
- Apply lmm specification in engineering contexts — Apply lmm specification in engineering contexts
- Apply interpretation in engineering contexts — Apply interpretation in engineering contexts
- Apply estimation: reml and ml in engineering contexts — Apply estimation: reml and ml in engineering contexts
Data and technology
- Use software to explore mixed models problems numerically — Use software to explore mixed models problems numerically
- Interpret computational results against analytic predictions — Interpret computational results against analytic predictions
- Build spreadsheets or scripts for routine calculations — Build spreadsheets or scripts for routine calculations
- Visualize functions, fields, or datasets tied to course topics — Visualize functions, fields, or datasets tied to course topics
- Connect course methods to lab, industry, or research workflows — Connect course methods to lab, industry, or research workflows
Problem-solving practice
- BLUPs and shrinkage — BLUPs and shrinkage
- Crossed and nested random effects — Crossed and nested random effects
- GLMMs for binary and count outcomes — GLMMs for binary and count outcomes
- Laplace approximation — Laplace approximation
- Quadrature — Quadrature
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Linear mixed models
Hierarchical data
Coming soon - Generalized LMMs
GLMMs for binary and count outcomes
Coming soon - Extensions
Multilevel models for longitudinal data
Coming soon
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$1,162 · Mixed models · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle.