Generalized linear models
Graduate · Statistics
Syllabus focus
Standard syllabus · Theoretical / proof-based
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.
Topics typically covered
Standard syllabus
GLM framework
- Exponential family distributions
- Link functions and linear predictors
- Iteratively reweighted least squares
- Deviance and analysis of deviance
- Quasi-likelihood for overdispersion
Common models
- Logistic regression for binomial data
- Poisson and negative binomial regression
- Gamma regression for continuous positive data
- Ordinal and multinomial models (introduction)
- Zero-inflated and hurdle models (overview)
Diagnostics and extensions
- Residuals for GLMs: Pearson and deviance
- Influence and separation in logistic regression
- Generalized additive models (introduction)
- GEE for correlated data (preview)
Theoretical / proof-based
GLM theory
- Properties of exponential families
- Canonical links and canonical parameters
- Asymptotic theory for MLE in GLMs
- Score tests and likelihood ratio in GLMs
- Information matrices and optimal designs (intro)
- Proofs of IRLS convergence (under conditions)
Additional applied practice
- Reviewing assumptions with domain experts
- Documenting analysis choices for reproducibility
- Sensitivity analyses for key modeling decisions
- Connecting results to the original research or business question
Notes
Standard graduate course following linear models. Theoretical track emphasizes derivations; standard track focuses on application and diagnostics.