This course deals with a variety of statistical models and methods that generalize classical linear
regression to include many others that have been found useful in statistical analysis and applications. We
will first review key concepts in linear regression, expand the scope in depth to generalized linear
models, and then head for several important directions: linear and generalized linear mixed models,
generalized estimating equations, nonparametric regression and generalized additive models, survival
analysis, and neural networks (if time permits). The course is a mixture of theory and applications and
includes lab exercises featuring R programming.
| Week | Date | Topics | References | Assignments/Notes |
| 1 | 2/24 | Review of linear algebra | Rao et al. App. A | |
| 2 | 3/28 | Review of multivariate normal distribution | Shao Sec. 1.3 | |
| 3/3 | Prediction, nearest neighbor | UML Chap. 19 | |
| 3 | 3/10 | Curse of dimensionality, estimability in linear models | UML Sec. 19.2.2, Shao Sec. 3.3 | |
| 4 | 3/14 | Ordinary least squares, restricted estimation | Rao et al. Secs. 3.1–3.5, 5.2 | |
| 3/17 | Inference for linear models, multiple testing | Rao et al. Secs. 3.8, 3.19 | Homework 1 |
| 5 | 3/24 | Examples of generalized linear models | McCullagh & Nelder Sec. 1.2 | |
| 6 | 3/28 | One-parameter exponential families | Efron Secs. 1.1–1.4 | |
| 3/31 | Examples of one-parameter exponential families | Efron Secs. 1.5, 1.8–1.10 | |
| 7 | 4/7 | Multiparameter exponential families | Efron Chap. 2 | Homework 2 |
| 8 | 4/11 | Generalized linear models | McCullagh & Nelder Sec. 2.2 | |
| 4/14 | Goodness of fit, iteratively reweighted least squares | McCullagh & Nelder Secs. 2.3–2.5 | |
| 9 | 4/21 | Binomial regression, case-control studies | McCullagh & Nelder Sec. 4.3 | |
| 10 | 4/25 | Logistic regression, overdispersion | McCullagh & Nelder Secs. 4.4, 4.5 | |
| 4/28 | Poisson and log-linear models, gamma regression | McCullagh & Nelder Chaps. 6 & 8 | |
| 11 | No class | | | |
| 12 | 5/9 | Multinomial regression | McCullagh & Nelder Chap. 5 | |
| 5/12 | Quasi-likelihood methods | McCullagh & Nelder Chap. 9 | |
| 13 | 5/19 | Longitudinal data, generalized linear mixed models | LDA Chap. 4 | |
| 14 | 5/23 | Generalized estimating equations | LDA Chap. 3 | |
| 5/26 | Nonparametric regression | Wasserman Secs. 5.1–5.5 | |
| 15 | 6/2 | Inference, local likelihood, multiple regression | Wasserman Secs. 5.6–5.13 | Homework 3 |
| 16 | 6/6 | Survival data, Kaplan–Meier estimator | Kalbfleisch & Prentice Chap. 1 | |
| 6/9 | Cox model, partial likelihood | Kalbfleisch & Prentice Chap. 4 | |
| 6/16 | Final exam | | Mean = 54, median = 55, Q1 = 41, Q3 = 65, high score = 84
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