Regression methods
Summary
General graduate course on regression methods
Content
Linear regression and analysis of variance. Geometric interpretation. Properties of estimators. Orthogonality and balance. Diagnostics. Transformations. Variable selection and post-selection inference. Robustness and estimating equations. Quantile regression.
PIWLS algorithm and general regression models. Generalized linear models: variance and link functions; proportion and binary responses; logistic regession; count data and Poisson responses; log-linear models; overdispersion.
Penalised regression: ridge, lasso, thresholding.
Components of variance: nested and crossed effects, mixed models. REML.
Spline smoothing, estimation and inference. Additive models. Generalised additive models.
Keywords
Binary response. Count data. Deviance. Least squares. Likelihood. Mixed model. Overdispersion. Penalised regression model. Random effects. Ridge regression.
Learning Prerequisites
Required courses
Courses on basic probability and statistics (e.g., MATH-240, MATH-230) and a first course on the linear model (e.g., MATH-341).
Important concepts to start the course
Linear regession. Likelihood inference. Use of computer package R.
Learning Outcomes
By the end of the course, the student must be able to:
- Develop elements needed in a regression analysis
- Apply the statistical package R for the analysis of data
- Assess / Evaluate the quality of a model
- Formulate a suitable regression model and assess its validity
Transversal skills
- Demonstrate the capacity for critical thinking
- Demonstrate a capacity for creativity.
- Write a scientific or technical report.
Teaching methods
Ex cathedra lectures; homework both theoretical and applied; mini-project
Expected student activities
Attending lectures; solving theoretical problems; solving applied problems using suitable software
Assessment methods
Written final exam. Mini-project.
Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.
Supervision
| Office hours | No |
| Assistants | Yes |
| Forum | Yes |
Resources
Virtual desktop infrastructure (VDI)
No
Bibliography
Davison, A. C. (2003) Statistical Models.
Ressources en bibliothèque
Notes/Handbook
See moodle page
Moodle Link
In the programs
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Regression methods
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Regression methods
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Regression methods
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Regression methods
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Regression methods
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Regression methods
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Regression methods
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: mandatory
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Regression methods
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: mandatory