# Coursebooks

## Modern regression methods

#### Lecturer(s) :

Davison Anthony C.

English

#### Remarque

Course given every two years (given in 2019-20)

#### Summary

A second course on regression modelling, dealing with nonlinear effects of explanatory variables, and non-normal and dependent response variables.

#### Content

Revision of linear regession and likelihood inference

Fitting algorithms for nonlinear models and related diagnostics

Generalised linear model; exponential families; variance and link functions

Proportion and binary responses; logistic regession

Count data and Poisson responses; log-linear models

Overdispersion and quasilikelihood; estimating functions

Mixed models, random effects, generalised additive models and penalized regression

#### Keywords

Binary response; Count data; Deviance; EM algorithm; Estimating function; Iterative weighted least squares algorithm; Lasso; Likelihood; Logistic regression; Longitudinal data; Mixed model; Multinomial distribution; Overdispersion; Poisson distribution; Quasi-likelihood; Random effects

#### Learning Prerequisites

##### Required courses

Knowledge of basic probability and statistics, at, for example, the levels of MATH-240 and MATH-230

Linear models (MATH-341) or equivalent

##### Important concepts to start the course

Linear regression; likelihood inference; R

#### Learning Outcomes

By the end of the course, the student must be able to:
• Develop theoretical elements needed in regression analysis
• Apply the statistical package R to the analysis of data
• Assess / Evaluate the quality of a model fitted to regression data, and suggest improvements
• Choose a suitable regression model

#### Transversal skills

• Demonstrate a capacity for creativity.
• Demonstrate the capacity for critical thinking
• Write a scientific or technical report.

#### Teaching methods

Ex cathedra lectures; homework both theoretical and practical; mini-project

#### Expected student activities

Attending lectures; solving theoretical problems; solving applied problems using statistical 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 Yes Assistants Yes Forum Yes

#### Resources

##### Bibliography

Davison, A. C. (2003) Statistical Models. Cambridge University Press.

### In the programs

• Mathematics - master program, 2019-2020, Master semester 2
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Modern regression methods
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 2
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Modern regression methods
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 4
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Modern regression methods
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Financial engineering, 2019-2020, Master semester 2
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Modern regression methods
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Financial engineering, 2019-2020, Master semester 4
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Modern regression methods
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks

### Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction
Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German