Generalized linear models

This course introduces the general framework of linear models, which seek to express a response variable as a function of a linear combination of predictors. By assuming both a specific relationship between the mean response and the predictors (link function) and a specific distribution of the random variation of the response around its mean, it is possible to represent binary data (e.g., presence/absence, mortality/survival) or count data (e.g., number of individuals, number of species). Thanks to this general framework, it is then possible to model non-normally distributed variables. The use and interpretation of logistic, binomial, and Poisson regression models will be detailed in particular.

Be able to model the relationship between a response variable, whether continuous, discrete, or categorical. Know how to implement a numerical method for estimation, testing, and diagnostics, and know how to compare and choose a model within the framework of a GLM.

Level L probabilities, linear model, inferential statistics




Recommended prerequisites: M1 in statistics

Introduction: review of the linear (Gaussian) model

• Exponential family: definition and properties
• Linear predictors and classic link functions: identity, logit, logarithm
• Estimation: likelihood equations, Fisher scores
• Logistics model and discrimination
• Counting models: binomial and Poisson
• Over- and under-dispersion models

Hours:
CM: 21 hours
TD:
TP:
Fieldwork: