Generalized linear models

This course introduces the general framework of linear models where we try 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), as well as 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 counts (e.g. number of individuals, number of species). Thanks to this general framework, we can then model non-normally distributed variables. The use and interpretation of logistic, binomial and Poisson regression models will be discussed in detail.

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

L-level probability, linear model, inferential statistics




Recommended prerequisites: M1 in statistics

Introduction: reminders on the linear (Gaussian) model

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

Hourly volumes:
CM: 21h
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TP:
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