Generalized Linear Models

This course introduces the general framework of linear models, in which we 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 in the response around its mean, it is possible to model binary data (e.g., presence/absence, mortality/survival) or count data (e.g., number of individuals, number of species). Using 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 discussed in detail.

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

Level L Probability, Linear Models, Inferential Statistics




Recommended prerequisites: Master’s degree (M1) in statistics

Introduction: A Review of the Linear (Gaussian) Model

• Exponential family: definition and properties
• Linear predictors and classical link functions: identity, logit, logarithm
• Estimation: likelihood equations, Fisher's scores
• Logistics Model and Discrimination
• Counting Models: Binomial and Poisson
• Overdispersion and Underdispersion Models

Hours:
Lectures: 9:00 p.m.
Tutorials:
Lab:
Fieldwork: