Generalized linear models Outline for today
• What is a generalized linear model
• Linear predictors and link functions
• Example: estimate a proportion
• Analysis of deviance
• Example: fit dose-response data using logistic regression
• Example: fit count data using a log-linear model
• Advantages and assumptions of glm • Quasi-likelihood models when there is excessive variance Review: what is a (general) linear model A model of the following form:
Y = β0 + β1X1 + β2 X 2 + ...+ error • Y is the response variable • The X ‘s are the explanatory variables • The β ‘s are the parameters of the linear equation • The errors are normally distributed with equal variance at all values of the X variables. • Uses least squares to fit model to data, estimate parameters • lm in R The predicted Y, symbolized here by µ, is modeled as
µ = β0 + β1X1 + β2 X 2 + ...