Unit 13 : The Generalized Linear Model

It's about time!!

Remember that the "y's" in our models are also called "responses", and the X's are called "explanatory" variables.

The table below gives the statistical methodologies for various combinations of explanatory and response variables. The Generalized Linear Model groups many of these analyses into one unified statisticall approach.

response categorical nominal
(> 2 categories)
continuous mixture
binary ordered
categorical binary contingency tables
logistic regression
loglinear models
bin-ordered generalized logistic regression
log-linear models
logistic regression
Generalized logistic regression
ordered ord-bin ord-ord b b b
(>2 categories)
contingency tables
loglinear models
nom-ord Contingency tables
log-linear models
Forest plots Multilevel structure
continuous t-test conts-ord Analysis of Variance multiple regression Analysis of Covariance
Multiple regression

Abapted from Dobson An Introduction to Generalized Linear Models(see references).

In 1972, Nelder and Wedderburn showed

Nelder, John; Wedderburn, Robert (1972). "Generalized Linear Models". Journal of the Royal Statistical Society. Series A (General). Blackwell Publishing. 135 (3): 370–384. doi:10.2307/2344614.

JSTOR 2344614. S2CID 14154576.

Table above copied from McCullagh and Nelder, Generalized Linear ModelsChapman and Hall, Second edition. (see references).

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