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.
| explanatory | |||||||||
| 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 |
dose-response logistic regression |
Generalized logistic regression | |||
| ordered | ord-bin | ord-ord | b | b | b | ||||
|
nominal (>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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