相互作用之间的区别：和 * StatsModels OLS 回归中公式的术语

Question

Hi I'm learning Statsmodel and can't figure out the difference between: and * (interaction terms) for formulas in StatsModels OLS regression. Could you please give me a hint to figure this out?

Thank you!

The documentation: http://statsmodels.sourceforge.net/devel/example_formulas.html

Answer 1

":" will give a regression without the level itself. just the interaction you have mentioned.

"*" will give a regression with the level itself + the interaction you have mentioned.

for example

a . GLMmodel = glm("y ~ a: b" , data = df)

you'll have only one independent variable which is the results of "a" multiply by "b"

b . GLMmodel = glm("y ~ a * b" , data = df)

you'll have 3 independent variables which is the results of "a" multiply by "b" + "a" itself + "b" itself

Answer 2

Using A*B is really just shorthand for A + B + A:B

A:B specifies the interaction itself. This is literally the product of the two variables. As such, it rarely makes sense to fit a model with only this term, so we almost always fit the main effects, A and B too (see here for reasons why). Since this is so common, the shorthand notation A*B for this is quite common in many statistical software packages/platforms.