Difference between the interaction : and * term for formulas in StatsModels OLS regression

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