"*" vs ":" in R for simulation

Question

I am sure that this question must have been asked, but I was not lucky to find it in the archives. In any case, I always thought that ":" or "*" mean the same thing when adding interaction conditions. For instance:

gas quantity ~ temperature * gas type gas quantity ~ temperature: gas type

However, now that I started using GLM, I see that they generate different AIC ratings, different ratings, etc. when I switch between them. Can someone explain to me why this is happening? Is this a problem with statistics package in R?

Thanks!

Answer 1

From help(formula) :

  In addition to '+' and ':', a number of other operators are useful in model formulae. The '*' operator denotes factor crossing: 'a*b' interpreted as 'a+b+a:b'.