r - expanding factor interactions within a formula

Question

I have many formulas (of class formula or Formula) of the form y ~ a*b, where a and b are factors.

I need to write a function that takes such a formula and returns a formula with all of the terms in the interaction "spelled out." Here is an example:

fac1 <- factor(c('a', 'a', 'b', 'b'))
fac2 <- factor(c('c', 'd', 'c', 'd'))
BigFormula(formula(x ~ fac1*fac2))

where BigFormula returns formula(x ~ a + b + c + d + a:c + a:d + b:c + b:d).

Is there a simple way to do this?

(The context: I am running many commands of the form anova(mod1, mod2), where mod2 nests in mod1, and where the right-hand side of both models contains terms like fac1*fac2. The point of these commands is to calculate F-statistics. The problem is that anova treats fac1*fac2 as three variables, even though it usually represents more than three variables. (In the code above, for example, fac1*fac2 represents eight variables.) As a result, anova underestimates the number of restrictions in the nested model, and it overestimates my degrees of freedom.)

Answer 1

Look at the help for formula there may be existing things that will work for you.

For example the formula y ~ (a + b + c + d)^2 will give you all main effects and all 2 way interactions and the formula y ~ (a + b) * (c + d) gives the expansion that you show above. You can also subtract terms so y ~ a*b*c - a:b:c will not include the 3 way interaction.