MuMIn::dredge(). Exclude models only including main effect, keep only models with interactions

Question

Is it possible to make a general logical statement for subsetting away (exclude) all potential models that only include the main effect of e.g. A?

y ~ A + B + C + A:C + A:B

For models including A, only include those where A is a part of an interaction (as the relationship y~A would make no sense by itself).

Answer 1

Either !A || {A:B} || {A:C} or dc(A:B, A) && dc(A:C, A) but there is no notation for specifying "any interaction containing A".

Update: In MuMIn >= 1.42.3 (for the time being, on R-Forge) you can use the dot . pseudo-function to specify any or all interaction containing specific first-order term. For example .(A, 2:100) includes models if they contain any 2nd to 100-th order interaction terms with A. It is still experimental feature, so check if you get what you expected.

Answer 2

An inelegant solution I arrived at (after noticing how dredge() worked with poly() terms; including or excluding the entire n x power matrix, not the individual columns) was to create a little function called "int" to create a similar matrix out of two predictors and their interaction. I called the elements produced "a", "b", and "a:b" following the convention of poly(), which calls its two elements "1" and "2".

int = function(a,b){
      matOut = matrix(c(a,b,a*b),nrow=length(a))
      dimnames(matOut) =list(NULL,c("a","b","a:b"))
      return(matOut)}

Let's use the mtcars data set as an example, using "carb" instead of A, "gear" instead of B, and "am" instead of C to predict "mpg". Starting with the standard approach, we might try this.

require(MuMIn)
data(mtcars)

fm = lm(mpg ~ carb*gear + carb*am, mtcars,na.action=na.fail)
length(dredge(fm))

This produces 11 possible models with all combinations of the three linear terms and the two interaction terms.

Now, if we use int() instead of *, we see we only get four models; each interaction, their combination, and the null model. All models are excluded that contain linear terms without the interaction.

fm = lm(mpg ~ int(carb,gear) + int(carb,am), mtcars,na.action=na.fail)
length(dredge(fm))