Generating interaction variables in R dataframes

Question

Is there a way - other than a for loop - to generate new variables in an R dataframe, which will be all the possible 2-way interactions between the existing ones? i.e. supposing a dataframe with three numeric variables V1, V2, V3, I would like to generate the following new variables:

Inter.V1V2 (= V1 * V2) 
Inter.V1V3 (= V1 * V3)
Inter.V2V3 (= V2 * V3)

Example using for loop :

x <- read.table(textConnection('
   V1 V2 V3 V4
1  9   25   18
2  5   20   10
3  4   30   12
4  4   34   16'
), header=TRUE)

dim.init <- dim(x)[2]
for (i in 1: (dim.init - 1) ) {
        for (j in (i + 1) : (dim.init) ) {
                x[dim(x)[2] + 1]    <- x[i] * x[j]
                names(x)[dim(x)[2]] <- paste("Inter.V",i,"V",j,sep="")

        }
}

Answer 1

Here is a one liner for you that also works if you have factors:

> model.matrix(~(V1+V2+V3+V4)^2,x)
  (Intercept) V1 V2 V3 V4 V1:V2 V1:V3 V1:V4 V2:V3 V2:V4 V3:V4
1           1  1  9 25 18     9    25    18   225   162   450
2           1  2  5 20 10    10    40    20   100    50   200
3           1  3  4 30 12    12    90    36   120    48   360
4           1  4  4 34 16    16   136    64   136    64   544
attr(,"assign")
 [1]  0  1  2  3  4  5  6  7  8  9 10

Answer 2

Here you go, using combn and apply:

> x2 <- t(apply(x, 1, combn, 2, prod))

Setting the column names can be done with two paste commands:

> colnames(x2) <- paste("Inter.V", combn(1:4, 2, paste, collapse="V"), sep="")

Lastly, if you want all your variables together, just cbind them:

> x <- cbind(x, x2)
>   V1 V2 V3 V4 Inter.V1V2 Inter.V1V3 Inter.V1V4 Inter.V2V3 Inter.V2V4 Inter.V3V4
1  1  9 25 18          9         25         18        225        162        450
2  2  5 20 10         10         40         20        100         50        200
3  3  4 30 12         12         90         36        120         48        360
4  4  4 34 16         16        136         64        136         64        544

Answer 3

I think this question should be complemented with the poly/polym function, which goes futher: it generates not only interactions between the variables, but its power until the selected degree. And orthogonal iteractions, which may be very usefull.

The directly solution to the asked problem would be:

> polym(x$V1, x$V2, x$V3, x$V4, degree = 2, raw = T)
     1.0.0.0 2.0.0.0 0.1.0.0 1.1.0.0 0.2.0.0 0.0.1.0 1.0.1.0 0.1.1.0 0.0.2.0 0.0.0.1 1.0.0.1 0.1.0.1 0.0.1.1 0.0.0.2
[1,]       1       1       9       9      81      25      25     225     625      18      18     162     450     324
[2,]       2       4       5      10      25      20      40     100     400      10      20      50     200     100
[3,]       3       9       4      12      16      30      90     120     900      12      36      48     360     144
[4,]       4      16       4      16      16      34     136     136    1156      16      64      64     544     256
attr(,"degree")
 [1] 1 2 1 2 2 1 2 2 2 1 2 2 2 2

The columns 4, 7, 8, 11, 12, 13 has the requested in the question. Other columns have other kinds of interactions. If you would like to get orthogonal interactions, just set raw = FALSE.