Model matrix with all pairwise interactions between columns

Question

Let\'s say that I have a numeric data matrix with columns w, x, y, z and I also want to add in the columns that are equivalent to w*x, w*y, w*z, x*y, x*z,

Answer 1

If you are doing a regression, you can just do something like

reg <- lm(w ~ (x + y + z)^2

and it will figure things out for you. For example,

lm(Petal.Width ~ (Sepal.Length + Sepal.Width + Petal.Length)^2, iris)
# Call:
# lm(formula = Petal.Width ~ (Sepal.Length + Sepal.Width + Petal.Length)^2,
#     data = iris)
#      # Coefficients:
#               (Intercept)               Sepal.Length                Sepal.Width
#                  -1.05768                    0.07628                    0.22983
#              Petal.Length   Sepal.Length:Sepal.Width  Sepal.Length:Petal.Length
#                   0.47586                   -0.03863                   -0.03083
#  Sepal.Width:Petal.Length
#                   0.06493