[R] how to create model matrix of second order terms

[Stephen Bond]

Folks,

I appreciate your effort, but maybe I was not explicit enough, so let
me try again.

The current setup for formulas does not allow for I(x^2) terms as
explained in the MASS book at the end of Section 6.2 the x:x
interaction is treated as x.

So I need to write my own code, which is clumsy unless you can refer me
to a package that already exists or give me an idea how to improve my
code. Also, writing out terms is not feasible when there are 1000
variables, so the code needs to deal with taking a wide data frame or
matrix with column names for convenience. 

Let me know your ideas :-)

On Mon, 2025-03-24 at 02:43 -0700, Bert Gunter wrote:
> Full disclosure: I did not attempt to decipher your code.
> 
> But ~(A+B +C)^2 - (A + B + C)
> gives all 2nd order interactions whether the terms are factors or
> numeric.
> 
> ~I(A^2) + I(B^2) gives quadratics in A and B, which must be numeric,
> not factors, of course
> 
> You can combine these as necessary to get a formula expression for
> just 2nd order terms. Wrapping this in model.matrix() should then
> give you the model matrix using "treatment" contrasts for the
> contrasts involving factors (you can change the contrast types using
> the 'contrasts.arg' argument of model.matrix())
> 
> 1. Does this help?
> 2. Do check this to make sure I'm correct
> 
> Cheers,
> Bert
> 
> "An educated person is one who can entertain new ideas, entertain
> others, and entertain herself."
> 
> 
> 
> On Mon, Mar 24, 2025 at 12:22 AM Stephen Bond via R-help
> <r-help using r-project.org> wrote:
> > I am sending to this forum as stackoverflow has devolved into sth
> > pretty bad.
> > Below code shows how to get what I want in a clumsy way.
> > 
> > cols <- letters[1:4]
> > a1 <- outer(cols,cols,paste0)
> > b1 <- a1[!lower.tri(a1)]
> > 
> > X <- matrix(rnorm(80),ncol=4)
> > colnames(X) <- cols
> > X <- as.data.frame(X)
> > XX <- matrix(0,nrow=nrow(X),ncol=length(b1))
> > colnames(XX) <- b1
> > 
> > for (k in 1:length(b1)){
> >     XX[,k] <- X[,substr(b1[k],1,1)]*X[,substr(b1[k],2,2)]
> > }
> > 
> > 
> > 
> > Is there a way to get that using a formula or some neat trick? The
> > above will not work for factors, so I will need to create the
> > factor
> > crossings using formula a*b*c and then cross with the numerics,
> > which
> > is even more clumsy.
> > Thanks everybody
> > 
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