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

[Ebert,Timothy Aaron]

You could try writing code to write code. However, you need to tell the program which variables are factor and which are continuous. If you are lucky and all integer data are factor and all non-integers are continuous, then you can sort for that. However, in a broad data perspective this is a bad assumption.

I have (somehow) sorted the variables into factor and non-factor variables. Non-factor variables are in vars1, and factor variables are in vars2. The code might look something like this.

vars1 <- c("x1", "x2", "x3")
vars2 <- c("F1", "F2", "F3")
interactions <- as.vector(outer(vars1, vars1, function(x, y) ifelse(x < y, paste(x, y, sep = ":"), NA)))
interactions <- interactions[!is.na(interactions)]
result <- c(vars1, interactions)
result <- c(result, vars2)
formula <- as.formula(paste("y ~", paste(result, collapse = " + ")))
model <- lda(formula, data = mydata)


Tim

-----Original Message-----
From: R-help <r-help-bounces using r-project.org> On Behalf Of Stephen Bond via R-help
Sent: Monday, March 24, 2025 11:29 AM
To: Bert Gunter <bgunter.4567 using gmail.com>
Cc: r-help using r-project.org
Subject: Re: [R] how to create model matrix of second order terms

[External Email]

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
> >
> > ______________________________________________
> > R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://st/
> > at.ethz.ch%2Fmailman%2Flistinfo%2Fr-help&data=05%7C02%7Ctebert%40ufl
> > .edu%7C4e92d4943a594be971d508dd6b2270b0%7C0d4da0f84a314d76ace60a6233
> > 1e1b84%7C0%7C0%7C638784517844383573%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0
> > eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIs
> > IldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=%2FXX2ZHU5NpqeUYbjKRLzBa%2BXpGu%
> > 2F2ddcdqXfbdnUW50%3D&reserved=0
> > PLEASE do read the posting guide
> > https://ww/
> > w.r-project.org%2Fposting-guide.html&data=05%7C02%7Ctebert%40ufl.edu
> > %7C4e92d4943a594be971d508dd6b2270b0%7C0d4da0f84a314d76ace60a62331e1b
> > 84%7C0%7C0%7C638784517844402770%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1h
> > cGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldU
> > IjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=CW0bStnd5O6BPQECRuyfTJDnWXPDIZMlDIUm
> > DUoQTJc%3D&reserved=0 and provide commented, minimal,
> > self-contained, reproducible code.

______________________________________________
R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide https://www.r-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.