lm() and interactions in model formula for x passed as matrix

Suppose I have x variables x1, x2, x3 (however in general I don't know
how many x variables there are). I can do
X<-cbind(x1,x2,x3)
lm(y ~ X)
This fits the no-interaction model with b0, b1, b2, b3.

How can I get lm() to fit the model that includes interactions when I
pass X to lm()? For my example,
lm(y~x1*x2*x3)
I am looking for something along the lines of
lm(y~X ...)
where ... is some extra stuff I need to fill in.

The formula syntax in R allows you to specify interactions with the  
"^" operator but some testing makes me think you cannot use either y  
~ .^3 or y ~ X^3 with matrix data arguments, here assuming you only  
want interaction up to third order.

Assuming you know how to use do.call("cbind", varlist)
perhaps:

  form = as.formula( paste("y ~ (",
                            paste(colnames(X), collapse="+"),
                              ")^3", sep="")  )
lm(form)


--- output------
Call:
lm(formula = form)

Coefficients:
(Intercept)           x1           x2           x3        x1:x2         
x1:x3
   -0.383296    -0.333429     0.003976     0.332982    -0.001130      
0.100698
       x2:x3     x1:x2:x3
    0.366745     0.122111

David Winsemius, MD
West Hartford, CT

Hi Bill,

If you can put all (and only) your variables into a dataframe, (for example:
X <- data.frame(y, x1, x2, x3)
)

then another alternative to David's solution would be:

lm(y ~ .^3, data = X)

'.' will expand to every column except y, and then the ^3 will get you
up to 3-way interactions.

Cheers,

Josh

On Sun, Dec 5, 2010 at 12:19 PM, William Simpson

Suppose I have x variables x1, x2, x3 (however in general I don't know
how many x variables there are). I can do
X<-cbind(x1,x2,x3)
lm(y ~ X)
This fits the no-interaction model with b0, b1, b2, b3.

How can I get lm() to fit the model that includes interactions when I
pass X to lm()? For my example,
lm(y~x1*x2*x3)
I am looking for something along the lines of
lm(y~X ...)
where ... is some extra stuff I need to fill in.

Thanks for any help.
Bill

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and provide commented, minimal, self-contained, reproducible code.

Joshua Wiley
Ph.D. Student, Health Psychology
University of California, Los Angeles
http://www.joshuawiley.com/

Thanks for the replies.

I was just thinking that, for a two variable example, doing
X<-cbind(x1,x2,x1*x2)
lm(y~X)
would work. So maybe that's what I'll do. This also allows me to pick
and choose which interactions to include.

Cheers
Bill

On Sun, Dec 5, 2010 at 8:19 PM, William Simpson

Suppose I have x variables x1, x2, x3 (however in general I don't know
how many x variables there are). I can do
X<-cbind(x1,x2,x3)
lm(y ~ X)
This fits the no-interaction model with b0, b1, b2, b3.

How can I get lm() to fit the model that includes interactions when I
pass X to lm()? For my example,
lm(y~x1*x2*x3)
I am looking for something along the lines of
lm(y~X ...)
where ... is some extra stuff I need to fill in.

Thanks for any help.
Bill