Yes, I think these two are equivalent.  You ran into problems with V3:V3
because in R the form X:X is considered the same as X (see the MASS4 book
for additional info, if you have it handy).
 
In any case, you can check the models yourself by checking the corresponding
model matrices:
 
model.matrix(y~1+v2:v3)
model.matrix(y~1+I(v2*v3)
 
This will show you how the formula is interpreted to built the model matrix
for the linear model.
 
-Christos  

  _____  

From: Luke [mailto:jyzz88@gmail.com] 
Sent: Monday, April 17, 2006 11:46 AM
To: christos@silicoinsights.com
Cc: R-help@stat.math.ethz.ch
Subject: Re: [R] interaction terms in formula of lm or glm


Thanks, Christos. Another relevant question:

If  I want to include the interaction term consisting of V2 and V3 (they are
numeric vectors), should I use:

y ~ 1 + V2:V3 or y ~ 1 + I(V2*V3)

or both are good? 

-Luke


On 4/17/06, Christos Hatzis <christos@silicoinsights.com> wrote: 

If you want the quadratic term, you need to pass it as an argument in
function I():

y ~ 1 + V1 + V3 + I(V3^2)

This is documented in ?formula

-Christos

-----Original Message-----
From: r-help-bounces@stat.math.ethz.ch
[mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Luke
Sent: Monday, April 17, 2006 12:08 AM
To: R-help@stat.math.ethz.ch
Subject: [R] interaction terms in formula of lm or glm

I would like to include pairwise interaction terms for lm(). For example, I
want to include the quadratic term of variable "V3". 

> my.formula
y ~ 1 + V1 + V3 + V3:V3

> my.data
   y V1 V2  V3
1 31  1 42 140
2 32  0 43 120
3 33  0 57 150
4 34  0 55 132

> foo <- lm(my.formula, data = my.data)

> foo$coefficients
(Intercept)          V1          V3
29.47368421 -2.15789474  0.02631579

Why do the foo coefficients not include V3:V3 ?

I thought that the variable "V3:V3" has the values of squares of V3 
elements, that is,
V3:V3
140*140
120*120
....
Am I wrong?

If I specify a fouth varaible "V4" with square values of V3, and the formula
is y ~ 1 + V1 + V3 + V4, it seems that the foo will give me different in and

out-sample predictions.

-Luke

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