[R] In a formula, what is the interaction of the intercept and a factor?

[Prof Brian Ripley]

Try it for yourself:

> model.matrix(y ~ 1:group, data = dat)
    (Intercept)
1            1
...

Or to do

'interact "1+x" with "group"'

> model.matrix(y ~ (1+x):group, data = dat)
    (Intercept) x:groupA x:groupB
1            1        0        1
...

Note that you usually want to do '*' when you say 'interact with':
> model.matrix(y ~ (1+x)*group, data = dat)
    (Intercept)  x groupB x:groupB
1            1  1      1        1
...


On Tue, 31 May 2011, Kevin Wright wrote:

> For a pedagogical purpose, I was trying to show how the formula for a simple
> regression line (~1+x) could be crossed with a factor (~1:group + x:group)
> to fit separate regressions by group.  For example:
>
> set.seed(201108)
> dat <- data.frame(x=1:15, y=1:15+rnorm(15),
>            group = sample(c('A','B'), size=15,
>                    replace=TRUE))
>
> m1 <- lm(y~ 1 + x, data=dat)
> m2 <- lm(y ~ group + x:group, data=dat)
> m3 <- lm(y ~ 1:group + x:group, data=dat)
> m4 <- lm(y ~ 1 + x:group, data=dat)
>
> The simple regression is model m1.
>
> The usual way to write the by-group regression is model m2.
>
> In model m3 was trying to be explicitly clear and interact "1+x" with
> "group".
>
> Looking only at the coefficients, it appears that model m3 is simplified to
> model m4.
>
> R> coef(m3)
> (Intercept)    groupA:x    groupB:x
>  0.3775140   0.9213835   0.9879690
>
> R> coef(m4)
> (Intercept)    x:groupA    x:groupB
>  0.3775140   0.9213835   0.9879690
>
> I wonder if anyone can shed some light on what R is doing with the "1:group"
> term.
>
> Kevin
>
> 	[[alternative HTML version deleted]]
>
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-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595