[SOLVED] What does an ampersand in an lm formula do?

What does an ampersand in an lm formula do?

In a linear model (lm()) formula with R, what does the ampersand (&) do?

For example using a + give this result:

x <- 1:10 + rnorm(10)
z <- rep(c(0,4), 5) 
y <- x + z
lm(y ~ x + z)

Produces:

Call:
lm(formula = y ~ x + z)

Coefficients:
(Intercept)            x            z  
 -1.685e-15    1.000e+00    1.000e+00

And using an & gives this result.

lm(y ~ x & z)

Call:
lm(formula = y ~ x & z)

Coefficients:
(Intercept)    x & zTRUE  
      4.666        5.731

Lastly, a search for "[r] ampersand formula" on this site produced not hits, please let me know if you found an answer, what terms you used to search for.

Solution

In formula, it does nothing, just make independend variabla logical(or zero-one).

> lm(y ~ x & z)

Call:
lm(formula = y ~ x & z)

Coefficients:
(Intercept)    x & zTRUE  
      5.287        4.580

You can see x & z and as.logical(z) is identical, that x does not have 0 values, so every x is TRUE.

> x & z
 [1] FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE  TRUE
> as.logical(z)
 [1] FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE  TRUE
> as.logical(x)
 [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE



> lm(y ~ as.numeric(as.logical(z)))

Call:
lm(formula = y ~ as.numeric(as.logical(z)))

Coefficients:
              (Intercept)  as.numeric(as.logical(z))  
                    5.287                      4.580