[R] Order of formula terms in model.matrix

[Lars Bishop]

I’d appreciate your help on understanding the following. 

It is not very clear to me from the model.matrix documentation, why simply changing the order of terms in the formula may change the number of resulting columns. Please note I’m purposely not including main effects in the model formula in this case. 
 

set.seed(1)
x1 <- rnorm(100)
f1 <- factor(sample(letters[1:3], 100, replace = TRUE))
trt <- sample(c(-1,1), 100, replace = TRUE)
df <- data.frame(x1=x1, f1=f1, trt=trt)

dim(model.matrix( ~ x1:trt + f1:trt, data = df))
[1] 100 4

dim(model.matrix(~ f1:trt + x1:trt, data = df))
[1] 100 5


Thanks,
Lars.