Fixed effect on overlap of factors - r

Question

I'm trying to generate a model.matrix that puts dummy variables for a categorical variable if it exists in either of a pair of factors. Here is an example:
group1 <- factor(c("A","A","A","A","B",
"B","B","C","C","D"),
levels=c("A","B","C","D","E"))
group2 <- factor(c("B","C","D","E","C",
"D","E","D","E","E"),
levels=levels(group1))
set.seed(8)
val <- rnorm(10,1,.25)
control1 <- rnorm(10,2,.5)
df <- data.frame(group1,
group2,
val,
control1)
This results in 10 rows for the (5*(5-1)/2) pairs of (A,B,C,D,E):
df
group1 group2 val control1
1 A B 0.9788535 1.620103
2 A C 1.2101000 2.146025
3 A D 0.8841293 2.210699
4 A E 0.8622912 1.352755
5 B C 1.1840101 2.034643
6 B D 0.9730296 1.593481
7 B E 0.9574277 2.755427
8 C D 0.7279171 1.864196
9 C E 0.2472371 2.779127
10 D E 0.8517064 1.881325
I want to control for a fixed effect in a linear model when a particular level is in either group1 or group2. I can construct a model matrix for this:
tmp1 <- model.matrix(~ 0+group1,df)
tmp2 <- model.matrix(~ 0+group2,df)
tmp3 <- (tmp1|tmp2)*1
tmp3
group1A group1B group1C group1D group1E
1 1 1 0 0 0
2 1 0 1 0 0
3 1 0 0 1 0
4 1 0 0 0 1
5 0 1 1 0 0
6 0 1 0 1 0
7 0 1 0 0 1
8 0 0 1 1 0
9 0 0 1 0 1
10 0 0 0 1 1
A few questions:
Doing it this way does not leave me a lot of options in terms of other covariates. How can I construct such a dummy variable as represented by the model matrix tmp3 and then use it in a call to lm with other covariates such as control1?
The idea is that there is a fixed effect on whether an individual (A,B,C,D,E) is in either group1 or group2. This seems like a reasonable assumption, but I haven't found any references. Am I missing something obvious or does this have a common name in statistics?
Thanks for any help.

Answer 1

I am not sure if model.matrix does provide any options from this, but at least in your example you can reconstruct the matrix you are after without too much effort.
model_mat <- data.frame(tmp3[,-1], val = df$val, control1 = df$control1)
lm(val ~ ., data = model_mat)
You need to remove one of the dummies, I have removed A but you can of course pick any of the others as reference category.

Answer 2

Here's a solution using akrun's idea:
group1 <- factor(c("A","A","A","A","B",
"B","B","C","C","D"),
levels=c("A","B","C","D","E"))
group2 <- factor(c("B","C","D","E","C",
"D","E","D","E","E"),
levels=levels(group1))
set.seed(8)
val <- rnorm(10,1,.25)
control1 <- rnorm(10,2,.5)
df <- data.frame(group1,
group2,
val,
control1)
tmpval <- as.data.frame(Reduce('|',lapply(df[1:2], function(group) model.matrix(~0+group)))*1)
indf <- cbind(df,tmpval)
mod1 <- lm(val ~ 0+groupA+groupB+groupC+groupD+groupE,
indf)
summary(mod1)