creating a Instrument variable formula form formula object

Question

Given a formula object like:

obj1 <- formula(y~x1+x2+x3)

I want to create a formula for an instrumental variable approach ( e.g.: aer::ivreg), replacing x1 by z1.

I want to achieve obj2 <- formula(y~x1+x2+x3|z1+x2+x3) but not doing it manually (as in my original data I have more x, which I want to exchange in some estimations.)

Answer 1

Formulas are language objects. You can achieve this with computing on the language. It is useful to look at the abstract syntax tree to investigate the nested calls.

obj1 <- y~x1+x2+x3
lobstr::ast(!!obj1)
# █─`~` 
# ├─y 
# └─█─`+` 
#   ├─█─`+` 
#   │ ├─x1 
#   │ └─x2 
#   └─x3

obj2 <- y~x1+x2+x3|z1+x2+x3
lobstr::ast(!!obj2)
# █─`~` 
# ├─y 
# └─█─`|` 
#   ├─█─`+` 
#   │ ├─█─`+` 
#   │ │ ├─x1 
#   │ │ └─x2 
#   │ └─x3 
#   └─█─`+` 
#     ├─█─`+` 
#     │ ├─z1 
#     │ └─x2 
#     └─x3 

obj1[[3]] <- call("|", obj1[[3]], obj1[[3]])
obj1[[3]][[3]][[2]][[2]] <- quote(z1) #or as.name("z1")
obj1
#y ~ x1 + x2 + x3 | z1 + x2 + x3
all.equal(obj1, obj2)
#[1] TRUE

Edit:

A more general solution that crawls the call tree:

crawler <- function(e, f, r) {
  if (e == as.name(f)) return(as.name(r))
  if (length(e) == 1L) return(e)
  for (i in seq_along(e)) e[[i]] <- crawler(e[[i]], f = f, r = r)
  e
}

obj1 <- y~x1+x2+x3
obj1[[3]] <- call("|", obj1[[3]], obj1[[3]])
obj1[[3]][[3]] <- crawler(obj1[[3]][[3]], "x1", "z1")
obj1
#y ~ x1 + x2 + x3 | z1 + x2 + x3