Add offset() in as.formula(paste0(...))

Question

I need to add an offset(of variable) in an as.formula(paste0(...)) in R's glm.nb function, but I get errors using update() or unliste(offset()).

Is there a way to do it?

Here is my attempt:

z <- c("T3", "T3", "T3", "T2", "T2", "T3", "T3", "T2", "T2", "T2", "T3", "T3", "T3", "T3", "T2", "T3", "T2", "T2", "T1", "T3", "T3", "T2", "T2", "T2", "T2", "T2", "T2", "T3", "T2", "T3", "T2", "T2", "T2", "T2", "T3", "T3", "T2", "T2", "T3", "T3", "T3", "T3", "T3", "T3", "T3", "T2", "T3", "T2", "T3", "T3", "T3", "T2", "T1", "T3", "T3", "T3", "T3", "T2", "T3", "T3", "T2", "T2", "T2", "T2", "T2", "T3", "T2", "T3", "T2", "T3", "T3", "T3", "T3", "T2", "T2", "T2", "T2", "T2", "T2", "T3", "T3", "T3", "T3", "T3", "T3", "T2", "T2", "T2", "T2", "T2", "T3", "T3", "T3", "T3", "T3", "T2", "T3", "T2", "T3", "T2", "T2", "T2", "T2", "T3", "T3", "T3", "T2", "T2", "T3", "T2", "T3", "T3", "T2", "T2")
x <- c("B-", "B-", "B+", "B+", "B-", "B-", "B+", "B-", "B-", "B-", "B-", "B-", "B-", "B-", "B+", "B-", "B-", "B-", "B+", "B-", "B+", "B+", "B-", "B-", "B+", "B-", "B+", "B+", "B-", "B-", "B+", "B+", "B+", "B-", "B-", "B-", "B-", "B-", "B+", "B+", "B-", "B-", "B+", "B+", "B+", "B-", "B-", "B-", "B-", "B-", "B+", "B-", "B-", "B+", "B+", "B+", "B-", "B-", "B-", "B-", "B-", "B+", "B-", "B+", "B+", "B+", "B-", "B-", "B+", "B-", "B-", "B-", "B-", "B-", "B-", "B+", "B-", "B-", "B-", "B-", "B-", "B+", "B+", "B+", "B-", "B+", "B+", "B+", "B-", "B-", "B+", "B-", "B-", "B-", "B-", "B-", "B+", "B-", "B-", "B-", "B-", "B-", "B+", "B+", "B-", "B-", "B+", "B+", "B-", "B+", "B+", "B-", "B-", NA )
Y <- c(0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 13, 19, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 1, 0, 2, 0, 0, 6, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 10, 0, 0, 0, 0, 0, 0, 3)
y1 <- c(1, 3, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 1, 0, 5, 0, 2, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 12, 1, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 16, 0, 14, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 6, 0, 0, 1, 0, 0, 1, 13)
of <- rnorm(114,0,1)

data <- data.frame(Y, y1, z, x, of)

f1 <- "Y"
f2 <- "x * (z) + y1"
offset <- data.frame(of)

glm.nb(as.formula(paste0(f1, " ~ ", f2, " + offset(offset)")), data = data)
glm.nb(as.formula(paste0(f1, " ~ ", f2, " + offset(of)")), data = data)

And here are the errors :

> glm.nb(as.formula(paste0(f1, " ~ ", f2, " + offset(offset)")), data = data)
Error in model.frame.default(formula = as.formula(paste0(f1, " ~ ", f2,  : 
  invalid type (list) for variable 'offset(offset)'

> glm.nb(as.formula(paste0(f1, " ~ ", f2, " + offset(of)")), data = data)
Error in model.frame.default(formula = as.formula(paste0(f1, " ~ ", f2,  : 
  variable lengths differ (found for 'offset(of)')


> glm.nb(update(as.formula(paste0(f1, " ~ ", f2)), .~.- offset(of)), data = data)
Error in model.frame.default(formula = update(as.formula(paste0(f1, " ~ ",  : 
  variable lengths differ (found for 'offset(of)')


> glm.nb(update(as.formula(paste0(f1, " ~ ", f2)), .~.- offset(offset)), data = data)
Error in model.frame.default(formula = update(as.formula(paste0(f1, " ~ ",  : 
  invalid type (list) for variable 'offset(offset)'

Thank you for Help !