Easiest way to determine if a model formula only has an intercept

Question

In R formula syntax, occasionally a user will specify a very simple model that only has an intercept, e.g.

fit = lm(Response ~ 1, data)

These models allow for simplification relative to more complex models, e.g. lm(Response ~ A + B + A:B, ...) and I would like to have an easy way to detect when the RHS of the equation only contains a 1 and no other terms. Text manipulations seem possible, but are there any other ways to do this using the R formula class or other methods?

Answer 1

The answer with terms is probably the canonical answer, but you can also use subsetting to drop the LHS of the formula and test it against ~1:

fit = lm(Response ~ 1, data=data.frame(Response=1:10))
identical(formula(fit)[-2],~1)

• This assumes a two-sided formula
• To understand the subsetting, you need to know that a two-sided formula is treated as a binary operation and stored as a parse tree of (~,Response,1): the first element is the operator, the second element is the first argument (the LHS), and the right element is the second argument (the RHS). [-2] drops the second element and makes the formula into a one-sided formula.

@G.Grothendieck offers a slightly less hacky variant (no need to know or understand the internal structure of formula objects) in the comments, using update to overwrite the response variable with 0:

identical(update(formula(fit), 0 ~ .), 0 ~ 1) 

Answer 2

The most straightforward way is

names(coef(fit))

If this only shows "(Intercept)", then you know.

---

Another way is to check "terms" object. In fact, this is lm independent. You create a formula:

f <- Response ~ 1

then terms(f) creates "terms" object. Later, lmObject inherits this.

Check out

attr(terms(fit), "intercept")
## to use formula only without actually fitting a model, do
## attr(terms(f), "intercept")

If this is 1, then you have intercept; if 0, you don't have it.

Now, check out

length(attr(terms(fit), "term.labels"))
## to use formula only without actually fitting a model, do
## attr(terms(f), "terms.labels")

If bigger than 0, you have other covariates; if 0, bingo.