diff --git a/formulaic/parser/parser.py b/formulaic/parser/parser.py
index 3100c21..c0d12a6 100644
--- a/formulaic/parser/parser.py
+++ b/formulaic/parser/parser.py
@@ -228,6 +228,23 @@ def power(arg: OrderedSet[Term], power: OrderedSet[Term]) -> OrderedSet[Term]:
                 for term in itertools.product(*[arg] * int(power_term.factors[0].expr))
             )
 
+        def sub_formula(lhs, rhs):
+            def get_terms(terms):
+                return [
+                    Term(
+                        factors=[Factor(str(t) + "_hat", eval_method="lookup")],
+                        origin=t,
+                    )
+                    for t in terms
+                ]
+
+            if isinstance(lhs, Structured):
+                lhs_hat = lhs._update(root=get_terms(lhs.root))
+            else:
+                lhs_hat = get_terms(lhs)
+
+            return Structured(lhs_hat, deps=(Structured(lhs=lhs, rhs=rhs),))
+
         return [
             Operator(
                 "~",
@@ -248,6 +265,15 @@ def power(arg: OrderedSet[Term], power: OrderedSet[Term]) -> OrderedSet[Term]:
                 accepts_context=lambda context: len(context) == 0,
                 structural=True,
             ),
+            Operator(
+                "~",
+                arity=2,
+                precedence=-100,
+                associativity=None,
+                to_terms=sub_formula,
+                accepts_context=lambda context: context and context[-1] == "[",
+                structural=True,
+            ),
             Operator(
                 "|",
                 arity=2,
diff --git a/formulaic/parser/types/term.py b/formulaic/parser/types/term.py
index 1cb575d..56a388f 100644
--- a/formulaic/parser/types/term.py
+++ b/formulaic/parser/types/term.py
@@ -1,6 +1,6 @@
 from __future__ import annotations
 
-from typing import Any, Iterable, TYPE_CHECKING
+from typing import Any, Iterable, Optional, TYPE_CHECKING
 
 if TYPE_CHECKING:
     from .factor import Factor  # pragma: no cover
@@ -15,10 +15,13 @@ class Term:
 
     Attributes:
         factors: The set of factors to be multiplied to form the term.
+        origin: If this `Term` has been derived from another `Term`, for example
+            in subformulae, a reference to the original term.
     """
 
-    def __init__(self, factors: Iterable["Factor"]):
+    def __init__(self, factors: Iterable["Factor"], origin: Optional[Term] = None):
         self.factors = tuple(dict.fromkeys(factors))
+        self.origin = origin
         self._factor_key = tuple(factor.expr for factor in sorted(self.factors))
         self._hash = hash(":".join(self._factor_key))