BUG: groupby.nth should be a filter

doc/source/user_guide/groupby.rst

@@ -1354,9 +1354,14 @@ This shows the first or last n rows from each group.
 Taking the nth row of each group
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
-To select from a DataFrame or Series the nth item, use
-:meth:`~pd.core.groupby.DataFrameGroupBy.nth`. This is a reduction method, and
-will return a single row (or no row) per group if you pass an int for n:
+To select the nth item from each group, use :meth:`.DataFrameGroupBy.nth` or
+:meth:`.SeriesGroupBy.nth`. Arguments supplied can be any integer, lists of integers,
+slices, or lists of slices; see below for examples. When the nth element of a group
+does not exist an error is *not* raised; instead no corresponding rows are returned.
+
+In general this operation acts as a filtration. In certain cases it will also return
+one row per group, making it also a reduction. However because in general it can
+return zero or multiple rows per group, pandas treats it as a filtration in all cases.
 
 .. ipython:: python
 
@@ -1367,6 +1372,14 @@ will return a single row (or no row) per group if you pass an int for n:
    g.nth(-1)
    g.nth(1)
 
+If the nth element of a group does not exist, then no corresponding row is included
+in the result. In particular, if the specified ``n`` is larger than any group, the
+result will be an empty DataFrame.
+
+.. ipython:: python
+
+   g.nth(5)
+
 If you want to select the nth not-null item, use the ``dropna`` kwarg. For a DataFrame this should be either ``'any'`` or ``'all'`` just like you would pass to dropna:
 
 .. ipython:: python
@@ -1376,21 +1389,11 @@ If you want to select the nth not-null item, use the ``dropna`` kwarg. For a Dat
    g.first()
 
    # nth(-1) is the same as g.last()
-   g.nth(-1, dropna="any")  # NaNs denote group exhausted when using dropna
+   g.nth(-1, dropna="any")
    g.last()
 
    g.B.nth(0, dropna="all")
 
-As with other methods, passing ``as_index=False``, will achieve a filtration, which returns the grouped row.
-
-.. ipython:: python
-
-   df = pd.DataFrame([[1, np.nan], [1, 4], [5, 6]], columns=["A", "B"])
-   g = df.groupby("A", as_index=False)
-
-   g.nth(0)
-   g.nth(-1)
-
 You can also select multiple rows from each group by specifying multiple nth values as a list of ints.
 
 .. ipython:: python
@@ -1400,6 +1403,13 @@ You can also select multiple rows from each group by specifying multiple nth val
    # get the first, 4th, and last date index for each month
    df.groupby([df.index.year, df.index.month]).nth([0, 3, -1])
 
+You may also use a slices or lists of slices.
+
+.. ipython:: python
+
+   df.groupby([df.index.year, df.index.month]).nth[1:]
+   df.groupby([df.index.year, df.index.month]).nth[1:, :-1]
+
 Enumerate group items
 ~~~~~~~~~~~~~~~~~~~~~
 

doc/source/whatsnew/v2.0.0.rst

@@ -58,7 +58,7 @@ Notable bug fixes
 
 These are bug fixes that might have notable behavior changes.
 
-.. _whatsnew_200.notable_bug_fixes.notable_bug_fix1:
+.. _whatsnew_200.notable_bug_fixes.cumsum_cumprod_overflow:
 
 :meth:`.GroupBy.cumsum` and :meth:`.GroupBy.cumprod` overflow instead of lossy casting to float
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
@@ -88,10 +88,40 @@ We return incorrect results with the 6th value.
 
 We overflow with the 7th value, but the 6th value is still correct.
 
-.. _whatsnew_200.notable_bug_fixes.notable_bug_fix2:
+.. _whatsnew_200.notable_bug_fixes.groupby_nth_filter:
 
-notable_bug_fix2
-^^^^^^^^^^^^^^^^
+:meth:`.DataFrameGroupBy.nth` and :meth:`.SeriesGroupBy.nth` now behave as filtrations
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+In previous versions of pandas, :meth:`.DataFrameGroupBy.nth` and
+:meth:`.SeriesGroupBy.nth` acted as if they were aggregations. However, for most
+inputs ``n``, they may return either zero or multiple rows per group. This means
+that they are filtrations, similar to e.g. :meth:`.DataFrameGroupBy.head`. pandas
+now treats them as filtrations (:issue:`13666`).
+
+.. ipython:: python
+
+    df = pd.DataFrame({"a": [1, 1, 2], "b": [3, 4, 5]})
+    gb = df.groupby("a")
+
+*Old Behavior*
+
+.. code-block:: ipython
+
+    In [5]: gb.nth(n=1)
+    Out[5]:
+       b
+    a
+    1  4
+
+*New Behavior*
+
+.. ipython:: python
+
+    gb.nth(n=1)
+
+In particular, the index of the result is derived from the input by selecting
+the appropriate rows.
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_200.api_breaking:
@@ -365,7 +395,6 @@ Groupby/resample/rolling
 - Bug in :meth:`DataFrameGroupBy.sample` raises ``ValueError`` when the object is empty (:issue:`48459`)
 - Bug in :meth:`Series.groupby` raises ``ValueError`` when an entry of the index is equal to the name of the index (:issue:`48567`)
 - Bug in :meth:`DataFrameGroupBy.resample` produces inconsistent results when passing empty DataFrame (:issue:`47705`)
--
 
 Reshaping
 ^^^^^^^^^

pandas/core/groupby/base.py

@@ -40,7 +40,6 @@ class OutputKey:
         "mean",
         "median",
         "min",
-        "nth",
         "nunique",
         "prod",
         # as long as `quantile`'s signature accepts only
@@ -112,6 +111,7 @@ def maybe_normalize_deprecated_kernels(kernel) -> Literal["bfill", "ffill"]:
         "indices",
         "ndim",
         "ngroups",
+        "nth",
         "ohlc",
         "pipe",
         "plot",

pandas/core/groupby/groupby.py

@@ -3001,97 +3001,68 @@ def nth(
         ...                    'B': [np.nan, 2, 3, 4, 5]}, columns=['A', 'B'])
         >>> g = df.groupby('A')
         >>> g.nth(0)
-             B
-        A
-        1  NaN
-        2  3.0
+           A   B
+        0  1 NaN
+        2  2 3.0
         >>> g.nth(1)
-             B
-        A
-        1  2.0
-        2  5.0
+           A   B
+        1  1 2.0
+        4  2 5.0
         >>> g.nth(-1)
-             B
-        A
-        1  4.0
-        2  5.0
+           A   B
+        3  1 4.0
+        4  2 5.0
         >>> g.nth([0, 1])
-             B
-        A
-        1  NaN
-        1  2.0
-        2  3.0
-        2  5.0
+           A   B
+        0  1 NaN
+        1  1 2.0
+        2  2 3.0
+        4  2 5.0
         >>> g.nth(slice(None, -1))
-             B
-        A
-        1  NaN
-        1  2.0
-        2  3.0
+           A   B
+        0  1 NaN
+        1  1 2.0
+        2  2 3.0
 
         Index notation may also be used
 
         >>> g.nth[0, 1]
-             B
-        A
-        1  NaN
-        1  2.0
-        2  3.0
-        2  5.0
+           A   B
+        0  1 NaN
+        1  1 2.0
+        2  2 3.0
+        4  2 5.0
         >>> g.nth[:-1]
-             B
-        A
-        1  NaN
-        1  2.0
-        2  3.0
+           A   B
+        0  1 NaN
+        1  1 2.0
+        2  2 3.0
 
-        Specifying `dropna` allows count ignoring ``NaN``
+        Specifying `dropna` allows ignoring ``NaN`` values
 
         >>> g.nth(0, dropna='any')
-             B
-        A
-        1  2.0
-        2  3.0
+           A   B
+        1  1 2.0
+        2  2 3.0
 
-        NaNs denote group exhausted when using dropna
+        When the specified ``n`` is larger than any of the groups, an
+        empty DataFrame is returned
 
         >>> g.nth(3, dropna='any')
-            B
-        A
-        1 NaN
-        2 NaN
-
-        Specifying `as_index=False` in `groupby` keeps the original index.
-
-        >>> df.groupby('A', as_index=False).nth(1)
-           A    B
-        1  1  2.0
-        4  2  5.0
+        Empty DataFrame
+        Columns: [A, B]
+        Index: []
         """
         if not dropna:
-            with self._group_selection_context():
-                mask = self._make_mask_from_positional_indexer(n)
+            mask = self._make_mask_from_positional_indexer(n)
 
-                ids, _, _ = self.grouper.group_info
+            ids, _, _ = self.grouper.group_info
 
-                # Drop NA values in grouping
-                mask = mask & (ids != -1)
+            # Drop NA values in grouping
+            mask = mask & (ids != -1)
 
-                out = self._mask_selected_obj(mask)
-                if not self.as_index:
-                    return out
-
-                result_index = self.grouper.result_index
-                if self.axis == 0:
-                    out.index = result_index[ids[mask]]
-                    if not self.observed and isinstance(result_index, CategoricalIndex):
-                        out = out.reindex(result_index)
-
-                    out = self._reindex_output(out)
-                else:
-                    out.columns = result_index[ids[mask]]
-
-                return out.sort_index(axis=self.axis) if self.sort else out
+            out = self._mask_selected_obj(mask)
+            return out
 
         # dropna is truthy
         if not is_integer(n):
@@ -3108,7 +3079,6 @@ def nth(
         # old behaviour, but with all and any support for DataFrames.
         # modified in GH 7559 to have better perf
         n = cast(int, n)
-        max_len = n if n >= 0 else -1 - n
         dropped = self.obj.dropna(how=dropna, axis=self.axis)
 
         # get a new grouper for our dropped obj
@@ -3138,22 +3108,7 @@ def nth(
         grb = dropped.groupby(
             grouper, as_index=self.as_index, sort=self.sort, axis=self.axis
         )
-        sizes, result = grb.size(), grb.nth(n)
-        mask = (sizes < max_len)._values
-
-        # set the results which don't meet the criteria
-        if len(result) and mask.any():
-            result.loc[mask] = np.nan
-
-        # reset/reindex to the original groups
-        if len(self.obj) == len(dropped) or len(result) == len(
-            self.grouper.result_index
-        ):
-            result.index = self.grouper.result_index
-        else:
-            result = result.reindex(self.grouper.result_index)
-
-        return result
+        return grb.nth(n)
 
     @final
     def quantile(

pandas/tests/groupby/test_categorical.py

@@ -515,11 +515,7 @@ def test_observed_nth():
     df = DataFrame({"cat": cat, "ser": ser})
 
     result = df.groupby("cat", observed=False)["ser"].nth(0)
-
-    index = Categorical(["a", "b", "c"], categories=["a", "b", "c"])
-    expected = Series([1, np.nan, np.nan], index=index, name="ser")
-    expected.index.name = "cat"
-
+    expected = df["ser"].iloc[[0]]
     tm.assert_series_equal(result, expected)
 
 

pandas/tests/groupby/test_function.py

@@ -413,7 +413,6 @@ def test_median_empty_bins(observed):
         ("last", {"df": [{"a": 1, "b": 2}, {"a": 2, "b": 4}]}),
         ("min", {"df": [{"a": 1, "b": 1}, {"a": 2, "b": 3}]}),
         ("max", {"df": [{"a": 1, "b": 2}, {"a": 2, "b": 4}]}),
-        ("nth", {"df": [{"a": 1, "b": 2}, {"a": 2, "b": 4}], "args": [1]}),
         ("count", {"df": [{"a": 1, "b": 2}, {"a": 2, "b": 2}], "out_type": "int64"}),
     ],
 )

pandas/tests/groupby/test_grouping.py

@@ -851,6 +851,8 @@ def test_groupby_with_single_column(self):
         exp = DataFrame(index=Index(["a", "b", "s"], name="a"))
         tm.assert_frame_equal(df.groupby("a").count(), exp)
         tm.assert_frame_equal(df.groupby("a").sum(), exp)
+
+        exp = df.iloc[[3, 4, 5]]
         tm.assert_frame_equal(df.groupby("a").nth(1), exp)
 
     def test_gb_key_len_equal_axis_len(self):