BUG Fixing columns dropped from multi index in group by transform GH4…
…7787

- [x] closes #47787  
- [x] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [x] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [x] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

Hello @mattB1989! Thanks for updating this PR. We checked the lines you've touched for [PEP 8](https://www.python.org/dev/peps/pep-0008) issues, and found:





There are currently no PEP 8 issues detected in this Pull Request. Cheers! :beers: 

##### Comment last updated at 2022-08-16 17:05:43 UTC @github-actions pre-commit @mroeschke This is similar to #47672 but targets a different use case @rhshadrach let me know if there is anything else you'd like me to change @mattB1989 - what do you think of this:

```
def test_group_on_empty_multiindex(transformation_func):
    # GH 47787
    # Ensure empty vs non-empty frame/series gives same results
    df = DataFrame(
        data=[[1, Timestamp("today"), 3, 4]],
        columns=["col_1", "col_2", "col_3", "col_4"],
    )
    df = df.set_index(["col_1", "col_2"])
    args = get_groupby_method_args(transformation_func, df)

    result = df.iloc[:0].groupby(["col_1"]).transform(transformation_func, *args)
    expected = df.groupby(["col_1"]).transform(transformation_func, *args)[:0]
    if transformation_func in ("diff", "shift"):
        expected = expected.astype(int)
    tm.assert_equal(result, expected)

    result = df["col_3"].iloc[:0].groupby(["col_1"]).transform(transformation_func, *args)
    expected = df["col_3"].groupby(["col_1"]).transform(transformation_func, *args).iloc[:0]
    if transformation_func in ("diff", "shift"):
        expected = expected.astype(int)
    tm.assert_equal(result, expected)
``` > @mattB1989 - what do you think of this:
> 
> ```
> def test_group_on_empty_multiindex(transformation_func):
>     # GH 47787
>     # Ensure empty vs non-empty frame/series gives same results
>     df = DataFrame(
>         data=[[1, Timestamp("today"), 3, 4]],
>         columns=["col_1", "col_2", "col_3", "col_4"],
>     )
>     df = df.set_index(["col_1", "col_2"])
>     args = get_groupby_method_args(transformation_func, df)
> 
>     result = df.iloc[:0].groupby(["col_1"]).transform(transformation_func, *args)
>     expected = df.groupby(["col_1"]).transform(transformation_func, *args)[:0]
>     if transformation_func in ("diff", "shift"):
>         expected = expected.astype(int)
>     tm.assert_equal(result, expected)
> 
>     result = df["col_3"].iloc[:0].groupby(["col_1"]).transform(transformation_func, *args)
>     expected = df["col_3"].groupby(["col_1"]).transform(transformation_func, *args).iloc[:0]
>     if transformation_func in ("diff", "shift"):
>         expected = expected.astype(int)
>     tm.assert_equal(result, expected)
> ```

That's much better than what I have. Committed it now there seems to be issues unrelated with the pr - not sure if I can rerun those manually  The 32-bit tests are failing for diff and shift:

```
tm.assert_equal(result, expected)
E       AssertionError: Attributes of DataFrame.iloc[:, 0] (column name="col_3") are different
E       
E       Attribute "dtype" are different
E       [left]:  int64
E       [right]: int32
```

Can you set the dtype to be np.int64 instead. Thanks @mattB1989  Thanks for all the work here @mattB1989!