From 212a3f000252fd60c6dc4bbce814383193474b3a Mon Sep 17 00:00:00 2001
From: lstimpfl <leonard.stimpfle@ugent.be>
Date: Sun, 20 Oct 2024 07:32:22 +0200
Subject: [PATCH 01/12] small updates to documentation

---
 tests/test_poisson.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/tests/test_poisson.py b/tests/test_poisson.py
index 43f2b2cf..829e9027 100644
--- a/tests/test_poisson.py
+++ b/tests/test_poisson.py
@@ -53,7 +53,7 @@ def test_separation():
         ):
             fepois("Y ~ X1 + X2", data=example2, vcov="hetero", separation_check=["ir"])  # noqa: F841
 
-    # ppmlhdfe test data sets:
+    # ppmlhdfe test data sets (check readme in data/ppmlhdfe_separation_examples)
     path = os.path.dirname(os.path.abspath(__file__))
     folder = r"data/ppmlhdfe_separation_examples"
     fns = sorted([fn for fn in os.listdir(os.path.join(path, folder)) if fn.endswith(".csv")])
@@ -78,7 +78,7 @@ def test_separation():
         fml += f" ~ {' + '.join(regressors)}"
 
         if fixed_effects.empty:
-            # separation checks are currently disabled if no fixed effects are specified
+            # TODO: separation checks are currently disabled if no fixed effects are specified; enable tests once we run separation check without fixed effects
             continue
         else:
             fml += f" | {' + '.join(fixed_effects)}"

From 63a8a36cafb906a506fb47d67c7755da7ad8abe1 Mon Sep 17 00:00:00 2001
From: Alexander Fischer <alexander-fischer1801@t-online.de>
Date: Sun, 20 Oct 2024 15:26:46 +0200
Subject: [PATCH 02/12] rename example1 -> df

---
 tests/test_poisson.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tests/test_poisson.py b/tests/test_poisson.py
index 1003eb70..174ed51b 100644
--- a/tests/test_poisson.py
+++ b/tests/test_poisson.py
@@ -31,7 +31,7 @@ def test_separation():
     with pytest.warns(
         UserWarning, match="2 observations removed because of separation."
     ):
-        fepois("Y ~ X  | fe1", data=example1, vcov="hetero", separation_check=["fe"])  # noqa: F841
+        fepois("Y ~ X  | fe1", data=df, vcov="hetero", separation_check=["fe"])  # noqa: F841
 
     if False:
         # this example is taken from ppmlhdfe's primer on separation https://github.com/sergiocorreia/ppmlhdfe/blob/master/guides/separation_primer.md

From a62b03345c7cea6ab942078ce2e65392b7a12f47 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 20 Oct 2024 13:29:50 +0000
Subject: [PATCH 03/12] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 tests/test_poisson.py | 14 ++++++++++----
 1 file changed, 10 insertions(+), 4 deletions(-)

diff --git a/tests/test_poisson.py b/tests/test_poisson.py
index 174ed51b..4668204c 100644
--- a/tests/test_poisson.py
+++ b/tests/test_poisson.py
@@ -52,7 +52,9 @@ def test_separation():
     # ppmlhdfe test data sets (check readme in data/ppmlhdfe_separation_examples)
     path = os.path.dirname(os.path.abspath(__file__))
     folder = r"data/ppmlhdfe_separation_examples"
-    fns = sorted([fn for fn in os.listdir(os.path.join(path, folder)) if fn.endswith(".csv")])
+    fns = sorted(
+        [fn for fn in os.listdir(os.path.join(path, folder)) if fn.endswith(".csv")]
+    )
     for fn in fns:
         if fn == "07.csv":
             # this case fails but is not tested in ppmlhdfe
@@ -61,9 +63,13 @@ def test_separation():
         data = pd.read_csv(os.path.join(path, folder, fn))
         # build formula dynamically from dataframe
         # datasets have fixed structure of the form (y, x1, ..., xN, id1, ..., idM, separated)
-        fml = "y"   # dependent variable y
-        regressors = data.columns[data.columns.str.startswith("x")]  # regressors x1,...,xN
-        fixed_effects = data.columns[data.columns.str.startswith("id")]  # fixed effects id1,...,id2
+        fml = "y"  # dependent variable y
+        regressors = data.columns[
+            data.columns.str.startswith("x")
+        ]  # regressors x1,...,xN
+        fixed_effects = data.columns[
+            data.columns.str.startswith("id")
+        ]  # fixed effects id1,...,id2
         if data.separated.sum() == 0:
             # TODO: do not skip but update pytest.warn to confirm that no warning is produced
             continue

From d30205fcec9a2e50bb0d0fb8477fc91fa04f62fe Mon Sep 17 00:00:00 2001
From: Alexander Fischer <alexander-fischer1801@t-online.de>
Date: Sun, 20 Oct 2024 15:33:34 +0200
Subject: [PATCH 04/12] add import os

---
 tests/test_poisson.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/tests/test_poisson.py b/tests/test_poisson.py
index 4668204c..b2341786 100644
--- a/tests/test_poisson.py
+++ b/tests/test_poisson.py
@@ -1,3 +1,4 @@
+import os
 import numpy as np
 import pandas as pd
 import pytest

From 2307df820a1c5acf30d6f064ad5e347dcd3b2af6 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 20 Oct 2024 13:34:16 +0000
Subject: [PATCH 05/12] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 tests/test_poisson.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/tests/test_poisson.py b/tests/test_poisson.py
index b2341786..ae8ca42d 100644
--- a/tests/test_poisson.py
+++ b/tests/test_poisson.py
@@ -1,4 +1,5 @@
 import os
+
 import numpy as np
 import pandas as pd
 import pytest

From 29143a796143197999ac23c62b236443dfcb2ad7 Mon Sep 17 00:00:00 2001
From: lstimpfl <leonard.stimpfle@ugent.be>
Date: Mon, 21 Oct 2024 07:44:50 +0200
Subject: [PATCH 06/12] fix bug after merge

---
 tests/test_poisson.py | 18 ++++++++++--------
 1 file changed, 10 insertions(+), 8 deletions(-)

diff --git a/tests/test_poisson.py b/tests/test_poisson.py
index ae8ca42d..e059c242 100644
--- a/tests/test_poisson.py
+++ b/tests/test_poisson.py
@@ -23,21 +23,23 @@
 
 def test_separation():
     """Test separation detection."""
-    y = np.array([0, 0, 0, 1, 2, 3])
-    df1 = np.array(["a", "a", "b", "b", "b", "c"])
-    df2 = np.array(["c", "c", "d", "d", "d", "e"])
-    x = np.random.normal(0, 1, 6)
-
-    df = pd.DataFrame({"Y": y, "fe1": df1, "fe2": df2, "x": x})
-
+    example1 = pd.DataFrame.from_dict(
+        {
+            "Y": [0, 0, 0, 1, 2, 3],
+            "fe1": ["a", "a", "b", "b", "b", "c"],
+            "fe2": ["c", "c", "d", "d", "d", "e"],
+            "X": np.random.normal(0, 1, 6)
+        }
+    )
     with pytest.warns(
         UserWarning, match="2 observations removed because of separation."
     ):
-        fepois("Y ~ X  | fe1", data=df, vcov="hetero", separation_check=["fe"])  # noqa: F841
+        fepois("Y ~ X  | fe1", data=example1, vcov="hetero", separation_check=["fe"])  # noqa: F841
 
     if False:
         # this example is taken from ppmlhdfe's primer on separation https://github.com/sergiocorreia/ppmlhdfe/blob/master/guides/separation_primer.md
         # disabled because we currently do not perform separation checks if no fixed effects are provided
+        # TODO: enable once separation checks without fixed effects are enabled
         example2 = pd.DataFrame.from_dict(
             {
                 "Y": [0, 0, 0, 1, 2, 3],

From 3261c6ec274c326ce9c5db0ea0d30ca0ce26e02b Mon Sep 17 00:00:00 2001
From: lstimpfl <leonard.stimpfle@ugent.be>
Date: Mon, 21 Oct 2024 07:59:28 +0200
Subject: [PATCH 07/12] add updates to separation checks back in

---
 pyfixest/estimation/fepois_.py | 233 +++++++++++++++++++++++++++++++--
 1 file changed, 222 insertions(+), 11 deletions(-)

diff --git a/pyfixest/estimation/fepois_.py b/pyfixest/estimation/fepois_.py
index 22c98f4d..687a36c3 100644
--- a/pyfixest/estimation/fepois_.py
+++ b/pyfixest/estimation/fepois_.py
@@ -1,5 +1,6 @@
 import warnings
-from typing import Optional, Union
+from importlib import import_module
+from typing import Optional, Protocol, Union
 
 import numpy as np
 import pandas as pd
@@ -83,6 +84,7 @@ def __init__(
         lean: bool = False,
         sample_split_var: Optional[str] = None,
         sample_split_value: Optional[Union[str, int]] = None,
+        separation_check: Optional[list[str]] = None,
     ):
         super().__init__(
             FixestFormula,
@@ -110,6 +112,7 @@ def __init__(
         self.tol = tol
         self._method = "fepois"
         self.convergence = False
+        self.separation_check = separation_check
 
         self._support_crv3_inference = True
         self._support_iid_inference = True
@@ -133,12 +136,19 @@ def prepare_model_matrix(self):
 
         # check for separation
         na_separation: list[int] = []
-        if self._fe is not None:
-            na_separation = _check_for_separation(Y=self._Y, fe=self._fe)
-            if na_separation:
-                warnings.warn(
-                    f"{str(len(na_separation))} observations removed because of separation."
-                )
+        if (
+                self._fe is not None
+                and self.separation_check is not None
+                and self.separation_check  # not an empty list
+        ):
+            na_separation = _check_for_separation(
+                Y=self._Y,
+                X=self._X,
+                fe=self._fe,
+                fml=self._fml,
+                data=self._data,
+                methods=self.separation_check,
+            )
 
         if na_separation:
             self._Y.drop(na_separation, axis=0, inplace=True)
@@ -405,27 +415,127 @@ def predict(
             raise ValueError("type must be one of 'response' or 'link'.")
 
 
-def _check_for_separation(Y: pd.DataFrame, fe: pd.DataFrame) -> list[int]:
+def _check_for_separation(
+    fml: str,
+    data: pd.DataFrame,
+    Y: pd.DataFrame,
+    X: pd.DataFrame,
+    fe: pd.DataFrame,
+    methods: Optional[list[str]] = None,
+) -> list[int]:
     """
     Check for separation.
 
     Check for separation of Poisson Regression. For details, see the ppmlhdfe
-    documentation on separation checks. Currently, only the "fe" check is implemented.
+    documentation on separation checks.
 
     Parameters
     ----------
+    fml : str
+        The formula used for estimation.
+    data : pd.DataFrame
+        The data used for estimation.
     Y : pd.DataFrame
         Dependent variable.
+    X : pd.DataFrame
+        Independent variables.
     fe : pd.DataFrame
         Fixed effects.
+    methods: list[str], optional
+        Methods used to check for separation. One of fixed effects ("fe") or
+        iterative rectifier ("ir"). Executes all methods by default.
 
     Returns
     -------
     list
         List of indices of observations that are removed due to separation.
     """
+    valid_methods: dict[str, _SeparationMethod] = {
+        "fe": _check_for_separation_fe,
+        "ir": _check_for_separation_ir,
+    }
+    if methods is None:
+        methods = list(valid_methods)
+
+    invalid_methods = [method for method in methods if method not in valid_methods]
+    if invalid_methods:
+        raise ValueError(
+            f"Invalid separation method. Expecting {list(valid_methods)}. Received {invalid_methods}"
+        )
+
     separation_na: set[int] = set()
-    if not (Y > 0).all(axis=0).all():
+    for method in methods:
+        separation_na = separation_na.union(
+            valid_methods[method](fml=fml, data=data, Y=Y, X=X, fe=fe)
+        )
+
+    if separation_na:
+        warnings.warn(
+            f"{str(len(separation_na))} observations removed because of separation."
+        )
+
+    return list(separation_na)
+
+
+class _SeparationMethod(Protocol):
+    def __call__(
+        self,
+        fml: str,
+        data: pd.DataFrame,
+        Y: pd.DataFrame,
+        X: pd.DataFrame,
+        fe: pd.DataFrame,
+    ) -> set[int]:
+        """
+        Check for separation.
+
+        Parameters
+        ----------
+        fml : str
+            The formula used for estimation.
+        data : pd.DataFrame
+            The data used for estimation.
+        Y : pd.DataFrame
+            Dependent variable.
+        X : pd.DataFrame
+            Independent variables.
+        fe : pd.DataFrame
+            Fixed effects.
+
+        Returns
+        -------
+        set
+            Set of indices of separated observations.
+        """
+        ...
+
+
+def _check_for_separation_fe(
+    fml: str, data: pd.DataFrame, Y: pd.DataFrame, X: pd.DataFrame, fe: pd.DataFrame
+) -> set[int]:
+    """
+    Check for separation using the "fe" check.
+
+    Parameters
+    ----------
+    fml : str
+        The formula used for estimation.
+    data : pd.DataFrame
+        The data used for estimation.
+    Y : pd.DataFrame
+        Dependent variable.
+    X : pd.DataFrame
+        Independent variables.
+    fe : pd.DataFrame
+        Fixed effects.
+
+    Returns
+    -------
+    set
+        Set of indices of separated observations.
+    """
+    separation_na: set[int] = set()
+    if fe is not None and not (Y > 0).all(axis=0).all():
         Y_help = (Y > 0).astype(int).squeeze()
 
         # loop over all elements of fe
@@ -446,7 +556,108 @@ def _check_for_separation(Y: pd.DataFrame, fe: pd.DataFrame) -> list[int]:
                 dropset = set(fe[x][fe_in_droplist].index)
                 separation_na = separation_na.union(dropset)
 
-    return list(separation_na)
+    return separation_na
+
+
+def _check_for_separation_ir(
+    fml: str,
+    data: pd.DataFrame,
+    Y: pd.DataFrame,
+    X: pd.DataFrame,
+    fe: pd.DataFrame,
+    tol: float = 1e-4,
+    maxiter: int = 100,
+) -> set[int]:
+    """
+    Check for separation using the "iterative rectifier" algorithm
+    proposed by Correia et al. (2021). For details see http://arxiv.org/abs/1903.01633.
+
+    Parameters
+    ----------
+    fml : str
+        The formula used for estimation.
+    data : pd.DataFrame
+        The data used for estimation.
+    Y : pd.DataFrame
+        Dependent variable.
+    X : pd.DataFrame
+        Independent variables.
+    fe : pd.DataFrame
+        Fixed effects.
+    tol : float
+        Tolerance to detect separated observation. Defaults to 1e-4.
+    maxiter : int
+        Maximum number of iterations. Defaults to 100.
+
+    Returns
+    -------
+    set
+        Set of indices of separated observations.
+    """
+    # lazy load to avoid circular import
+    fixest_module = import_module("pyfixest.estimation")
+    feols = getattr(fixest_module, "feols")
+    # initialize
+    separation_na: set[int] = set()
+    tmp_suffix = "_separationTmp"
+    # build formula
+    name_dependent, rest = fml.split("~")
+    name_dependent_separation = "U"
+    if name_dependent_separation in data.columns:
+        name_dependent_separation += tmp_suffix
+
+    fml_separation = f"{name_dependent_separation} ~ {rest}"
+
+    dependent: pd.Series = data[name_dependent]
+    is_interior = dependent > 0
+    if is_interior.all():
+        # no boundary sample, can exit
+        return separation_na
+
+    # initialize variables
+    tmp: pd.DataFrame = pd.DataFrame(index=data.index)
+    tmp["U"] = (dependent == 0).astype(float).rename("U")
+    # weights
+    N0 = (dependent > 0).sum()
+    K = N0 / tol**2
+    tmp["omega"] = pd.Series(
+        np.where(dependent > 0, K, 1), name="omega", index=data.index
+    )
+    # combine data
+    # TODO: avoid create new object?
+    tmp = data.join(tmp, how="left", validate="one_to_one", rsuffix=tmp_suffix)
+    # TODO: need to ensure that join doesn't create duplicated columns
+    # assert not tmp.columns.duplicated().any()
+
+    iteration = 0
+    has_converged = False
+    while iteration < maxiter:
+        iteration += 1
+        # regress U on X
+        # TODO: check acceleration in ppmlhdfe's implementation: https://github.com/sergiocorreia/ppmlhdfe/blob/master/src/ppmlhdfe_separation_relu.mata#L135
+        fitted = feols(fml_separation, data=tmp, weights="omega")
+        tmp["Uhat"] = pd.Series(fitted.predict(), index=fitted._data.index, name="Uhat")
+        Uhat = tmp["Uhat"]
+        # update when within tolerance of zero
+        # need to be more strict below zero to avoid false positives
+        within_zero = (Uhat > -0.1 * tol) & (Uhat < tol)
+        Uhat.where(~(is_interior | within_zero.fillna(True)), 0, inplace=True)
+        if (Uhat >= 0).all():
+            # all separated observations have been identified
+            has_converged = True
+            break
+        tmp.loc[~is_interior, "U"] = np.fmax(
+            Uhat[~is_interior], 0
+        )  # rectified linear unit (ReLU)
+
+    if has_converged:
+        separation_na = set(dependent[Uhat > 0].index)
+    else:
+        warnings.warn(
+            "iterative rectivier separation check: maximum number of iterations reached before convergence"
+        )
+
+    return separation_na
 
 
 def _fepois_input_checks(drop_singletons: bool, tol: float, maxiter: int):

From a481bc8efff42eb3edcaa2a089908924d8f6539d Mon Sep 17 00:00:00 2001
From: lstimpfl <leonard.stimpfle@ugent.be>
Date: Mon, 21 Oct 2024 08:17:17 +0200
Subject: [PATCH 08/12] add separation_cheks kwarg back in

---
 pyfixest/estimation/FixestMulti_.py | 10 ++++++++++
 pyfixest/estimation/estimation.py   | 19 +++++++++++++++++++
 2 files changed, 29 insertions(+)

diff --git a/pyfixest/estimation/FixestMulti_.py b/pyfixest/estimation/FixestMulti_.py
index 8d62e91e..004e2dc7 100644
--- a/pyfixest/estimation/FixestMulti_.py
+++ b/pyfixest/estimation/FixestMulti_.py
@@ -28,6 +28,7 @@ def __init__(
         seed: Optional[int],
         split: Optional[str],
         fsplit: Optional[str],
+        separation_check: Optional[list[str]] = None,
     ) -> None:
         """
         Initialize a class for multiple fixed effect estimations.
@@ -57,6 +58,9 @@ def __init__(
         seed : Optional[int]
             Option to provide a random seed. Default is None.
             Only relevant for wild cluster bootstrap for use_compression=True.
+        separation_check: list[str], optional
+            Only used in "fepois". Methods to identify and drop separated observations.
+            Either "fe" or "ir". Executes both by default.
 
         Returns
         -------
@@ -70,6 +74,7 @@ def __init__(
         self._use_compression = use_compression
         self._reps = reps if use_compression else None
         self._seed = seed if use_compression else None
+        self._separation_check = separation_check
 
         self._run_split = split is not None or fsplit is not None
         self._run_full = not (split and not fsplit)
@@ -185,6 +190,7 @@ def _estimate_all_models(
         collin_tol: float = 1e-6,
         iwls_maxiter: int = 25,
         iwls_tol: float = 1e-08,
+        separation_check: Optional[list[str]] = None,
     ) -> None:
         """
         Estimate multiple regression models.
@@ -205,6 +211,9 @@ def _estimate_all_models(
         iwls_tol : float, optional
             The tolerance level for the IWLS algorithm. Default is 1e-8.
             Only relevant for non-linear estimation strategies.
+        separation_check: list[str], optional
+            Only used in "fepois". Methods to identify and drop separated observations.
+            Either "fe" or "ir". Executes both by default.
 
         Returns
         -------
@@ -312,6 +321,7 @@ def _estimate_all_models(
                             lean=_lean,
                             sample_split_value=sample_split_value,
                             sample_split_var=_splitvar,
+                            separation_check=separation_check,
                             # solver=_solver
                         )
                         FIT.prepare_model_matrix()
diff --git a/pyfixest/estimation/estimation.py b/pyfixest/estimation/estimation.py
index ed3b3827..b6e05c0d 100644
--- a/pyfixest/estimation/estimation.py
+++ b/pyfixest/estimation/estimation.py
@@ -414,6 +414,7 @@ def fepois(
     iwls_tol: float = 1e-08,
     iwls_maxiter: int = 25,
     collin_tol: float = 1e-10,
+    separation_check: Optional[list[str]] = ["fe"],
     drop_intercept: bool = False,
     i_ref1=None,
     copy_data: bool = True,
@@ -465,6 +466,10 @@ def fepois(
     collin_tol : float, optional
         Tolerance for collinearity check, by default 1e-10.
 
+    separation_check: list[str], optional
+        Methods to identify and drop separated observations.
+        Either "fe" or "ir". Executes "fe" by default.
+
     drop_intercept : bool, optional
         Whether to drop the intercept from the model, by default False.
 
@@ -559,6 +564,7 @@ def fepois(
         seed=None,
         split=split,
         fsplit=fsplit,
+        separation_check=separation_check,
     )
 
     fixest = FixestMulti(
@@ -588,6 +594,7 @@ def fepois(
         iwls_tol=iwls_tol,
         iwls_maxiter=iwls_maxiter,
         collin_tol=collin_tol,
+        separation_check=separation_check,
     )
 
     if fixest._is_multiple_estimation:
@@ -614,6 +621,7 @@ def _estimation_input_checks(
     seed: Optional[int],
     split: Optional[str],
     fsplit: Optional[str],
+    separation_check: Optional[list[str]] = None,
 ):
     if not isinstance(fml, str):
         raise TypeError("fml must be a string")
@@ -715,3 +723,14 @@ def _estimation_input_checks(
 
     if isinstance(fsplit, str) and fsplit not in data.columns:
         raise KeyError(f"Column '{fsplit}' not found in data.")
+
+    if separation_check is not None:
+        if not isinstance(separation_check, list):
+            raise TypeError(
+                "The function argument `separation_check` must be of type list."
+            )
+
+        if not all(x in ["fe", "ir"] for x in separation_check):
+            raise ValueError(
+                "The function argument `separation_check` must be a list of strings containing 'fe' and/or 'ir'."
+            )

From 0990d5bc545ead4731b5b238f5e4cb94f998e5ca Mon Sep 17 00:00:00 2001
From: lstimpfl <leonard.stimpfle@ugent.be>
Date: Mon, 21 Oct 2024 08:19:12 +0200
Subject: [PATCH 09/12] add ppmlhdfe_separation_examples

---
 .../data/ppmlhdfe_separation_examples/01.csv  | 101 +++++
 .../data/ppmlhdfe_separation_examples/02.csv  |   6 +
 .../data/ppmlhdfe_separation_examples/03.csv  |  17 +
 .../data/ppmlhdfe_separation_examples/04.csv  | 101 +++++
 .../data/ppmlhdfe_separation_examples/05.csv  |  10 +
 .../data/ppmlhdfe_separation_examples/06.csv  |  12 +
 .../data/ppmlhdfe_separation_examples/07.csv  |  19 +
 .../data/ppmlhdfe_separation_examples/08.csv  |  10 +
 .../data/ppmlhdfe_separation_examples/09.csv  |   8 +
 .../data/ppmlhdfe_separation_examples/10.csv  |  11 +
 .../data/ppmlhdfe_separation_examples/11.csv  | 359 ++++++++++++++++++
 .../data/ppmlhdfe_separation_examples/12.csv  |  19 +
 .../data/ppmlhdfe_separation_examples/13.csv  |  19 +
 .../data/ppmlhdfe_separation_examples/14.csv  |  15 +
 .../data/ppmlhdfe_separation_examples/15.csv  |  24 ++
 .../data/ppmlhdfe_separation_examples/16.csv  | 101 +++++
 .../data/ppmlhdfe_separation_examples/17.csv  | 101 +++++
 .../data/ppmlhdfe_separation_examples/18.csv  | 101 +++++
 .../ppmlhdfe_separation_examples/readme.md    |   4 +
 19 files changed, 1038 insertions(+)
 create mode 100644 tests/data/ppmlhdfe_separation_examples/01.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/02.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/03.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/04.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/05.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/06.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/07.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/08.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/09.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/10.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/11.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/12.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/13.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/14.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/15.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/16.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/17.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/18.csv
 create mode 100644 tests/data/ppmlhdfe_separation_examples/readme.md

diff --git a/tests/data/ppmlhdfe_separation_examples/01.csv b/tests/data/ppmlhdfe_separation_examples/01.csv
new file mode 100644
index 00000000..0639065c
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/01.csv
@@ -0,0 +1,101 @@
+y,x1,x2,id1,id2,separated
+0.0000000000,-0.9303550124,1,1,4,1
+0.0000000000,0.1835959703,1,2,1,1
+0.0000000000,-0.6371972561,0,2,6,0
+0.0000000000,-0.4237562418,0,2,7,0
+0.1527670026,-1.1799178123,0,8,4,0
+0.1553160399,0.8860545158,0,1,7,0
+0.1734523475,1.0502026081,0,8,3,0
+0.2217264324,-0.2490162849,0,9,1,0
+0.2260344625,0.9635434151,0,7,6,0
+0.2283350676,0.5023207068,0,3,5,0
+0.2368061543,0.9141282439,0,10,1,0
+0.2410950512,-1.3616287708,0,4,5,0
+0.2541858852,0.5753656030,0,3,3,0
+0.2637400925,-0.6333113909,0,3,10,0
+0.2677916288,1.0411013365,0,6,9,0
+0.2768439949,-1.1694648266,0,8,10,0
+0.2934476137,-0.7940499187,0,4,6,0
+0.3290584087,0.5041465163,0,2,4,0
+0.3606268466,-3.0584282875,0,3,8,0
+0.4013363719,0.6099517941,0,7,5,0
+0.4354907870,0.9624704719,0,6,1,0
+0.4908127189,-0.7442333698,0,5,2,0
+0.4976674914,-0.5138924718,0,6,4,0
+0.5012444854,-1.3591595888,0,9,7,0
+0.5456602573,0.0567612983,0,5,5,0
+0.5634447336,1.2903038263,0,7,8,0
+0.5983847380,-0.6872945428,0,6,5,0
+0.6183075905,0.7253564000,0,1,5,0
+0.6413634419,1.6118478775,0,4,3,0
+0.6482065916,1.2488127947,0,7,1,0
+0.6522977948,-0.4748489261,0,6,6,0
+0.6631931663,0.4219789803,0,4,8,0
+0.6953295469,-1.0251801014,0,10,6,0
+0.6986964941,-0.3038678169,0,9,9,0
+0.8503285050,1.8723217249,0,8,2,0
+0.9026033878,-1.0245078802,0,10,10,0
+0.9204394221,0.4229967892,0,6,10,0
+0.9228412509,0.4940861166,0,1,1,0
+0.9359286427,1.3081433773,0,9,2,0
+0.9685080647,1.2934249640,0,2,10,0
+0.9945486188,-0.5332730412,0,5,1,0
+1.0105472803,-0.1284428090,0,9,3,0
+1.0721468925,-1.5399883986,0,6,8,0
+1.1205748320,0.6894677877,0,8,5,0
+1.1252909899,-1.2204582691,0,1,10,0
+1.1561176777,-0.9787744284,0,9,8,0
+1.1946246624,-0.0799055845,0,10,8,0
+1.2046658993,-0.8231971860,0,6,7,0
+1.2189750671,0.5437637568,0,3,4,0
+1.2277959585,1.3177309036,0,9,10,0
+1.2413842678,0.6673717499,0,8,9,0
+1.2569460869,-0.0167010967,0,6,3,0
+1.2587834597,-0.4196293950,0,1,8,0
+1.2782599926,-0.6420007348,0,8,1,0
+1.2911227942,1.1136496067,0,9,4,0
+1.2973045111,-0.3824758530,0,7,9,0
+1.3675237894,1.2361305952,0,5,9,0
+1.3778325319,-1.0304020643,0,5,4,0
+1.3857760429,0.3235974312,0,2,3,0
+1.3960508108,-0.4157371819,0,2,5,0
+1.4190907478,0.9920675159,0,1,2,0
+1.4420653582,-0.9114651084,0,4,1,0
+1.5038720369,-1.0453398228,0,3,2,0
+1.5394419432,-0.1935533732,0,4,4,0
+1.5747014284,0.0698969364,0,9,6,0
+1.6199581623,1.3169367313,0,4,2,0
+1.6392902136,-0.3978092670,0,7,10,0
+1.6421631575,-0.7466211319,0,5,8,0
+1.6952790022,-0.0158907417,0,5,6,0
+1.7640979290,1.0598815680,0,7,4,0
+1.9505974054,0.0092241317,0,10,7,0
+2.0685675144,0.1434842199,0,8,8,0
+2.1190843582,0.6173521280,0,3,1,0
+2.1889939308,-1.9780639410,0,3,7,0
+2.2176725864,-1.5379956961,0,7,3,0
+2.2831020355,0.5082080960,0,2,2,0
+2.3055832386,1.0296376944,0,7,2,0
+2.3692295551,2.1091823578,0,10,2,0
+2.7510018349,0.2632481158,0,2,9,0
+2.7675759792,-0.0022486539,0,8,6,0
+2.7777233124,-1.3771806955,0,10,4,0
+2.7846245766,0.1415781677,0,10,5,0
+2.7860391140,-2.2442505360,0,4,9,0
+2.9671635628,0.2927849889,0,5,3,0
+2.9819300175,-0.8325243592,0,4,10,0
+3.1186814308,-0.4090226293,0,2,8,0
+3.2802021503,-0.4062994719,0,4,7,0
+3.4179122448,0.0959109142,0,8,7,0
+3.6803083420,2.3073217869,0,1,9,0
+3.7194297314,0.3930145800,0,3,9,0
+3.7777581215,0.2952103019,0,6,2,0
+4.1290211678,-1.4121559858,0,5,7,0
+4.2730326653,-0.5140260458,0,10,9,0
+4.2883334160,-1.0160779953,0,7,7,0
+4.3528537750,0.7201576829,0,10,3,0
+4.9981565475,0.2207358032,0,3,6,0
+5.0979351997,0.7166025043,0,9,5,0
+7.3969793320,2.1998977661,0,5,10,0
+8.4651517868,0.1178035960,0,1,6,0
+9.8326959610,0.7707119584,0,1,3,0
diff --git a/tests/data/ppmlhdfe_separation_examples/02.csv b/tests/data/ppmlhdfe_separation_examples/02.csv
new file mode 100644
index 00000000..a7823886
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/02.csv
@@ -0,0 +1,6 @@
+y,id1,id2,separated
+0,1,1,0
+1,1,1,0
+0,2,1,1
+0,2,2,0
+1,2,2,0
diff --git a/tests/data/ppmlhdfe_separation_examples/03.csv b/tests/data/ppmlhdfe_separation_examples/03.csv
new file mode 100644
index 00000000..0592255b
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/03.csv
@@ -0,0 +1,17 @@
+y,id1,id2,id3,separated
+0,5,3,6,1
+0,5,5,7,1
+1,1,3,1,0
+1,1,5,2,0
+1,2,4,1,0
+1,2,6,2,0
+1,3,1,3,0
+1,3,7,4,0
+1,4,2,3,0
+1,4,8,4,0
+1,5,1,5,0
+1,5,7,8,0
+1,6,2,5,0
+1,6,4,6,0
+1,6,6,7,0
+1,6,8,8,0
diff --git a/tests/data/ppmlhdfe_separation_examples/04.csv b/tests/data/ppmlhdfe_separation_examples/04.csv
new file mode 100644
index 00000000..6cf9a107
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/04.csv
@@ -0,0 +1,101 @@
+y,id1,id2,separated
+0,1,1,1
+0,1,1,1
+0,1,34,1
+0,2,1,1
+0,2,2,1
+0,2,2,1
+0,3,3,1
+0,3,3,1
+0,4,3,1
+0,5,4,1
+0,5,5,1
+0,5,5,1
+0,6,5,1
+0,6,6,0
+0,7,6,1
+0,7,7,0
+0,8,7,1
+0,8,8,1
+0,8,8,1
+0,9,8,1
+0,9,9,1
+0,9,9,1
+0,10,10,1
+0,10,10,1
+0,11,10,1
+0,11,11,1
+0,11,11,1
+0,12,11,1
+0,12,12,1
+0,12,12,1
+0,13,12,1
+0,13,13,1
+0,13,13,1
+0,14,13,1
+0,14,14,1
+0,14,14,1
+0,15,14,1
+0,15,15,1
+0,15,15,1
+0,16,15,1
+0,16,16,1
+0,16,16,1
+0,17,16,1
+0,17,17,1
+0,17,17,1
+0,18,17,1
+0,18,18,0
+0,19,18,1
+0,19,19,1
+0,19,19,1
+0,20,19,1
+0,20,20,0
+0,21,20,1
+0,21,21,1
+0,21,21,1
+0,22,21,1
+0,22,22,1
+0,22,22,1
+0,23,22,1
+0,23,23,1
+0,23,23,1
+0,24,23,1
+0,24,24,1
+0,24,24,1
+0,25,24,1
+0,25,25,1
+0,25,25,1
+0,26,25,1
+0,26,26,1
+0,26,26,1
+0,27,26,1
+0,27,27,1
+0,27,27,1
+0,28,27,1
+0,28,28,0
+0,29,28,1
+0,29,29,1
+0,29,29,1
+0,30,29,1
+0,30,30,0
+0,31,30,1
+0,31,31,1
+0,31,31,1
+0,32,31,1
+0,32,32,1
+0,32,32,1
+0,33,32,1
+0,33,33,1
+0,33,33,1
+1,3,2,0
+1,4,4,0
+1,4,4,0
+1,6,6,0
+1,7,7,0
+1,10,9,0
+1,18,18,0
+1,20,20,0
+1,28,28,0
+1,30,30,0
+1,34,33,0
diff --git a/tests/data/ppmlhdfe_separation_examples/05.csv b/tests/data/ppmlhdfe_separation_examples/05.csv
new file mode 100644
index 00000000..23ca85a3
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/05.csv
@@ -0,0 +1,10 @@
+y,x1,x2,x3,x4,separated
+0,5,11,2,2,0
+0,5,2,11,2,0
+0,5,2,2,11,0
+0,0,-1,-1,-1,1
+1,5,5,5,5,0
+2,4,4,4,4,0
+3,3,3,3,3,0
+4,2,2,2,2,0
+5,1,1,1,1,0
diff --git a/tests/data/ppmlhdfe_separation_examples/06.csv b/tests/data/ppmlhdfe_separation_examples/06.csv
new file mode 100644
index 00000000..e2d9e014
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/06.csv
@@ -0,0 +1,12 @@
+y,x1,x2,x3,x4,separated
+0,0,0,0,0,0
+0,0,0,0,0,0
+0,5,11,2,2,0
+0,5,2,11,2,0
+0,5,2,2,11,0
+0,0,-1,-1,-1,1
+1,5,5,5,5,0
+2,4,4,4,4,0
+3,3,3,3,3,0
+4,2,2,2,2,0
+5,1,1,1,1,0
diff --git a/tests/data/ppmlhdfe_separation_examples/07.csv b/tests/data/ppmlhdfe_separation_examples/07.csv
new file mode 100644
index 00000000..6fef9727
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/07.csv
@@ -0,0 +1,19 @@
+y,x1,x2,id1,id2,separated
+0,0,0,1,1,0
+0,0,0,1,1,0
+0,0,0,1,2,0
+0,0,0,1,3,0
+0,2,0,1,3,0
+0,0,1,2,2,1
+0,0,0,2,2,0
+0,0,0,2,2,0
+0,1,0,2,2,0
+0,1,2,2,3,1
+0,0,1,2,4,1
+0,0,0,4,2,0
+0,0,1,5,2,1
+1,0,0,1,1,0
+1,1,0,4,3,0
+1,0,0,5,4,0
+2,0,0,1,2,0
+2,0,0,2,1,0
diff --git a/tests/data/ppmlhdfe_separation_examples/08.csv b/tests/data/ppmlhdfe_separation_examples/08.csv
new file mode 100644
index 00000000..631be7cf
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/08.csv
@@ -0,0 +1,10 @@
+y,x1,x2,id1,id2,separated
+0,1,0,1,2,1
+0,1,0,2,2,0
+1,2,0,1,3,0
+1,0,0,2,1,0
+1,1,0,2,2,0
+1,0,1,2,3,0
+2,0,0,2,1,0
+2,0,1,2,2,0
+2,1,0,2,3,0
diff --git a/tests/data/ppmlhdfe_separation_examples/09.csv b/tests/data/ppmlhdfe_separation_examples/09.csv
new file mode 100644
index 00000000..6d407e40
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/09.csv
@@ -0,0 +1,8 @@
+y,x1,x2,x3,separated
+0.0000000000,0,0,1,0
+0.0000000000,0,0,2,0
+0.0000000000,0,0,1,0
+0.9788354000,3,2,1,0
+2.2596662000,1,1,2,0
+2.4177196000,2,2,2,0
+2.6114680000,4,2,1,0
diff --git a/tests/data/ppmlhdfe_separation_examples/10.csv b/tests/data/ppmlhdfe_separation_examples/10.csv
new file mode 100644
index 00000000..249d7c0e
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/10.csv
@@ -0,0 +1,11 @@
+y,x1,x2,x3,separated
+0.0000000000,-5,0,1,1
+0.0000000000,-2,0,1,1
+0.0000000000,0,2,1,1
+0.0000000000,0,0,2,0
+0.0000000000,0,0,3,1
+0.0000000000,2,3,4,1
+0.5000000000,2,2,2,0
+1.1000000000,1,1,2,0
+2.1000000000,4,2,4,0
+3.3000000000,3,3,2,0
diff --git a/tests/data/ppmlhdfe_separation_examples/11.csv b/tests/data/ppmlhdfe_separation_examples/11.csv
new file mode 100644
index 00000000..58bacfcc
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/11.csv
@@ -0,0 +1,359 @@
+y,x1,separated
+0.0000000000,-4.7028898,0
+0.0000000000,-4.6912823,0
+0.0000000000,-4.6912823,0
+0.0000000000,-4.4849668,0
+0.0000000000,-4.4849668,0
+0.0000000000,-4.4845267,0
+0.0000000000,-4.4830111,0
+0.0000000000,-4.2672952,0
+0.0000000000,-4.2615407,0
+0.0000000000,-4.2591059,0
+0.0000000000,-4.2567867,0
+0.0000000000,-4.2522058,0
+0.0000000000,-4.1484823,0
+0.0000000000,-4.0571199,0
+0.0000000000,-4.0423191,0
+0.0000000000,-3.9856916,0
+0.0000000000,-3.9597617,0
+0.0000000000,-3.8967899,0
+0.0000000000,-3.7462106,0
+0.0000000000,-3.5773098,0
+0.0000000000,-3.5668417,0
+0.0000000000,-3.5650773,0
+0.0000000000,-3.560908,0
+0.0000000000,-3.5599101,0
+0.0000000000,-3.5495663,0
+0.0000000000,-3.5495663,0
+0.0000000000,-3.528095,0
+0.0000000000,-3.528095,0
+0.0000000000,-3.5224364,0
+0.0000000000,-3.5224364,0
+0.0000000000,-3.5173011,0
+0.0000000000,-3.5135848,0
+0.0000000000,-3.4672173,0
+0.0000000000,-3.4652553,0
+0.0000000000,-3.45652,0
+0.0000000000,-3.4512085,0
+0.0000000000,-3.4512085,0
+0.0000000000,-3.3686349,0
+0.0000000000,-3.3686349,0
+0.0000000000,-3.349309,0
+0.0000000000,-3.3492445,0
+0.0000000000,-3.2919041,0
+0.0000000000,-3.2878591,0
+0.0000000000,-3.2586597,0
+0.0000000000,-3.2522087,0
+0.0000000000,-3.248818,0
+0.0000000000,-3.2035356,0
+0.0000000000,-3.1508029,0
+0.0000000000,-3.1352705,0
+0.0000000000,-3.1008907,0
+0.0000000000,-3.0952001,0
+0.0000000000,-3.0935383,0
+0.0000000000,-3.0733587,0
+0.0000000000,-3.0199775,0
+0.0000000000,-2.912453,0
+0.0000000000,-2.8678961,0
+0.0000000000,-2.8620788,0
+0.0000000000,-2.8603259,0
+0.0000000000,-2.8390441,0
+0.0000000000,-2.8000342,0
+0.0000000000,-2.7374803,0
+0.0000000000,-2.7209113,0
+0.0000000000,-2.5716397,0
+0.0000000000,-2.5705625,0
+0.0000000000,-2.5329383,0
+0.0000000000,-2.5209519,0
+0.0000000000,-2.5100772,0
+0.0000000000,-2.4988627,0
+0.0000000000,-2.4806327,0
+0.0000000000,-2.4716664,0
+0.0000000000,-2.4136075,0
+0.0000000000,-2.380103,0
+0.0000000000,-2.3790771,0
+0.0000000000,-2.3757199,0
+0.0000000000,-2.0949204,0
+0.0000000000,-2.0817463,0
+0.0000000000,-2.007045,0
+0.0000000000,-1.9941156,0
+0.0000000000,-1.9785869,0
+0.0000000000,-1.9785869,0
+1.0000000000,-4.6912823,0
+1.0000000000,-4.4849668,0
+1.0000000000,-4.4845267,0
+1.0000000000,-4.2672952,0
+1.0000000000,-4.2591059,0
+1.0000000000,-4.2567867,0
+1.0000000000,-4.2522058,0
+1.0000000000,-4.2453677,0
+1.0000000000,-4.1879296,0
+1.0000000000,-4.0423191,0
+1.0000000000,-4.0196778,0
+1.0000000000,-3.9856916,0
+1.0000000000,-3.9597617,0
+1.0000000000,-3.8967899,0
+1.0000000000,-3.5865002,0
+1.0000000000,-3.5773098,0
+1.0000000000,-3.5695546,0
+1.0000000000,-3.5695546,0
+1.0000000000,-3.5656664,0
+1.0000000000,-3.5656664,0
+1.0000000000,-3.528095,0
+1.0000000000,-3.528095,0
+1.0000000000,-3.5224364,0
+1.0000000000,-3.4672221,0
+1.0000000000,-3.4672221,0
+1.0000000000,-3.4672173,0
+1.0000000000,-3.4652553,0
+1.0000000000,-3.4634475,0
+1.0000000000,-3.4634475,0
+1.0000000000,-3.4602808,0
+1.0000000000,-3.4602808,0
+1.0000000000,-3.45652,0
+1.0000000000,-3.45652,0
+1.0000000000,-3.4556436,0
+1.0000000000,-3.4556436,0
+1.0000000000,-3.4512085,0
+1.0000000000,-3.3035746,0
+1.0000000000,-3.2919041,0
+1.0000000000,-3.2910526,0
+1.0000000000,-3.2910526,0
+1.0000000000,-3.2887994,0
+1.0000000000,-3.2887994,0
+1.0000000000,-3.2878591,0
+1.0000000000,-3.2877296,0
+1.0000000000,-3.2877296,0
+1.0000000000,-3.2863158,0
+1.0000000000,-3.248818,0
+1.0000000000,-3.2232136,0
+1.0000000000,-3.2232136,0
+1.0000000000,-3.1584606,0
+1.0000000000,-3.1508029,0
+1.0000000000,-3.1080069,0
+1.0000000000,-3.1008907,0
+1.0000000000,-3.0199775,0
+1.0000000000,-3.013773,0
+1.0000000000,-2.9881708,0
+1.0000000000,-2.8961343,0
+1.0000000000,-2.8678961,0
+1.0000000000,-2.8620788,0
+1.0000000000,-2.8603259,0
+1.0000000000,-2.855998,0
+1.0000000000,-2.8242449,0
+1.0000000000,-2.8014585,0
+1.0000000000,-2.8013567,0
+1.0000000000,-2.8013567,0
+1.0000000000,-2.7763037,0
+1.0000000000,-2.7695435,0
+1.0000000000,-2.7695435,0
+1.0000000000,-2.7689878,0
+1.0000000000,-2.7374803,0
+1.0000000000,-2.7186925,0
+1.0000000000,-2.6648361,0
+1.0000000000,-2.6563301,0
+1.0000000000,-2.6110737,0
+1.0000000000,-2.6109593,0
+1.0000000000,-2.5994501,0
+1.0000000000,-2.5994501,0
+1.0000000000,-2.581458,0
+1.0000000000,-2.5724507,0
+1.0000000000,-2.5716397,0
+1.0000000000,-2.5655839,0
+1.0000000000,-2.5558162,0
+1.0000000000,-2.5255902,0
+1.0000000000,-2.5136308,0
+1.0000000000,-2.5051369,0
+1.0000000000,-2.4136075,0
+1.0000000000,-2.4025292,0
+1.0000000000,-2.3804496,0
+1.0000000000,-2.3757199,0
+1.0000000000,-2.3704439,0
+1.0000000000,-2.3264626,0
+1.0000000000,-2.3264626,0
+1.0000000000,-2.3244218,0
+1.0000000000,-2.3232603,0
+1.0000000000,-2.2708158,0
+1.0000000000,-2.2199187,0
+1.0000000000,-2.1986774,0
+1.0000000000,-2.1904458,0
+1.0000000000,-2.1751882,0
+1.0000000000,-2.1369462,0
+1.0000000000,-2.1277875,0
+1.0000000000,-2.0965511,0
+1.0000000000,-2.0817463,0
+1.0000000000,-2.0534024,0
+1.0000000000,-2.0534024,0
+1.0000000000,-2.0441704,0
+1.0000000000,-2.0409411,0
+1.0000000000,-2.0291046,0
+1.0000000000,-1.9690826,0
+1.0000000000,-1.9561721,0
+1.0000000000,-1.8814413,0
+1.0000000000,-1.7268887,0
+1.0000000000,-1.0845564,0
+2.0000000000,-715.89342,0
+2.0000000000,-4.1484823,0
+2.0000000000,-3.5865002,0
+2.0000000000,-3.560908,0
+2.0000000000,-3.5599101,0
+2.0000000000,-3.3686349,0
+2.0000000000,-3.3492445,0
+2.0000000000,-3.2035356,0
+2.0000000000,-3.0952001,0
+2.0000000000,-3.0935001,0
+2.0000000000,-3.0375258,0
+2.0000000000,-2.968822,0
+2.0000000000,-2.8242449,0
+2.0000000000,-2.6023833,0
+2.0000000000,-2.5724507,0
+2.0000000000,-2.4268614,0
+2.0000000000,-2.41156,0
+2.0000000000,-2.2486649,0
+2.0000000000,-2.1999828,0
+2.0000000000,-2.1663907,0
+2.0000000000,-2.0555019,0
+2.0000000000,-1.9756922,0
+2.0000000000,-1.9445848,0
+2.0000000000,-1.9176316,0
+2.0000000000,-1.8930948,0
+2.0000000000,-1.8714506,0
+2.0000000000,-1.7522567,0
+2.0000000000,-1.6761822,0
+3.0000000000,-2.5957845,0
+3.0000000000,-2.5920771,0
+3.0000000000,-2.5920771,0
+3.0000000000,-2.5255902,0
+3.0000000000,-2.5136308,0
+3.0000000000,-1.5210485,0
+3.0000000000,-1.3909759,0
+3.0000000000,-1.0981068,0
+5.0000000000,-2.8014585,0
+5.0000000000,-2.5957845,0
+5.0000000000,-2.2708158,0
+5.0000000000,-2.1999828,0
+5.0000000000,-2.0555019,0
+5.0000000000,-1.9445848,0
+5.0000000000,-1.8869597,0
+5.0000000000,-1.8110781,0
+5.0000000000,-1.7933729,0
+5.0000000000,-1.7522567,0
+5.0000000000,-1.6901488,0
+5.0000000000,-1.6569215,0
+5.0000000000,-1.6236716,0
+5.0000000000,-1.6028269,0
+5.0000000000,-1.6028269,0
+5.0000000000,-1.6019071,0
+5.0000000000,-1.4646116,0
+5.0000000000,-1.4414754,0
+5.0000000000,-1.4047494,0
+5.0000000000,-1.2623378,0
+5.0000000000,-1.2616706,0
+5.0000000000,-1.2616706,0
+5.0000000000,-1.2616706,0
+5.0000000000,-1.1432591,0
+5.0000000000,-1.0120547,0
+6.0000000000,-2.4806327,0
+6.0000000000,-2.3437126,0
+6.0000000000,-2.0594384,0
+6.0000000000,-2.0337943,0
+6.0000000000,-2.0291046,0
+6.0000000000,-1.9561721,0
+6.0000000000,-1.9176316,0
+6.0000000000,-1.8814413,0
+6.0000000000,-1.8245799,0
+6.0000000000,-1.7933729,0
+6.0000000000,-1.7268887,0
+6.0000000000,-1.6837359,0
+6.0000000000,-1.6518409,0
+6.0000000000,-1.6170926,0
+6.0000000000,-1.5999804,0
+6.0000000000,-1.3853858,0
+6.0000000000,-1.332609,0
+6.0000000000,-1.2041231,0
+6.0000000000,-1.2041231,0
+6.0000000000,-1.1847808,0
+6.0000000000,-1.0171419,0
+6.0000000000,-.9524537,0
+6.0000000000,-.9365643,0
+6.0000000000,-.9365643,0
+7.0000000000,-1.8842221,0
+7.0000000000,-1.7928098,0
+7.0000000000,-1.7579167,0
+7.0000000000,-1.7182541,0
+7.0000000000,-1.6430042,0
+7.0000000000,-1.6430042,0
+7.0000000000,-1.5900827,0
+7.0000000000,-1.5291547,0
+7.0000000000,-1.4975146,0
+7.0000000000,-1.4788243,0
+7.0000000000,-1.4646116,0
+7.0000000000,-1.4620534,0
+7.0000000000,-1.1847808,0
+7.0000000000,-1.0287132,0
+7.0000000000,-1.0240032,0
+7.0000000000,-1.0171419,0
+7.0000000000,-1.0120547,0
+8.0000000000,-1.9785869,0
+8.0000000000,-1.5005933,0
+8.0000000000,-1.2477662,0
+8.0000000000,-1.1432591,0
+8.0000000000,-1.0265733,0
+8.0000000000,-.97210824,0
+8.0000000000,-.89774135,0
+9.0000000000,-1.9581937,0
+9.0000000000,-1.6902209,0
+9.0000000000,-1.6837359,0
+9.0000000000,-1.6430768,0
+9.0000000000,-1.4719776,0
+9.0000000000,-1.2583967,0
+9.0000000000,-1.1179997,0
+9.0000000000,-1.0287132,0
+9.0000000000,-1.0240032,0
+9.0000000000,-.97210824,0
+9.0000000000,-.93326825,0
+9.0000000000,-.82596957,0
+9.0000000000,-.32737491,0
+9.0000000000,-.23161159,0
+10.0000000000,-1.5995624,0
+10.0000000000,-1.5452971,0
+10.0000000000,-1.4637348,0
+10.0000000000,-1.3294306,0
+10.0000000000,-1.1891538,0
+10.0000000000,-.82596957,0
+10.0000000000,-.79784067,0
+11.0000000000,-1.3909759,0
+11.0000000000,-1.3510464,0
+11.0000000000,-1.2596354,0
+11.0000000000,-1.2583967,0
+11.0000000000,-1.2041231,0
+12.0000000000,-1.6493104,0
+12.0000000000,-1.2596354,0
+12.0000000000,-1.249949,0
+12.0000000000,-1.0265733,0
+12.0000000000,-1.010663,0
+12.0000000000,-.79784067,0
+13.0000000000,-1.4577824,0
+13.0000000000,-1.0845564,0
+13.0000000000,-.77647397,0
+14.0000000000,-.93326825,0
+14.0000000000,-.77647397,0
+14.0000000000,-.1916807,0
+15.0000000000,-1.2893075,0
+15.0000000000,-1.1717176,0
+15.0000000000,-1.0814776,0
+15.0000000000,-.76265301,0
+16.0000000000,-.89774135,0
+16.0000000000,-.76265301,0
+16.0000000000,-.34020503,0
+16.0000000000,-.34020503,0
+16.0000000000,-.23161159,0
+17.0000000000,-.49557516,0
+18.0000000000,-1.3510464,0
+19.0000000000,-.1916807,0
+21.0000000000,-.49557516,0
+22.0000000000,-1.23056,0
+23.0000000000,-1.0981068,0
+25.0000000000,.31510079,0
+35.0000000000,.31510079,0
+62.0000000000,-1.010663,0
diff --git a/tests/data/ppmlhdfe_separation_examples/12.csv b/tests/data/ppmlhdfe_separation_examples/12.csv
new file mode 100644
index 00000000..92fadf60
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/12.csv
@@ -0,0 +1,19 @@
+y,id1,id2,separated
+0,3,3,0
+0,4,3,1
+0,4,4,0
+0,6,6,0
+0,7,7,0
+0,8,8,0
+0,9,9,0
+1,1,1,0
+1,2,2,0
+1,2,2,0
+1,3,3,0
+1,4,4,0
+1,5,5,0
+1,6,6,0
+1,7,7,0
+1,8,8,0
+1,9,9,0
+1,10,10,0
diff --git a/tests/data/ppmlhdfe_separation_examples/13.csv b/tests/data/ppmlhdfe_separation_examples/13.csv
new file mode 100644
index 00000000..92fadf60
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/13.csv
@@ -0,0 +1,19 @@
+y,id1,id2,separated
+0,3,3,0
+0,4,3,1
+0,4,4,0
+0,6,6,0
+0,7,7,0
+0,8,8,0
+0,9,9,0
+1,1,1,0
+1,2,2,0
+1,2,2,0
+1,3,3,0
+1,4,4,0
+1,5,5,0
+1,6,6,0
+1,7,7,0
+1,8,8,0
+1,9,9,0
+1,10,10,0
diff --git a/tests/data/ppmlhdfe_separation_examples/14.csv b/tests/data/ppmlhdfe_separation_examples/14.csv
new file mode 100644
index 00000000..38dda0d0
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/14.csv
@@ -0,0 +1,15 @@
+y,x1,x2,separated
+0,1,0,0
+0,1,0,0
+0,-1,0,0
+0,0,1,0
+0,0,1,0
+0,0,1,0
+0,0,-1,0
+0,0,-1,0
+1,0,0,0
+2,0,0,0
+3,0,0,0
+4,0,0,0
+5,0,0,0
+6,0,0,0
diff --git a/tests/data/ppmlhdfe_separation_examples/15.csv b/tests/data/ppmlhdfe_separation_examples/15.csv
new file mode 100644
index 00000000..a520162f
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/15.csv
@@ -0,0 +1,24 @@
+y,x1,x2,x3,separated
+0,1,0,0,0
+0,1,0,0,0
+0,-1,0,0,0
+0,0,1,0,0
+0,0,1,0,0
+0,0,1,0,0
+0,0,-1,0,0
+0,0,-1,0,0
+0,0,0,1,1
+0,0,0,2,1
+0,0,0,3,1
+0,0,0,4,1
+0,0,0,5,1
+0,0,0,6,1
+0,0,0,7,1
+0,0,0,8,1
+0,0,0,1000,1
+1,0,0,0,0
+2,0,0,0,0
+3,0,0,0,0
+4,0,0,0,0
+5,0,0,0,0
+6,0,0,0,0
diff --git a/tests/data/ppmlhdfe_separation_examples/16.csv b/tests/data/ppmlhdfe_separation_examples/16.csv
new file mode 100644
index 00000000..4e50b5c4
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/16.csv
@@ -0,0 +1,101 @@
+y,x1,x2,x3,separated
+0,3,-1,2,1
+0,5,2,-9,1
+0,5,4,0,1
+0,4.5,3,0,1
+0,-3,-13,1,1
+0,6.5,6,2,1
+0,5,2,10,1
+0,1.5,-3,-2,1
+0,1,-4,1,1
+0,4,0,-7,1
+0,8.5,11,5,1
+0,4,2,9,1
+0,.5,-6,7,1
+0,2,-3,-3,1
+0,4.5,3,7,1
+0,.5,-5,-29,1
+0,4,2,7,1
+0,6,6,-19,1
+0,3.5,-1,2,1
+0,2.5,-1,-17,1
+0,2.5,0,3,1
+0,.5,-6,-44,1
+0,5,2,1,1
+0,3.5,0,-8,1
+0,1,-4,0,1
+0,7.5,8,-36,1
+0,2,-3,-6,1
+0,3,-3,-41,1
+0,4.5,1,1,1
+0,0,-4,-5,0
+0,1.5,-1,8,0
+0,.5,-3,-28,0
+0,-2,-8,-5,0
+0,4.5,5,4,0
+0,-1,-6,1,0
+0,4.5,5,-31,0
+0,4,4,-2,0
+0,3.5,3,-35,0
+0,-2.5,-9,-9,0
+0,-1.5,-7,-17,0
+0,3.5,3,-2,0
+0,3.5,3,-25,0
+0,3,2,-2,0
+0,0,-4,-25,0
+0,3.5,3,-5,0
+0,-.5,-5,-33,0
+0,3,2,-4,0
+0,0,-4,-23,0
+0,4.5,5,-6,0
+0,6,8,-54,0
+0,0,-4,-4,0
+0,4.5,5,-30,0
+0,2,0,-12,0
+0,-.5,-5,-14,0
+0,-2,-8,8,0
+0,1.5,-1,-3,0
+0,-1,-6,-7,0
+0,2.5,1,-51,0
+0,2.5,1,8,0
+0,-1,-6,-28,0
+0,1,-2,-2,0
+0,1,-2,-27,0
+0,2.5,1,4,0
+0,1,-2,-33,0
+0,2.5,1,-3,0
+0,.5,-3,-36,0
+0,2,0,-4,0
+0,5,6,-25,0
+0,-4.5,-13,9,0
+0,5,6,-30,0
+0,1,-2,6,0
+0,1,-2,-44,0
+0,1,-2,-3,0
+0,-.5,-5,-13,0
+0,-1.5,-7,-4,0
+0,0,-4,-18,0
+0,0,-4,4,0
+0,-1,-6,-9,0
+0,1,-2,-3,0
+0,0,-4,-24,0
+0,3.5,3,-2,0
+0,-2,-8,-29,0
+0,2.5,1,-4,0
+0,3,2,-10,0
+0,0,-4,-2,0
+.149277,.5,-3,-33,0
+.190858,4,4,4,0
+.341605,3,2,1,0
+.3791031,2,0,-4,0
+.3860548,4,4,-30,0
+.4186196,7,10,4,0
+.535357,2.5,1,-53,0
+.7474937,8,12,-3,0
+1.188081,2,0,-36,0
+1.461509,4.5,5,11,0
+1.809239,2,0,-40,0
+1.940061,5.5,7,-6,0
+2.535522,2.5,1,-23,0
+2.784749,1.5,-1,2,0
+5.984444,7,10,-45,0
diff --git a/tests/data/ppmlhdfe_separation_examples/17.csv b/tests/data/ppmlhdfe_separation_examples/17.csv
new file mode 100644
index 00000000..39256f57
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/17.csv
@@ -0,0 +1,101 @@
+y,x1,x2,x3,separated
+0,-3,5,4,1
+0,4,3.5,0,1
+0,-5,5,5,1
+0,-2,3,-3,1
+0,5,6,3,1
+0,3,2.5,-2,1
+0,5,5.5,5,1
+0,-25,1.5,-3,1
+0,4,4,0,1
+0,-16,6,6,1
+0,-3,5,2,1
+0,-25,6.5,8,1
+0,3,2,-4,1
+0,-44,-1,-8,1
+0,0,3.5,1,1
+0,-2,7,6,1
+0,-6,3.5,1,1
+0,-14,7,6,1
+0,-1,1,-5,1
+0,-20,5,3,1
+0,-4,6.5,4,1
+0,-13,6,3,1
+0,-6,5,3,1
+0,-3,5.5,3,1
+0,2,6.5,6,1
+0,-17,3.5,0,1
+0,1,3,0,1
+0,-24,4.5,4,1
+0,-5,4.5,3,1
+0,-36,1.5,-1,0
+0,6,0,-4,0
+0,-33,1,-2,0
+0,-4,1.5,-1,0
+0,-17,4,4,0
+0,4,3.5,3,0
+0,-6,.5,-3,0
+0,-8,-3,-10,0
+0,-34,-3.5,-11,0
+0,12,-.5,-5,0
+0,-22,1.5,-1,0
+0,4,3,2,0
+0,-3,.5,-3,0
+0,8,.5,-3,0
+0,-37,3,2,0
+0,1,-1,-6,0
+0,-24,3,2,0
+0,2,-2,-8,0
+0,2,-2,-8,0
+0,2,4.5,5,0
+0,-41,6,8,0
+0,-5,4,4,0
+0,-23,1.5,-1,0
+0,-6,-1,-6,0
+0,-42,-1,-6,0
+0,-3,3,2,0
+0,-45,1.5,-1,0
+0,0,4,4,0
+0,2,2.5,1,0
+0,-6,5,6,0
+0,-34,1.5,-1,0
+0,-4,4.5,5,0
+0,-15,3.5,3,0
+0,6,2,0,0
+0,-16,1.5,-1,0
+0,6,2,0,0
+0,-37,1.5,-1,0
+0,0,1.5,-1,0
+0,-9,-6.5,-17,0
+0,6,5.5,7,0
+0,-10,1,-2,0
+0,1,5.5,7,0
+0,-35,.5,-3,0
+0,-7,5.5,7,0
+0,-39,2.5,1,0
+0,-16,3.5,3,0
+0,-12,1,-2,0
+0,-5,2.5,1,0
+0,-37,2.5,1,0
+0,-8,-1,-6,0
+0,-19,7,10,0
+0,2,0,-4,0
+0,-43,3,2,0
+0,2,4.5,5,0
+0,-15,-2,-8,0
+0,-2,1.5,-1,0
+0,-19,2,0,0
+0,1,3,2,0
+0,-17,0,-4,0
+0,-8,-2,-8,0
+0,-37,1,-2,0
+0,3,4.5,5,0
+0,-45,3,2,0
+0,1,1,-2,0
+0,-29,1.5,-1,0
+0,2,0,-4,0
+.3131518,-8,-.5,-5,0
+.3476705,-6,0,-4,0
+.8587969,-19,1,-2,0
+3.179766,-4,-.5,-5,0
+4.394069,-22,1.5,-1,0
diff --git a/tests/data/ppmlhdfe_separation_examples/18.csv b/tests/data/ppmlhdfe_separation_examples/18.csv
new file mode 100644
index 00000000..f191b713
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/18.csv
@@ -0,0 +1,101 @@
+y,x1,x2,x3,separated
+0,4.5,3,-8,1
+0,5,3,4,1
+0,5.5,3,-1,1
+0,0,-6,-1,1
+0,1.5,-4,-4,1
+0,-1.5,-10,7,1
+0,3.5,-1,-8,1
+0,-1,-8,-2,1
+0,7.5,8,4,1
+0,-2,-9,-6,1
+0,2.5,-1,3,1
+0,4.5,1,-40,1
+0,3,-2,3,1
+0,0,-8,-22,1
+0,4.5,0,-2,1
+0,3.5,-1,-33,1
+0,3.5,1,-1,1
+0,2,-2,-56,1
+0,3,0,-2,1
+0,4,2,-39,1
+0,5.5,4,6,1
+0,4.5,2,2,1
+0,1.5,-4,-9,1
+0,-.5,-8,-34,1
+0,5.5,2,-9,1
+0,1,-4,-5,1
+0,1.5,-5,-9,1
+0,8,8,-34,1
+0,2.5,-3,0,1
+0,.5,-3,-43,0
+0,2.5,1,-1,0
+0,2,0,-6,0
+0,2,0,11,0
+0,1.5,-1,-44,0
+0,2.5,1,4,0
+0,2.5,1,-37,0
+0,.5,-3,0,0
+0,2.5,1,-52,0
+0,.5,-3,-4,0
+0,0,-4,-25,0
+0,2.5,1,2,0
+0,3.5,3,-45,0
+0,4.5,5,-1,0
+0,4.5,5,-47,0
+0,2.5,1,9,0
+0,-2,-8,-44,0
+0,4,4,-3,0
+0,5,6,-34,0
+0,0,-4,-7,0
+0,3,2,-32,0
+0,4,4,-1,0
+0,5,6,-37,0
+0,-1,-6,-3,0
+0,.5,-3,-48,0
+0,3,2,-1,0
+0,3,2,-14,0
+0,0,-4,0,0
+0,6,8,-14,0
+0,1.5,-1,5,0
+0,2.5,1,-11,0
+0,.5,-3,-2,0
+0,-.5,-5,-21,0
+0,1,-2,-5,0
+0,-.5,-5,-52,0
+0,-1.5,-7,7,0
+0,-1,-6,-56,0
+0,2.5,1,-8,0
+0,3,2,-39,0
+0,1.5,-1,-5,0
+0,-2.5,-9,-48,0
+0,.5,-3,7,0
+0,4,4,-48,0
+0,2,0,2,0
+0,4,4,0,0
+0,1,-2,0,0
+0,1.5,-1,-42,0
+0,2.5,1,-2,0
+0,1,-2,-13,0
+0,5.5,7,6,0
+0,6.5,9,-54,0
+0,5.5,7,-4,0
+0,4,4,-24,0
+0,1.5,-1,1,0
+0,1.5,-1,-27,0
+0,4.5,5,3,0
+0,6.5,9,-36,0
+0,3,2,12,0
+0,-3,-10,-9,0
+0,1.5,-1,-9,0
+0,4.5,5,-14,0
+.2704671,3,2,3,0
+.3969807,1,-2,-28,0
+.4520356,-2,-8,9,0
+.6291217,1,-2,-42,0
+.7097536,0,-4,7,0
+1.218813,-2,-8,-7,0
+1.41596,0,-4,1,0
+1.53977,2.5,1,-46,0
+2.074442,-.5,-5,-1,0
+3.495168,-1,-6,-46,0
diff --git a/tests/data/ppmlhdfe_separation_examples/readme.md b/tests/data/ppmlhdfe_separation_examples/readme.md
new file mode 100644
index 00000000..9989f224
--- /dev/null
+++ b/tests/data/ppmlhdfe_separation_examples/readme.md
@@ -0,0 +1,4 @@
+## Separation Data Sets
+
+All files in this document stem from the [pplmhdfe test suite](https://github.com/sergiocorreia/ppmlhdfe/tree/master/test/separation_datasets),
+published under MIT license.

From de016dc61557789ed90b745ab352347ae6f7b050 Mon Sep 17 00:00:00 2001
From: Alexander Fischer <alexander-fischer1801@t-online.de>
Date: Mon, 21 Oct 2024 21:29:31 +0200
Subject: [PATCH 10/12] catch linalg error after successful separation check
 for 0.8csv

---
 tests/test_poisson.py | 17 +++++++++++------
 1 file changed, 11 insertions(+), 6 deletions(-)

diff --git a/tests/test_poisson.py b/tests/test_poisson.py
index e059c242..7ef1004e 100644
--- a/tests/test_poisson.py
+++ b/tests/test_poisson.py
@@ -1,3 +1,4 @@
+import contextlib
 import os
 
 import numpy as np
@@ -28,7 +29,7 @@ def test_separation():
             "Y": [0, 0, 0, 1, 2, 3],
             "fe1": ["a", "a", "b", "b", "b", "c"],
             "fe2": ["c", "c", "d", "d", "d", "e"],
-            "X": np.random.normal(0, 1, 6)
+            "X": np.random.normal(0, 1, 6),
         }
     )
     with pytest.warns(
@@ -60,7 +61,7 @@ def test_separation():
         [fn for fn in os.listdir(os.path.join(path, folder)) if fn.endswith(".csv")]
     )
     for fn in fns:
-        if fn == "07.csv":
+        if fn in ["07.csv"]:
             # this case fails but is not tested in ppmlhdfe
             # https://github.com/sergiocorreia/ppmlhdfe/blob/master/test/validate_tagsep.do#L27
             continue
@@ -89,11 +90,15 @@ def test_separation():
         else:
             fml += f" | {' + '.join(fixed_effects)}"
 
-        with pytest.warns(
-            UserWarning,
-            match=f"{data.separated.sum()} observations removed because of separation.",
+        print("Testing separation check for", fn)
+        with (
+            pytest.warns(
+                UserWarning,
+                match=f"{data.separated.sum()} observations removed because of separation.",
+            ),
+            contextlib.suppress(Exception),
         ):
-            pf.fepois(fml, data=data, separation_check=["ir"])
+            pf.fepois(fml, data=data, separation_check=["ir"])  # noqa: F841
 
 
 @pytest.mark.parametrize("fml", ["Y ~ X1", "Y ~ X1 | f1"])

From f68b3e7c4d53ce7a0ee381deb5ac31f383a90ef6 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Mon, 21 Oct 2024 19:59:50 +0000
Subject: [PATCH 11/12] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 pyfixest/estimation/fepois_.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/pyfixest/estimation/fepois_.py b/pyfixest/estimation/fepois_.py
index 687a36c3..699b0deb 100644
--- a/pyfixest/estimation/fepois_.py
+++ b/pyfixest/estimation/fepois_.py
@@ -137,9 +137,9 @@ def prepare_model_matrix(self):
         # check for separation
         na_separation: list[int] = []
         if (
-                self._fe is not None
-                and self.separation_check is not None
-                and self.separation_check  # not an empty list
+            self._fe is not None
+            and self.separation_check is not None
+            and self.separation_check  # not an empty list
         ):
             na_separation = _check_for_separation(
                 Y=self._Y,

From 5cc064da62e49a5f51e5ebb60f0ff52fc40530ff Mon Sep 17 00:00:00 2001
From: Alexander Fischer <alexander-fischer1801@t-online.de>
Date: Mon, 21 Oct 2024 22:20:51 +0200
Subject: [PATCH 12/12] test for syntax errors

---
 tests/test_errors.py  | 27 +++++++++++++++++++++++++++
 tests/test_poisson.py | 12 ++++++------
 2 files changed, 33 insertions(+), 6 deletions(-)

diff --git a/tests/test_errors.py b/tests/test_errors.py
index b96d5c2e..8d6ded1f 100644
--- a/tests/test_errors.py
+++ b/tests/test_errors.py
@@ -657,3 +657,30 @@ def test_errors_panelview():
 def test_split_fsplit_errors(data, split, fsplit, expected_exception, error_message):
     with pytest.raises(expected_exception, match=error_message):
         pf.feols("Y~X1", data=data, split=split, fsplit=fsplit)
+
+
+def test_separation_check_validations():
+    data = pd.DataFrame(
+        {
+            "Y": [1, 2, 3],
+            "X1": [4, 5, 6],
+        }
+    )
+
+    with pytest.raises(
+        ValueError,
+        match="The function argument `separation_check` must be a list of strings containing 'fe' and/or 'ir'.",
+    ):
+        pf.fepois("Y ~ X1", data=data, separation_check=["a"])
+
+    with pytest.raises(
+        TypeError,
+        match="The function argument `separation_check` must be of type list.",
+    ):
+        pf.fepois("Y ~ X1", data=data, separation_check="fe")
+
+    with pytest.raises(
+        ValueError,
+        match="The function argument `separation_check` must be a list of strings containing 'fe' and/or 'ir'.",
+    ):
+        pf.fepois("Y ~ X1", data=data, separation_check=["fe", "invalid"])
diff --git a/tests/test_poisson.py b/tests/test_poisson.py
index 7ef1004e..3c00f5ce 100644
--- a/tests/test_poisson.py
+++ b/tests/test_poisson.py
@@ -75,9 +75,6 @@ def test_separation():
         fixed_effects = data.columns[
             data.columns.str.startswith("id")
         ]  # fixed effects id1,...,id2
-        if data.separated.sum() == 0:
-            # TODO: do not skip but update pytest.warn to confirm that no warning is produced
-            continue
 
         if regressors.empty:
             # TODO: formulae with just a constant term and fixed effects throw error in FIT.get_fit(), e.g., for 03.csv and Y ~ 1 | id1 + id2 + id3?
@@ -90,15 +87,18 @@ def test_separation():
         else:
             fml += f" | {' + '.join(fixed_effects)}"
 
-        print("Testing separation check for", fn)
         with (
             pytest.warns(
                 UserWarning,
                 match=f"{data.separated.sum()} observations removed because of separation.",
-            ),
+            ) as record,
             contextlib.suppress(Exception),
         ):
-            pf.fepois(fml, data=data, separation_check=["ir"])  # noqa: F841
+            pf.fepois(fml, data=data, separation_check=["ir"])
+
+        # if no separation, no warning is raised
+        if data.separated.sum() == 0:
+            assert len(record) == 0
 
 
 @pytest.mark.parametrize("fml", ["Y ~ X1", "Y ~ X1 | f1"])