✨ Creation of the audit folder in which the MCARTest class is created. Implementation of the Little's test + unit test.

Author: adriencrtr

qolmat/audit/holes_characterization.py

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+from __future__ import annotations
+from typing import Literal, Optional, TYPE_CHECKING
+
+import numpy as np
+import pandas as pd
+from scipy.stats import chi2
+
+from qolmat.imputations.imputers import ImputerEM
+
+if TYPE_CHECKING:
+    from qolmat.imputations.imputers import _Imputer
+
+
+class MCARTest:
+    """
+    This class implements the statistical tests to test the MCAR case.
+
+    Parameters
+        ----------
+        method : Literal["little"]
+            The name of the statistical test. This should be handled by qolmat.
+        imputer : Optional[_Imputer], optional
+            If the selected test needs a imputer, you can provide the Imputer you want. Otherwise,
+            a default imputer will be used.
+    """
+
+    def __init__(self, method: Literal["little"], imputer: Optional[_Imputer] = None):
+        if method not in ["little"]:
+            raise ValueError(f"method` must be handled by qolmat, provided value is '{method}'")
+
+        self.method = method
+        self.imputer = imputer
+
+    def test(self, df: pd.DataFrame) -> float:
+        if self.method == "little":
+            return self.little_mcar_test(df)
+
+    def little_mcar_test(self, df: pd.DataFrame) -> float:
+        """
+        This method implements the Little's test. Use this test to test the homogenity of means
+        between all your missing patterns.
+        The null hypethoses is "The missing data mechanism is MCAR".
+        Be aware that this test won't detect the heterogeneity of covariance.
+
+        Parameters
+        ----------
+        df : pd.DataFrame
+            Your input data with missing values.
+
+        Returns
+        -------
+        float
+            The p-value of the test.
+        """
+        imputer = self.imputer or ImputerEM()
+        fitted_imputer = imputer._fit_element(df)
+
+        # Instanciant the stat, the degree of freedom and estimators.
+        d0 = 0
+        n_rows, degree_f = df.shape
+        degree_f = -degree_f
+        ml_means = fitted_imputer.means
+        ml_cov = n_rows / (n_rows - 1) * fitted_imputer.cov
+
+        # Iterate over the patterns
+        df_nan = df.notna()
+        for tup_pattern, df_nan_pattern in df_nan.groupby(df_nan.columns.tolist()):
+            n_rows_pattern, _ = df_nan_pattern.shape
+            ind_pattern = df_nan_pattern.index
+            df_pattern = df.loc[ind_pattern, list(tup_pattern)]
+            obs_mean = df_pattern.mean().to_numpy()
+
+            diff_means = obs_mean - ml_means[list(tup_pattern)]
+            inv_sigma_pattern = np.linalg.inv(ml_cov[:, tup_pattern][tup_pattern, :])
+
+            d0 += n_rows_pattern * np.dot(np.dot(diff_means, inv_sigma_pattern), diff_means.T)
+            degree_f += tup_pattern.count(True)
+
+        return 1 - chi2.cdf(d0, degree_f)

tests/audit/test_holes_characterization.py

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+import numpy as np
+import pandas as pd
+import pytest
+
+from qolmat.audit.holes_characterization import MCARTest
+from qolmat.imputations.imputers import ImputerEM
+
+
+np.random.seed(11)
+matrix = np.random.multivariate_normal(mean=[0, 0], cov=[[1, 0], [0, 1]], size=100)
+matrix_1, matrix_2, matrix_3 = map(np.copy, [matrix] * 3)
+
+# Case 1 : MCAR case detected by Little
+matrix_1.ravel()[np.random.choice(matrix_1.size, size=20, replace=False)] = np.nan
+df_1 = pd.DataFrame(matrix_1)
+
+# Case 2 : MAR case detected by Little
+matrix_2[np.argwhere(matrix_2[:, 0] > 1.96), 1] = np.nan
+df_2 = pd.DataFrame(matrix_2)
+
+# Case 3 : MAR case undetected by Little
+matrix_3[np.argwhere(abs(matrix_3[:, 0]) >= 1.95), 1] = np.nan
+df_3 = pd.DataFrame(matrix_3)
+
+
+@pytest.mark.parametrize("df_input, expected", [(df_1, True), (df_2, False), (df_3, True)])
+def test_little_mcar_test(df_input: pd.DataFrame, expected: bool):
+    mcar_test_little = MCARTest(method="little", imputer=ImputerEM(random_state=42))
+    result = mcar_test_little.test(df_input)
+    assert expected == (result > 0.05)