diff --git a/feature_importance/scripts/competing_methods_local.py b/feature_importance/scripts/competing_methods_local.py
index b92fb67..80f18a9 100644
--- a/feature_importance/scripts/competing_methods_local.py
+++ b/feature_importance/scripts/competing_methods_local.py
@@ -4,6 +4,7 @@
 import numpy as np
 import sklearn.base
 from sklearn.base import RegressorMixin, ClassifierMixin
+from sklearn.metrics import mean_squared_error
 from functools import reduce
 
 import shap
@@ -15,9 +16,7 @@ def tree_shap_local(X, y, fit):
     :param X: design matrix
     :param y: response
     :param fit: fitted model of interest (tree-based)
-    :return: dataframe - [Var, Importance]
-                         Var: variable name
-                         Importance: average absolute shap value
+    :return: dataframe of shape: (n_samples, n_features)
     """
     explainer = shap.TreeExplainer(fit)
     shap_values = explainer.shap_values(X, check_additivity=False)
@@ -27,7 +26,7 @@ def add_abs(a, b):
         results = reduce(add_abs, shap_values)
     else:
         results = abs(shap_values)
-    result_table = pd.DataFrame(results)
+    result_table = pd.DataFrame(results, columns=[f'Feature_{i}' for i in range(X.shape[1])])
     # results = results.mean(axis=0)
     # results = pd.DataFrame(data=results, columns=['importance'])
     # # Use column names from dataframe if possible
@@ -36,4 +35,65 @@ def add_abs(a, b):
     # results.index.name = 'var'
     # results.reset_index(inplace=True)
 
+    return result_table
+
+def permutation_local(X, y, fit, num_permutations=100):
+    """
+    Compute local permutation importance for each feature and sample.
+    :param X: design matrix
+    :param y: response
+    :param fit: fitted model of interest (tree-based)
+    :num_permutations: Number of permutations for each feature (default is 100)
+    :return: dataframe of shape: (n_samples, n_features)
+    """
+
+    # Get the number of samples and features
+    num_samples, num_features = X.shape
+
+    # Initialize array to store local permutation importance
+    lpi = np.zeros((num_samples, num_features))
+
+    # For each feature
+    for k in range(num_features):
+        # Permute X_k num_permutations times
+        for b in range(num_permutations):
+            X_permuted = X.copy()
+            X_permuted[:, k] = np.random.permutation(X[:, k])
+            
+            # Feed permuted data through the fitted model
+            y_pred_permuted = fit.predict(X_permuted)
+
+            # Calculate MSE for each sample
+            mse_values = mean_squared_error(y, y_pred_permuted)
+
+            # Store MSE values in the array
+            lpi[:, k] += mse_values
+
+        # Average MSE values across permutations for each sample
+        lpi[:, k] /= num_permutations
+
+    # Convert the array to a DataFrame
+    result_table = pd.DataFrame(lpi, columns=[f'Feature_{i}' for i in range(num_features)])
+
+    return result_table
+
+def MDI_plus_local(X, y, fit):
+    """
+    Compute local MDI+ importance for each feature and sample.
+    :param X: design matrix
+    :param y: response
+    :param fit: fitted model of interest (tree-based)
+    :return: dataframe of shape: (n_samples, n_features)
+
+    """
+
+    ## To Do for Zach: Please add the implementation of local MDI+ below
+    num_samples, num_features = X.shape
+
+
+    result = None
+
+    # Convert the array to a DataFrame
+    result_table = pd.DataFrame(result, columns=[f'Feature_{i}' for i in range(num_features)])
+
     return result_table
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