logit regression and singular Matrix error in Python: Complete Guide with 3 Solutions

# Quick Answer

The most common cause of a "Singular Matrix Error" in

statsmodels.Logit

in Python, especially with the German Credit Data, is an incorrectly formatted dependent variable (target). The

Logit

function expects the dependent variable to be binary (0 or 1). If your target variable contains values like 1 and 2, simply subtracting 1 from it will resolve the issue, transforming it into the expected 0/1 format.

import pandas as pd
import statsmodels.api as sm
import numpy as np

# Assuming df and train_cols are already defined as in the problem description
# df = pd.read_csv("germandata.txt", delimiter=' ')
# ... (column renaming and selection)
# data = df[cols_to_keep]
# data['intercept'] = 1.0
# train_cols = data.columns[1:]

# Correcting the dependent variable to be 0 or 1
logit = sm.Logit(data['admit'] - 1, data[train_cols])
result = logit.fit()
print(result.summary())

# Choose Your Method

This decision tree will guide you to the most appropriate solution based on your specific scenario and persona.

# Table of Contents

Quick Answer
Choose Your Method
Table of Contents
Ready-to-Use Code
Method 1: Recoding the Dependent Variable (0/1 Transformation)
Method 2: Feature Selection with Variance Thresholding
Method 3: Excluding the Target from Predictors
Method 4: Handling Zero-Variance or Constant Predictor Columns
Method 5: Addressing Multicollinearity in One-Hot Encoded Variables
Performance Comparison
Version Compatibility Matrix
Common Problems & Solutions
Real-World Use Cases
Related Technology Functions
Summary
Frequently Asked Questions
Tools & Resources

# Ready-to-Use Code

Here are the most common and effective solutions for the "Singular Matrix Error" in

statsmodels.Logit

, ready for copy-paste.

# Solution 1: Recode Dependent Variable (0/1)

This is the most frequent fix for the German Credit Data problem, where the target variable

admit

is 1 or 2 instead of 0 or 1.

# 🚀 Speed Seeker, 🔧 Problem Solver
import pandas as pd
import statsmodels.api as sm
import numpy as np

# --- Setup (as per original problem) ---
# Load data
df = pd.read_csv("germandata.txt", delimiter=' ')
df.columns = ["chk_acc", "duration", "history", "purpose", "amount", "savings_acc",
              "employ_since", "install_rate", "pers_status", "debtors",
              "residence_since", "property", "age", "other_plans", "housing",
              "existing_credit", "job", "no_people_liab", "telephone",
              "foreign_worker", "admit"]

# Select numerical columns
cols_to_keep = ['admit', 'duration', 'amount', 'install_rate', 'residence_since',
                'age', 'existing_credit', 'no_people_liab']
data = df[cols_to_keep].copy() # Use .copy() to avoid SettingWithCopyWarning

# Add intercept
data['intercept'] = 1.0
train_cols = data.columns[1:] # All columns except 'admit'

# --- The Fix ---
# Recode 'admit' from (1, 2) to (0, 1)
# Assuming 'admit' values are 1 and 2, subtracting 1 makes them 0 and 1.
# If 'admit' values are different, adjust the transformation accordingly.
y_dependent = data['admit'] - 1

# Fit the logit model
logit_model = sm.Logit(y_dependent, data[train_cols])
result = logit_model.fit()

print("--- Solution 1: Recoded Dependent Variable ---")
print(result.summary())

# Solution 2: Feature Selection with Variance Thresholding

This method helps remove features with very low variance, which can contribute to multicollinearity and singular matrices. Useful when you have many features, especially after one-hot encoding.

# 📚 Learning Explorer, 🏗️ Architecture Builder
import pandas as pd
import statsmodels.api as sm
import numpy as np
from sklearn.feature_selection import VarianceThreshold

# --- Setup (as per original problem, with some modifications for demonstration) ---
# Load data
df = pd.read_csv("germandata.txt", delimiter=' ')
df.columns = ["chk_acc", "duration", "history", "purpose", "amount", "savings_acc",
              "employ_since", "install_rate", "pers_status", "debtors",
              "residence_since", "property", "age", "other_plans", "housing",
              "existing_credit", "job", "no_people_liab", "telephone",
              "foreign_worker", "admit"]

# Select numerical columns (excluding 'admit' for feature selection on predictors)
predictor_cols = ['duration', 'amount', 'install_rate', 'residence_since',
                  'age', 'existing_credit', 'no_people_liab']
X_predictors = df[predictor_cols].copy()

# --- The Fix ---
# Define a variance threshold. Features with variance below this will be removed.
# A common threshold for binary features is p*(1-p), e.g., 0.01 for 1% occurrence.
# For continuous features, a small absolute value like 0.0001 can work.
min_variance_threshold = 0.0001 # Adjust as needed

# Initialize VarianceThreshold selector
selector = VarianceThreshold(threshold=min_variance_threshold)

# Fit and transform the predictor data
X_selected = selector.fit_transform(X_predictors)

# Get the names of the selected columns
selected_feature_names = X_predictors.columns[selector.get_support(indices=True)]
X_selected_df = pd.DataFrame(X_selected, columns=selected_feature_names, index=X_predictors.index)

print(f"Original predictor columns: {list(X_predictors.columns)}")
print(f"Columns removed by VarianceThreshold: {list(set(X_predictors.columns) - set(selected_feature_names))}")
print(f"Selected predictor columns: {list(selected_feature_names)}")

# Add intercept to the selected predictors
X_selected_df = sm.add_constant(X_selected_df, prepend=True) # prepend=True adds constant as first column

# Recode 'admit' from (1, 2) to (0, 1) for the dependent variable
y_dependent = df['admit'] - 1

# Fit the logit model with selected features
logit_model_vt = sm.Logit(y_dependent, X_selected_df)
result_vt = logit_model_vt.fit()

print("\n--- Solution 2: Feature Selection with Variance Thresholding ---")
print(result_vt.summary())

# Solution 3: Excluding the Target from Predictors

A common oversight, especially for beginners, is to accidentally include the dependent variable (

admit

in this case) among the independent variables (

train_cols

). This creates perfect multicollinearity.

# 🚀 Speed Seeker, 🔧 Problem Solver
import pandas as pd
import statsmodels.api as sm
import numpy as np

# --- Setup (as per original problem) ---
# Load data
df = pd.read_csv("germandata.txt", delimiter=' ')
df.columns = ["chk_acc", "duration", "history", "purpose", "amount", "savings_acc",
              "employ_since", "install_rate", "pers_status", "debtors",
              "residence_since", "property", "age", "other_plans", "housing",
              "existing_credit", "job", "no_people_liab", "telephone",
              "foreign_worker", "admit"]

# Select numerical columns
cols_to_keep = ['admit', 'duration', 'amount', 'install_rate', 'residence_since',
                'age', 'existing_credit', 'no_people_liab']
data = df[cols_to_keep].copy()

# Add intercept
data['intercept'] = 1.0

# --- The Fix ---
# Ensure 'admit' is NOT in train_cols
# A robust way is to explicitly drop it from all columns or define train_cols carefully.
# Assuming 'admit' is the first column in 'data' after selection
train_cols_fixed = data.drop(columns=['admit']).columns

# Recode 'admit' from (1, 2) to (0, 1) for the dependent variable
y_dependent = data['admit'] - 1

# Fit the logit model
logit_model_exclude = sm.Logit(y_dependent, data[train_cols_fixed])
result_exclude = logit_model_exclude.fit()

print("\n--- Solution 3: Excluding Target from Predictors ---")
print(result_exclude.summary())

# Method 1: Recoding the Dependent Variable (0/1 Transformation)

Persona: 🚀 Speed Seeker, 🔧 Problem Solver, 📚 Learning Explorer

The

statsmodels.Logit

function, like many logistic regression implementations, expects the dependent variable (the target or

endog

variable) to be binary, typically represented as 0 and 1. A "Singular Matrix Error" can occur if the dependent variable contains other values, such as 1 and 2, which is common in some datasets.

# Why it happens:

When

statsmodels

tries to fit the logistic regression model, it performs internal calculations involving the dependent variable. If these values are not strictly 0 and 1, the underlying optimization algorithms (like Maximum Likelihood Estimation) might encounter issues, leading to numerical instability or a singular Hessian matrix, which is crucial for calculating standard errors and convergence. The Hessian matrix becomes singular when there's perfect multicollinearity or, in this case, an unexpected structure in the dependent variable that prevents the model from uniquely determining parameters.

# The Solution:

The fix is straightforward: transform your dependent variable so that its values are 0 and 1. For the German Credit Data, where 'admit' typically has values 1 (good credit) and 2 (bad credit), subtracting 1 from each value will convert them to 0 and 1 respectively.

# Step-by-Step Implementation:

Load and Prepare Data: Start by loading your dataset and selecting the relevant columns, including your dependent variable and numerical predictors.
Identify Dependent Variable: Pinpoint the column that serves as your target.
Transform Values: Apply a simple arithmetic operation (e.g., subtraction) to convert the target values to 0 and 1.
Fit Logit Model: Use the transformed dependent variable with
```
sm.Logit
```
.

# Code Examples:

Let's walk through the full process with the German Credit Data.

# 📚 Learning Explorer: Understanding the data preparation
import pandas as pd
import statsmodels.api as sm
import numpy as np

# 1. Load the dataset
# Ensure 'germandata.txt' is in the same directory or provide the full path
try:
    df = pd.read_csv("germandata.txt", delimiter=' ')
except FileNotFoundError:
    print("Error: 'germandata.txt' not found. Please ensure the file is in the correct directory.")
    # Create a dummy dataframe for demonstration if file not found
    data_dict = {
        "chk_acc": [1, 2, 3, 1, 2], "duration": [6, 48, 12, 42, 24],
        "history": [4, 2, 4, 2, 3], "purpose": [6, 6, 8, 1, 3],
        "amount": [1169, 5951, 2096, 7882, 4870], "savings_acc": [5, 1, 1, 1, 1],
        "employ_since": [5, 3, 4, 4, 3], "install_rate": [4, 2, 2, 2, 3],
        "pers_status": [3, 2, 3, 3, 3], "debtors": [1, 1, 1, 3, 1],
        "residence_since": [4, 2, 3, 4, 4], "property": [2, 1, 1, 4, 4],
        "age": [67, 22, 49, 45, 53], "other_plans": [3, 3, 3, 3, 3],
        "housing": [2, 2, 2, 3, 3], "existing_credit": [2, 1, 1, 1, 2],
        "job": [3, 3, 2, 3, 3], "no_people_liab": [1, 1, 2, 2, 2],
        "telephone": [2, 1, 1, 1, 1], "foreign_worker": [1, 1, 1, 1, 1],
        "admit": [1, 2, 1, 1, 2] # Example values 1 and 2
    }
    df = pd.DataFrame(data_dict)
    print("Using dummy data for demonstration.")


# 2. Rename columns for clarity
df.columns = ["chk_acc", "duration", "history", "purpose", "amount", "savings_acc",
              "employ_since", "install_rate", "pers_status", "debtors",
              "residence_since", "property", "age", "other_plans", "housing",
              "existing_credit", "job", "no_people_liab", "telephone",
              "foreign_worker", "admit"]

# 3. Select numerical variables for this example
cols_to_keep = ['admit', 'duration', 'amount', 'install_rate', 'residence_since',
                'age', 'existing_credit', 'no_people_liab']
data = df[cols_to_keep].copy() # Use .copy() to prevent SettingWithCopyWarning

# 4. Add an intercept term to the independent variables
# This is crucial for statsmodels to estimate the intercept coefficient
data['intercept'] = 1.0

# 5. Define independent variables (predictors)
# All columns except 'admit' (our target)
train_cols = data.columns.drop('admit')

print(f"Original 'admit' values (first 5): {data['admit'].head().tolist()}")

# 6. Transform the dependent variable 'admit' from (1, 2) to (0, 1)
# 🔧 Problem Solver: This is the core fix.
y_dependent_transformed = data['admit'] - 1

print(f"Transformed 'admit' values (first 5): {y_dependent_transformed.head().tolist()}")

# 7. Fit the Logit model
logit_model = sm.Logit(y_dependent_transformed, data[train_cols])
result = logit_model.fit()

# 8. Print the summary
print("\n--- Logit Regression Results (Method 1: Recoded Dependent Variable) ---")
print(result.summary())

# 🎨 Output Focused: Visualizing the transformation
import matplotlib.pyplot as plt
import seaborn as sns

plt.figure(figsize=(10, 4))
plt.subplot(1, 2, 1)
sns.countplot(x=data['admit'])
plt.title("Original 'admit' Distribution (1, 2)")
plt.xlabel("Credit Status")
plt.ylabel("Count")

plt.subplot(1, 2, 2)
sns.countplot(x=y_dependent_transformed)
plt.title("Transformed 'admit' Distribution (0, 1)")
plt.xlabel("Credit Status (0=Good, 1=Bad)")
plt.ylabel("Count")
plt.tight_layout()
plt.show()

# Explanation of Output:

The

result.summary()

output provides a comprehensive overview of the logistic regression model.

Dep. Variable: Shows
```
admit
```
(or whatever your original column name was), but internally it's using the 0/1 transformed values.
No. Observations: Number of rows in your dataset.
Model: Logit.
Method: MLE (Maximum Likelihood Estimation), the standard for logistic regression.
Pseudo R-squ.: A measure of model fit, similar to R-squared in linear regression but interpreted differently.
Log-Likelihood: The log-likelihood of the model.
LL-Null: Log-likelihood of the null model (intercept-only).
LLR p-value: Likelihood Ratio Test p-value, testing if the model with predictors is significantly better than the null model.
Coefficients (coef): The estimated coefficients for each predictor.
Standard Error (std err): Standard error of the coefficients.
z-score (z): Wald z-statistic (coefficient / std err).
P>|z|: P-value for the z-statistic, indicating the statistical significance of each predictor.
[95.0% Conf. Int.]: 95% confidence interval for the coefficients.

This method directly addresses the core requirement of the

statsmodels.Logit

function, making it the primary solution for the German Credit Data scenario.

# Method 2: Feature Selection with Variance Thresholding

Persona: 📚 Learning Explorer, 🏗️ Architecture Builder, 🔧 Problem Solver

A "Singular Matrix Error" can also arise from multicollinearity among your independent variables. This means one or more predictor variables can be perfectly or near-perfectly predicted by a linear combination of other predictors. One common cause is having features with very low variance, meaning they are almost constant across your dataset. Such features provide little to no information to the model and can lead to numerical instability.

# Why it happens:

When a predictor variable has very low (or zero) variance, it means most (or all) of its values are the same. If a column is constant, it's perfectly correlated with the intercept term. If it's nearly constant, it can still cause issues. In the context of matrix inversion (which is part of solving for regression coefficients), a matrix with highly correlated columns (or columns with zero variance) becomes singular or near-singular, making it impossible or numerically unstable to invert.

# The Solution:

Feature selection techniques, specifically variance thresholding, can help identify and remove these problematic features.

sklearn.feature_selection.VarianceThreshold

is a simple yet effective tool for this. It removes all features whose variance does not meet a certain threshold.

# Step-by-Step Implementation:

Load and Prepare Data: Load your dataset and separate your dependent variable from your independent variables.
Apply Variance Thresholding: Use
```
VarianceThreshold
```
from
```
sklearn.feature_selection
```
to filter out low-variance features from your independent variables.
Add Intercept: Add an intercept term to your filtered independent variables.
Fit Logit Model: Fit the
```
statsmodels.Logit
```
model with the cleaned set of independent variables and your (0/1 transformed) dependent variable.

# Code Examples:

# 🏗️ Architecture Builder: Demonstrating a robust feature selection step
import pandas as pd
import statsmodels.api as sm
import numpy as np
from sklearn.feature_selection import VarianceThreshold
import matplotlib.pyplot as plt
import seaborn as sns

# --- Setup (using the same data loading as Method 1) ---
try:
    df = pd.read_csv("germandata.txt", delimiter=' ')
except FileNotFoundError:
    print("Error: 'germandata.txt' not found. Please ensure the file is in the correct directory.")
    # Create a dummy dataframe for demonstration if file not found
    data_dict = {
        "chk_acc": [1, 2, 3, 1, 2], "duration": [6, 48, 12, 42, 24],
        "history": [4, 2, 4, 2, 3], "purpose": [6, 6, 8, 1, 3],
        "amount": [1169, 5951, 2096, 7882, 4870], "savings_acc": [5, 1, 1, 1, 1],
        "employ_since": [5, 3, 4, 4, 3], "install_rate": [4, 2, 2, 2, 3],
        "pers_status": [3, 2, 3, 3, 3], "debtors": [1, 1, 1, 3, 1],
        "residence_since": [4, 2, 3, 4, 4], "property": [2, 1, 1, 4, 4],
        "age": [67, 22, 49, 45, 53], "other_plans": [3, 3, 3, 3, 3],
        "housing": [2, 2, 2, 3, 3], "existing_credit": [2, 1, 1, 1, 2],
        "job": [3, 3, 2, 3, 3], "no_people_liab": [1, 1, 2, 2, 2],
        "telephone": [2, 1, 1, 1, 1], "foreign_worker": [1, 1, 1, 1, 1],
        "admit": [1, 2, 1, 1, 2] # Example values 1 and 2
    }
    df = pd.DataFrame(data_dict)
    print("Using dummy data for demonstration.")

df.columns = ["chk_acc", "duration", "history", "purpose", "amount", "savings_acc",
              "employ_since", "install_rate", "pers_status", "debtors",
              "residence_since", "property", "age", "other_plans", "housing",
              "existing_credit", "job", "no_people_liab", "telephone",
              "foreign_worker", "admit"]

# Select numerical predictor variables (excluding 'admit')
predictor_cols = ['duration', 'amount', 'install_rate', 'residence_since',
                  'age', 'existing_credit', 'no_people_liab']
X_predictors = df[predictor_cols].copy()

# Recode 'admit' from (1, 2) to (0, 1) for the dependent variable
y_dependent = df['admit'] - 1

print(f"Original predictor columns: {list(X_predictors.columns)}")
print(f"Original predictor shape: {X_predictors.shape}")

# --- The Fix: Variance Thresholding ---
# 📚 Learning Explorer: Understanding the threshold
# The threshold can be adjusted. For binary features, a common threshold is p*(1-p)
# where p is the proportion of the minority class. For continuous, a small absolute value.
# Let's calculate variances to help decide a threshold.
print("\nVariance of original predictor columns:")
print(X_predictors.var())

# Example: If 'no_people_liab' had very low variance (e.g., almost all 1s),
# it might be removed. For this specific dataset, these columns might not have
# extremely low variance, but the principle applies.
min_variance_threshold = 0.0001 # A very small threshold to catch near-constant features

selector = VarianceThreshold(threshold=min_variance_threshold)

# Fit and transform the predictor data
X_selected_array = selector.fit_transform(X_predictors)

# Get the names of the selected columns
selected_feature_names = X_predictors.columns[selector.get_support(indices=True)]
X_selected_df = pd.DataFrame(X_selected_array, columns=selected_feature_names, index=X_predictors.index)

print(f"\nColumns removed by VarianceThreshold: {list(set(X_predictors.columns) - set(selected_feature_names))}")
print(f"Selected predictor columns: {list(selected_feature_names)}")
print(f"Shape after VarianceThreshold: {X_selected_df.shape}")

# Add intercept to the selected predictors
X_selected_df = sm.add_constant(X_selected_df, prepend=True)

# Fit the logit model with selected features
logit_model_vt = sm.Logit(y_dependent, X_selected_df)
result_vt = logit_model_vt.fit()

print("\n--- Logit Regression Results (Method 2: Variance Thresholding) ---")
print(result_vt.summary())

# 🎨 Output Focused: Visualizing feature variances
plt.figure(figsize=(12, 6))
X_predictors.var().sort_values(ascending=False).plot(kind='bar')
plt.title('Variance of Predictor Variables')
plt.xlabel('Feature')
plt.ylabel('Variance')
plt.axhline(y=min_variance_threshold, color='r', linestyle='--', label=f'Variance Threshold ({min_variance_threshold})')
plt.legend()
plt.tight_layout()
plt.show()

# When to use this:

When you have a large number of features, especially after one-hot encoding categorical variables, which can sometimes create columns with very few non-zero entries.
When you suspect some features are almost constant and provide little predictive power.
As a preprocessing step to reduce dimensionality and improve model stability.

# Considerations:

Threshold Value: Choosing the right
```
threshold
```
is crucial. A very high threshold might remove important features, while a very low one might not solve the multicollinearity issue. Experimentation is often needed.
Data Scaling: For continuous variables, it's often good practice to scale your data (e.g., using
```
StandardScaler
```
) before applying variance thresholding if you want the threshold to be interpreted consistently across features with different scales. However,
```
VarianceThreshold
```
works on raw variances, so scaling might change which features are removed.
Alternative: For more sophisticated multicollinearity detection, consider calculating the Variance Inflation Factor (VIF) for your predictors.

# Method 3: Excluding the Target from Predictors

Persona: 🚀 Speed Seeker, 🔧 Problem Solver

This is a classic "rookie mistake" that even experienced data scientists can make when rushing or refactoring code: accidentally including the dependent variable (the target

) in the set of independent variables (the predictors

# Why it happens:

If your target variable is included in your predictors, it creates a perfect linear relationship: the target variable is perfectly correlated with itself. This leads to perfect multicollinearity, making the design matrix singular. The model cannot distinguish the effect of the target variable as a predictor from its role as the outcome, leading to an unsolvable system of equations for the coefficients.

# The Solution:

Carefully define your set of independent variables (

train_cols

in the original problem) to explicitly exclude the dependent variable.

# Step-by-Step Implementation:

Load and Prepare Data: Load your dataset.
Identify Dependent Variable: Clearly define your target variable (e.g.,
```
data['admit']
```
).
Define Predictors: Construct your list or DataFrame of independent variables, ensuring the target variable is not included. A robust way is to start with all columns and then
```
drop()
```
the target.
Add Intercept: Add an intercept term to your independent variables.
Fit Logit Model: Fit the
```
statsmodels.Logit
```
model.

# Code Examples:

# 🚀 Speed Seeker: Direct fix for a common oversight
import pandas as pd
import statsmodels.api as sm
import numpy as np

# --- Setup (using the same data loading as Method 1) ---
try:
    df = pd.read_csv("germandata.txt", delimiter=' ')
except FileNotFoundError:
    print("Error: 'germandata.txt' not found. Please ensure the file is in the correct directory.")
    # Create a dummy dataframe for demonstration if file not found
    data_dict = {
        "chk_acc": [1, 2, 3, 1, 2], "duration": [6, 48, 12, 42, 24],
        "history": [4, 2, 4, 2, 3], "purpose": [6, 6, 8, 1, 3],
        "amount": [1169, 5951, 2096, 7882, 4870], "savings_acc": [5, 1, 1, 1, 1],
        "employ_since": [5, 3, 4, 4, 3], "install_rate": [4, 2, 2, 2, 3],
        "pers_status": [3, 2, 3, 3, 3], "debtors": [1, 1, 1, 3, 1],
        "residence_since": [4, 2, 3, 4, 4], "property": [2, 1, 1, 4, 4],
        "age": [67, 22, 49, 45, 53], "other_plans": [3, 3, 3, 3, 3],
        "housing": [2, 2, 2, 3, 3], "existing_credit": [2, 1, 1, 1, 2],
        "job": [3, 3, 2, 3, 3], "no_people_liab": [1, 1, 2, 2, 2],
        "telephone": [2, 1, 1, 1, 1], "foreign_worker": [1, 1, 1, 1, 1],
        "admit": [1, 2, 1, 1, 2] # Example values 1 and 2
    }
    df = pd.DataFrame(data_dict)
    print("Using dummy data for demonstration.")

df.columns = ["chk_acc", "duration", "history", "purpose", "amount", "savings_acc",
              "employ_since", "install_rate", "pers_status", "debtors",
              "residence_since", "property", "age", "other_plans", "housing",
              "existing_credit", "job", "no_people_liab", "telephone",
              "foreign_worker", "admit"]

# Select numerical columns, including 'admit' initially for convenience
cols_all = ['admit', 'duration', 'amount', 'install_rate', 'residence_since',
            'age', 'existing_credit', 'no_people_liab']
data = df[cols_all].copy()

# Recode 'admit' from (1, 2) to (0, 1) for the dependent variable
y_dependent = data['admit'] - 1

# --- The Fix: Explicitly define predictors by dropping the target ---
# 🔧 Problem Solver: This is the most robust way to ensure 'admit' is not included.
X_predictors = data.drop(columns=['admit'])

# Add an intercept term
X_predictors = sm.add_constant(X_predictors, prepend=True)

print(f"Predictor columns after excluding target: {list(X_predictors.columns)}")

# Fit the Logit model
logit_model_exclude = sm.Logit(y_dependent, X_predictors)
result_exclude = logit_model_exclude.fit()

print("\n--- Logit Regression Results (Method 3: Excluding Target from Predictors) ---")
print(result_exclude.summary())

# 🎨 Output Focused: Illustrating the column selection
print("\nOriginal 'data' columns:", data.columns.tolist())
print("Dependent variable 'y_dependent' is derived from 'admit'.")
print("Independent variables 'X_predictors' are derived from 'data' by dropping 'admit'.")

# Common Scenarios for this error:

Copy-pasting code: Reusing code snippets without fully understanding which variables are being passed as
```
endog
```
and
```
exog
```
.
DataFrame slicing: Using
```
df.iloc[:, :]
```
or similar broad selections that inadvertently include the target.
Feature engineering: Creating new features and then accidentally including the original target column in the feature set.

Always double-check the columns you are passing to

sm.Logit

exog

(independent variables) to ensure your dependent variable is not among them.

# Method 4: Handling Zero-Variance or Constant Predictor Columns

Persona: 🔧 Problem Solver, 📚 Learning Explorer

This method is closely related to Method 2 (Variance Thresholding) but focuses specifically on the extreme case where a predictor column has zero variance, meaning all its values are identical. This can happen with data cleaning, feature engineering, or when a dataset contains columns that are effectively constants.

# Why it happens:

If a column in your independent variable matrix (

exog

) has zero variance, it means every value in that column is the same. For example, a column named

is_always_true

where every entry is

. When

statsmodels

attempts to invert the design matrix (or perform calculations involving it), a column of identical values makes the matrix singular. This is because such a column provides no unique information and is perfectly collinear with the intercept term (if an intercept is included). The model cannot estimate a unique coefficient for a variable that doesn't vary.

# The Solution:

Identify and remove any predictor columns that have zero variance.

# Step-by-Step Implementation:

Load and Prepare Data: Load your dataset and separate your dependent variable from your independent variables.
Calculate Variance: For each independent variable, calculate its variance.
Identify Constant Columns: Filter out columns where the variance is zero.
Add Intercept: Add an intercept term to your filtered independent variables.
Fit Logit Model: Fit the
```
statsmodels.Logit
```
model with the cleaned set of independent variables and your (0/1 transformed) dependent variable.

# Code Examples:

# 🔧 Problem Solver: Direct approach to remove constant columns
import pandas as pd
import statsmodels.api as sm
import numpy as np

# --- Setup (using the same data loading as Method 1) ---
try:
    df = pd.read_csv("germandata.txt", delimiter=' ')
except FileNotFoundError:
    print("Error: 'germandata.txt' not found. Please ensure the file is in the correct directory.")
    # Create a dummy dataframe for demonstration if file not found
    data_dict = {
        "chk_acc": [1, 2, 3, 1, 2], "duration": [6, 48, 12, 42, 24],
        "history": [4, 2, 4, 2, 3], "purpose": [6, 6, 8, 1, 3],
        "amount": [1169, 5951, 2096, 7882, 4870], "savings_acc": [5, 1, 1, 1, 1],
        "employ_since": [5, 3, 4, 4, 3], "install_rate": [4, 2, 2, 2, 3],
        "pers_status": [3, 2, 3, 3, 3], "debtors": [1, 1, 1, 3, 1],
        "residence_since": [4, 2, 3, 4, 4], "property": [2, 1, 1, 4, 4],
        "age": [67, 22, 49, 45, 53], "other_plans": [3, 3, 3, 3, 3],
        "housing": [2, 2, 2, 3, 3], "existing_credit": [2, 1, 1, 1, 2],
        "job": [3, 3, 2, 3, 3], "no_people_liab": [1, 1, 2, 2, 2],
        "telephone": [2, 1, 1, 1, 1], "foreign_worker": [1, 1, 1, 1, 1],
        "admit": [1, 2, 1, 1, 2],
        "constant_feature": [10, 10, 10, 10, 10] # Added a constant feature for demonstration
    }
    df = pd.DataFrame(data_dict)
    print("Using dummy data for demonstration, including a 'constant_feature'.")

df.columns = ["chk_acc", "duration", "history", "purpose", "amount", "savings_acc",
              "employ_since", "install_rate", "pers_status", "debtors",
              "residence_since", "property", "age", "other_plans", "housing",
              "existing_credit", "job", "no_people_liab", "telephone",
              "foreign_worker", "admit", "constant_feature"] # Update columns for dummy data

# Select numerical predictor variables (excluding 'admit')
predictor_cols = ['duration', 'amount', 'install_rate', 'residence_since',
                  'age', 'existing_credit', 'no_people_liab', 'constant_feature']
X_predictors = df[predictor_cols].copy()

# Recode 'admit' from (1, 2) to (0, 1) for the dependent variable
y_dependent = df['admit'] - 1

print(f"Original predictor columns: {list(X_predictors.columns)}")
print(f"Original predictor shape: {X_predictors.shape}")

# --- The Fix: Remove constant columns ---
# 📚 Learning Explorer: Understanding how to identify constant columns
# Calculate variance for each column
variances = X_predictors.var()
print("\nVariances of predictor columns:")
print(variances)

# Identify columns with zero variance
constant_columns = variances[variances == 0].index.tolist()

if constant_columns:
    print(f"\nIdentified constant columns (zero variance): {constant_columns}")
    X_filtered = X_predictors.drop(columns=constant_columns)
    print(f"Predictor columns after removing constant features: {list(X_filtered.columns)}")
else:
    print("\nNo constant columns found.")
    X_filtered = X_predictors.copy()

# Add intercept to the filtered predictors
X_filtered = sm.add_constant(X_filtered, prepend=True)

# Fit the logit model
logit_model_constant = sm.Logit(y_dependent, X_filtered)
result_constant = logit_model_constant.fit()

print("\n--- Logit Regression Results (Method 4: Removed Constant Predictors) ---")
print(result_constant.summary())

# 🎨 Output Focused: Displaying the constant feature
if 'constant_feature' in df.columns:
    print(f"\nExample of a constant feature ('constant_feature'):")
    print(df['constant_feature'].value_counts())

# When to use this:

As a robust data cleaning step before model training.
When you suspect data collection errors or issues in feature engineering that might have created constant columns.
When
```
VarianceThreshold
```
with a very small threshold (like 0) is too aggressive, and you only want to remove strictly constant features.

This method is a specific application of the broader concept of multicollinearity handling, ensuring that your model's design matrix is well-conditioned.

# Method 5: Addressing Multicollinearity in One-Hot Encoded Variables

Persona: 🏗️ Architecture Builder, 📚 Learning Explorer

When dealing with categorical variables, one-hot encoding is a common technique to convert them into a numerical format suitable for regression models. However, if not handled correctly, one-hot encoding can introduce perfect multicollinearity, known as the "Dummy Variable Trap," leading to a Singular Matrix Error.

# Why it happens:

Consider a categorical variable

Gender

with two categories: 'Male' and 'Female'. If you one-hot encode it into two new columns,

Gender_Male

(1 if Male, 0 otherwise) and

Gender_Female

(1 if Female, 0 otherwise), you create a perfect linear dependency:

Gender_Male + Gender_Female = 1

for every observation. If your model also includes an intercept term (which

statsmodels

does by default or when you add

sm.add_constant

), then

Gender_Male + Gender_Female - 1 = 0

, meaning one of these dummy variables can be perfectly predicted by the other and the intercept. This perfect linear relationship makes the design matrix singular.

# The Solution:

To avoid the Dummy Variable Trap, you should always drop one of the dummy variables for each set of one-hot encoded categorical features. This is often referred to as "dropping the first" or "dropping the last" category.

# Step-by-Step Implementation:

Load and Prepare Data: Load your dataset. Identify categorical variables that need one-hot encoding.
One-Hot Encode with
drop_first=True
: Use
```
pd.get_dummies()
```
with the
```
drop_first=True
```
argument. This automatically drops the first category for each one-hot encoded variable, preventing multicollinearity.
Combine with Numerical Features: Merge the one-hot encoded features with your existing numerical features.
Add Intercept: Add an intercept term to the combined independent variables.
Fit Logit Model: Fit the
```
statsmodels.Logit
```
model.

# Code Examples:

For the German Credit Data, some columns like

chk_acc

history

purpose

savings_acc

, etc., are categorical, even though they are represented numerically. Let's demonstrate this with

chk_acc

and

purpose

# 🏗️ Architecture Builder: Implementing robust categorical feature handling
import pandas as pd
import statsmodels.api as sm
import numpy as np

# --- Setup (using the same data loading as Method 1) ---
try:
    df = pd.read_csv("germandata.txt", delimiter=' ')
except FileNotFoundError:
    print("Error: 'germandata.txt' not found. Please ensure the file is in the correct directory.")
    # Create a dummy dataframe for demonstration if file not found
    data_dict = {
        "chk_acc": [1, 2, 3, 1, 2], "duration": [6, 48, 12, 42, 24],
        "history": [4, 2, 4, 2, 3], "purpose": [6, 6, 8, 1, 3],
        "amount": [1169, 5951, 2096, 7882, 4870], "savings_acc": [5, 1, 1, 1, 1],
        "employ_since": [5, 3, 4, 4, 3], "install_rate": [4, 2, 2, 2, 3],
        "pers_status": [3, 2, 3, 3, 3], "debtors": [1, 1, 1, 3, 1],
        "residence_since": [4, 2, 3, 4, 4], "property": [2, 1, 1, 4, 4],
        "age": [67, 22, 49, 45, 53], "other_plans": [3, 3, 3, 3, 3],
        "housing": [2, 2, 2, 3, 3], "existing_credit": [2, 1, 1, 1, 2],
        "job": [3, 3, 2, 3, 3], "no_people_liab": [1, 1, 2, 2, 2],
        "telephone": [2, 1, 1, 1, 1], "foreign_worker": [1, 1, 1, 1, 1],
        "admit": [1, 2, 1, 1, 2]
    }
    df = pd.DataFrame(data_dict)
    print("Using dummy data for demonstration.")

df.columns = ["chk_acc", "duration", "history", "purpose", "amount", "savings_acc",
              "employ_since", "install_rate", "pers_status", "debtors",
              "residence_since", "property", "age", "other_plans", "housing",
              "existing_credit", "job", "no_people_liab", "telephone",
              "foreign_worker", "admit"]

# Recode 'admit' from (1, 2) to (0, 1) for the dependent variable
y_dependent = df['admit'] - 1

# Identify numerical and categorical columns for this example
numerical_cols = ['duration', 'amount', 'install_rate', 'residence_since',
                  'age', 'existing_credit', 'no_people_liab']
categorical_cols = ['chk_acc', 'purpose'] # Example categorical columns

# Extract numerical features
X_numerical = df[numerical_cols].copy()

# --- The Fix: One-Hot Encode with drop_first=True ---
# 📚 Learning Explorer: Understanding the 'drop_first' parameter
X_categorical_encoded = pd.get_dummies(df[categorical_cols], columns=categorical_cols, drop_first=True)

print(f"Original categorical columns: {categorical_cols}")
print(f"One-hot encoded columns (with drop_first=True): {list(X_categorical_encoded.columns)}")

# Combine numerical and encoded categorical features
X_predictors_combined = pd.concat([X_numerical, X_categorical_encoded], axis=1)

# Add an intercept term
X_predictors_combined = sm.add_constant(X_predictors_combined, prepend=True)

print(f"\nFinal predictor columns: {list(X_predictors_combined.columns)}")
print(f"Final predictor shape: {X_predictors_combined.shape}")

# Fit the Logit model
logit_model_ohe = sm.Logit(y_dependent, X_predictors_combined)
result_ohe = logit_model_ohe.fit()

print("\n--- Logit Regression Results (Method 5: One-Hot Encoding with drop_first=True) ---")
print(result_ohe.summary())

# 🎨 Output Focused: Illustrating the effect of drop_first
print("\nExample of 'chk_acc' original values and one-hot encoded columns:")
print(df[['chk_acc']].head())
print(pd.get_dummies(df[['chk_acc']], drop_first=False).head()) # Without drop_first
print(pd.get_dummies(df[['chk_acc']], drop_first=True).head())  # With drop_first

# When to use this:

Whenever you are using one-hot encoding for categorical variables in a regression model that includes an intercept.
To prevent perfect multicollinearity and ensure your model's design matrix is full rank.

# Important Considerations:

Interpretation: When you drop a dummy variable, the coefficients of the remaining dummy variables for that category are interpreted relative to the dropped (reference) category.
Interaction Terms: If you create interaction terms involving one-hot encoded variables, ensure that the base dummy variables are handled correctly to avoid multicollinearity in the interaction terms as well.
statsmodels.formula.api
: If you use
```
statsmodels.formula.api
```
(e.g.,
```
smf.logit
```
), it often handles dummy variable encoding and the dummy variable trap automatically. However, when using
```
sm.Logit
```
directly with
```
endog
```
and
```
exog
```
DataFrames, manual handling is required.

# Performance Comparison

This table compares the discussed methods based on various criteria relevant to different user personas.