How do I fit a Generalized Additive Model (GAM) and plot categorical variables?

Fitting a Generalized Additive Model (GAM) and plotting categorical variables involves several steps. Here's a breakdown using Python with the `pygam` and `matplotlib` libraries:

1. Install Necessary Libraries:

- Ensure you have `pygam`, `pandas`, `numpy`, and `matplotlib` installed. You can install them using pip:

pip install pygam pandas numpy matplotlib

2. Prepare Your Data:

- Load your data into a pandas DataFrame. Make sure your categorical variables are encoded as factors or strings. If they are numerical, convert them to strings or use one-hot encoding.

3. Fit the GAM:

- Use `pygam` to fit the GAM. You can specify smooth functions for numerical variables and use `te()` for interactions. For categorical variables, you can use `s()` with `by` to model different smooth functions for each category.

4. Plot Categorical Variables:

- After fitting the GAM, you can plot the effect of each categorical variable. This typically involves plotting the partial dependence of the model on each category.

5. Example Code:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from pygam import GAM, s, te

# Sample Data (Replace with your actual data)
data = {'numerical_var': np.random.rand(100),
'categorical_var': np.random.choice(['A', 'B', 'C'], 100),
'target': np.random.rand(100)}
df = pd.DataFrame(data)

# Convert categorical variable to string
df['categorical_var'] = df['categorical_var'].astype(str)

# Fit the GAM
gam = GAM(s(0) + s(1, by=df['categorical_var'])).fit(df[['numerical_var', 'categorical_var']], df['target'])

# Plotting
fig, axes = plt.subplots(1, len(df['categorical_var'].unique()), figsize=(15, 5))
for i, cat in enumerate(df['categorical_var'].unique()):
XX = gam.generate_X_grid(term=1, by=cat)
pdep, confi = gam.partial_dependence(term=1, X=XX, by=cat, width=0.95)
axes[i].plot(XX[:, 0], pdep)
axes[i].plot(XX[:, 0], confi, c='r', ls='--')
axes[i].set_title(f'Category: {cat}')
axes[i].set_xlabel('Numerical Variable')
axes[i].set_ylabel('Partial Dependence')
plt.tight_layout()
plt.show()


6. Explanation:

- The code first loads the data and converts the categorical variable to a string type. Then, it fits a GAM using `pygam`. The `s(0)` term models the smooth effect of the numerical variable, and `s(1, by=df['categorical_var'])` models separate smooth effects for each category of the categorical variable. Finally, it generates partial dependence plots for each category, showing how the model's prediction changes with the numerical variable for each category.

By following these steps, you can fit a GAM and visualize the effects of categorical variables effectively. Remember to adapt the code to your specific dataset and model requirements.

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