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One-hot-encoding

One-hot encoding creates new binary columns for each category in a categorical variable. In your example, data_encoded already includes the columns SubscriptionType_Standard and SubscriptionType_Premium because they were created by the one-hot encoding process. Let’s walk through how one-hot encoding works and how it results in the additional columns you’re seeing.

One-Hot Encoding

One-hot encoding is a technique used to convert categorical variables into a format that can be provided to machine learning algorithms to do a better job in prediction. Each category in a categorical variable is converted into a new binary column.

Let’s take an example to understand this better.

Suppose you have a categorical variable SubscriptionType with three categories:

Basic
Standard
Premium

Before One-Hot Encoding

Your DataFrame might look like this:

Age	Usage	Gender	SubscriptionType
25	200	Male	Basic
30	150	Female	Premium
22	300	Male	Standard
…	…	…	…

After One-Hot Encoding

One-hot encoding transforms the SubscriptionType column into three new columns: SubscriptionType_Basic, SubscriptionType_Standard, and SubscriptionType_Premium. For each row, the column corresponding to the subscription type of that row will have a 1, and the others will have a 0.

Age	Usage	Gender	SubscriptionType_Basic	SubscriptionType_Standard	SubscriptionType_Premium
25	200	Male	1	0	0
30	150	Female	0	0	1
22	300	Male	0	1	0
…	…	…	…	…	…

Similarly, if you apply one-hot encoding to the Gender column, it will result in Gender_Male (assuming you use drop_first=True to avoid multicollinearity):

Age	Usage	Gender_Male	SubscriptionType_Basic	SubscriptionType_Standard	SubscriptionType_Premium
25	200	1	1	0	0
30	150	0	0	0	1
22	300	1	0	1	0
…	…	…	…	…	…

Applying One-Hot Encoding in Python

Here’s how you can achieve this in Python using pandas:

import pandas as pd

# Assuming your original DataFrame is named 'data'
data = pd.DataFrame({
    'Age': [25, 30, 22],
    'Usage': [200, 150, 300],
    'Gender': ['Male', 'Female', 'Male'],
    'SubscriptionType': ['Basic', 'Premium', 'Standard']
})

# Applying one-hot encoding
data_encoded = pd.get_dummies(data, columns=['Gender', 'SubscriptionType'], drop_first=True)

print(data_encoded)

   Age  Usage  Gender_Male  SubscriptionType_Premium  SubscriptionType_Standard
0   25    200           1                       0                       0
1   30    150           0                       1                       0
2   22    300           1                       0                       1

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Understanding One-Hot Encoding and the Reference Category in Logistic Regression

In one-hot encoding, the “reference column” or “baseline category” is often omitted to avoid multicollinearity in the model. This is known as “dummy variable trap.” Let’s explain why this happens and the reasoning behind it.

Multicollinearity

Multicollinearity occurs when one predictor variable in a model can be linearly predicted from the others with a substantial degree of accuracy. This makes it difficult for the model to determine the individual effect of each predictor.

The Dummy Variable Trap

If you include all dummy variables for a categorical feature, one of them can be perfectly predicted from the others. For example, consider the SubscriptionType feature with categories Basic, Standard, and Premium. If you encode them all into separate dummy variables:

SubscriptionType_Basic
SubscriptionType_Standard
SubscriptionType_Premium

Every row in your dataset will satisfy the following relationship:

SubscriptionType_Basic+SubscriptionType_Standard+SubscriptionType_Premium=1

This perfect linear relationship among the dummy variables introduces multicollinearity.

Omitting the Reference Column

To avoid this, one category is chosen as the “reference category” or “baseline category” and is omitted. The omitted category serves as the baseline against which the effects of the other categories are compared.

For your example with the SubscriptionType feature:

Reference Category: Basic (omitted)
Included Dummy Variables: SubscriptionType_Standard, SubscriptionType_Premium

When the dummy variables for Standard and Premium are both 0, it implies the subscription type is Basic. Here’s how the categories are represented:

Basic: SubscriptionType_Standard = 0, SubscriptionType_Premium = 0
Standard: SubscriptionType_Standard = 1, SubscriptionType_Premium = 0
Premium: SubscriptionType_Standard = 0, SubscriptionType_Premium = 1

Why the Reference Category is Omitted

By omitting the reference category (Basic), we avoid multicollinearity, and the logistic regression model can correctly interpret the effects of Standard and Premium relative to Basic. The coefficients for SubscriptionType_Standard and SubscriptionType_Premium will represent the change in the log-odds of the outcome (e.g., renewal) relative to the reference category (Basic).

one-hot-encoding-py