Types of Logistic Regression

 

Types of Logistic Regression

Logistic Regression can be categorized based on the type and number of output classes in the problem.

1. Binary Logistic Regression

🔹 Definition:

Used when the dependent variable has only two possible outcomes.

🔹 Output:

  • 0 or 1
  • Yes / No
  • True / False

🔹 Examples:

  • Email classification → Spam / Not Spam
  • Disease detection → Positive / Negative
  • Loan approval → Approved / Rejected

🔹 How it works:

  • Predicts the probability of one class
  • Uses a threshold (usually 0.5) to decide the final class

2. Multinomial Logistic Regression

🔹 Definition:

Used when there are three or more categories, and no natural order between them.

🔹 Output:

  • One class out of many (mutually exclusive)

🔹 Examples:

  • Food preference → Veg / Non-Veg / Vegan
  • Handwritten digit recognition → 0–9
  • Type of animal → Dog / Cat / Bird

🔹 How it works:

  • Extends binary logistic regression
  • Uses techniques like:
    • Softmax function
    • One-vs-Rest (OvR) classification

3. Ordinal Logistic Regression

🔹 Definition:

Used when there are multiple categories with a meaningful order or ranking.

🔹 Output:

  • Ordered categories

🔹 Examples:

  • Movie ratings → 1 to 5 stars
  • Customer satisfaction → Low / Medium / High
  • Education level → School / College / Graduate

🔹 How it works:

  • Considers the order between categories
  • Predicts probabilities while maintaining ranking relationships

🔁 Quick Comparison

TypeNumber of Classes    Order Matters?    Example
Binary    2    ❌ No    Spam / Not Spam
Multinomial    3+    ❌ No    Food preference
Ordinal    3+    ✅ Yes    Ratings (1–5)

💡 Key Insight

Choosing the right type depends on:

  • Number of categories
  • Whether those categories have a natural order

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