Generalized Linear Models (GLMs) are a flexible extension of traditional linear regression that allow us to model a wide range of data types, including binary outcomes, counts, and more. GLMs link the mean of the response variable to the predictors through a link function and handle non-normal error distributions. This makes them very useful in real-world datasets where data rarely fits the assumptions of simple linear regression.
I decided to write about Generalized Linear Models because they form the backbone of modern applied statistics and data science. Whether you’re studying logistic regression, Poisson regression, or even multinomial models, they all fall under the GLM family. Understanding the core idea behind GLMs can help you grasp multiple modelling techniques faster, and it’s essential for competitive exams, research projects, or analytics work. I still remember struggling with the link function concept, and that’s why I’ve broken it down in this article for clarity. If you’re someone who wants to move beyond basic regression but finds the jump confusing, this is for you.
What are Generalized Linear Models?
Generalized Linear Models allow us to model the relationship between a dependent variable and one or more independent variables when the response variable does not follow a normal distribution.
A GLM has three key components:
- Random component: Distribution of the response variable (e.g., normal, binomial, Poisson)
- Systematic component: The linear predictor (a combination of explanatory variables)
- Link function: Connects the expected value of the response variable to the linear predictor
Common Types of GLMs
| GLM Type | Response Variable | Link Function | Use Case Example |
|---|---|---|---|
| Linear Regression | Continuous | Identity | Predicting house prices |
| Logistic Regression | Binary (0/1) | Logit | Customer churn prediction |
| Poisson Regression | Count data | Log | Modelling number of calls per day |
| Multinomial Logistic | Categorical (more than 2 classes) | Logit | Classifying news topics |
Why Use GLMs?
- Flexibility: Handles non-normal distributions
- Better Fit: Matches model to nature of the data
- Real-world applications: Used in healthcare, marketing, finance, and public policy
For example, if you’re trying to predict whether a customer will buy a product (yes or no), a linear regression will give invalid probabilities. Logistic regression (a type of GLM) is more appropriate here.
Important Concepts in GLMs
- Link Function: Helps us model relationships that are not linear in the raw data.
- Deviance: Similar to residual sum of squares in linear regression, used to assess model fit.
- Overdispersion: If variance > mean in Poisson models, GLMs like Quasi-Poisson or Negative Binomial are better.
- AIC/BIC: Used for model comparison and selection
Download PDF – Generalized Linear Models Notes
Download Link: [Click here to download PDF] (Insert actual link)
What’s inside the PDF:
- Full explanation of GLM structure
- Visual summary of GLM types
- Differences between linear models and GLMs
- Link function chart
- Practical examples and solved problems
- Code snippets in R and Python
Conclusion
Generalized Linear Models are powerful because they extend regression to handle a wider variety of real-world data. They’re used across domains like healthcare (predicting disease outcomes), business (modelling customer purchase decisions), and science (analysing experimental data). Once you get the basic structure and logic of GLMs, you can apply them confidently in many scenarios. The downloadable PDF will help you revise the topic quickly — whether for exams or interviews. Keep learning and keep experimenting with real datasets to get a stronger hold on these models.
