Generalised Linear Models (GLM): Going Beyond “Normal” Linear Regression

Classical linear regression is a strong starting point for prediction and explanation, but it rests on assumptions that are often unrealistic: the response is continuous, errors are normally distributed, and variance is roughly constant. Real-world data rarely behaves so neatly. Counts of website sign-ups, conversion rates, churn flags, defect occurrences, and insurance claims are not well represented by a normal distribution. This is where Generalised Linear Models (GLMs) become essential: they extend linear regression so the response variable can follow non-normal error distributions such as Binomial or Poisson. If you are exploring applied modelling through data science classes in Bangalore, GLMs are one of the most practical tools to master because they show up across product analytics, marketing, healthcare, finance, and operations.

Why Linear Regression Breaks for Many Business Problems

Linear regression is built for continuous outcomes where negative predictions and unbounded ranges are acceptable. But consider common scenarios:

• Binary outcomes: Will a lead convert (yes/no)? Will a user churn (true/false)?
• Counts: How many support tickets arrive per day? How many defects are observed per batch?
• Positive skewed measures: Claim amounts, time-to-fix, waiting times.

Using ordinary linear regression in such cases can produce nonsensical predictions (like negative counts) and misleading uncertainty estimates. GLMs solve this by letting you choose an error distribution that matches the response and by using a transformation (called a link function) that keeps predictions within valid ranges. This shift is not cosmetic; it changes how the model represents variance, how parameters are estimated, and how predictions should be interpreted.

The Core Structure of a GLM

A GLM is defined by three components:

1. Random component (distribution of the response)
2. The response YYY is assumed to follow a distribution from the exponential family (commonly Normal, Binomial, Poisson, Gamma).
   • Binomial: for proportions/binary outcomes
   • Poisson: for counts
   • Gamma: for positive, right-skewed continuous values
3. Systematic component (linear predictor)
4. This looks familiar:
5. η=β0+β1×1+⋯+βpxp\eta = \beta_0 + \beta_1 x_1 + \dots + \beta_p x_pη=β0​+β1​x1​+⋯+βp​xp​Here, η\etaη is the linear predictor built from features.
6. Link function (relationship between mean and linear predictor)
7. The link connects the expected value E[Y]=μE[Y]=\muE[Y]=μ to the linear predictor:
8. g(μ)=ηg(\mu) = \etag(μ)=ηThe choice of link ensures predictions stay in the correct range. For instance, logistic regression uses the logit link to keep probabilities between 0 and 1.

Common GLMs You’ll Use Most Often

Logistic Regression (Binomial + Logit Link)

Used for binary classification and probability modelling. Examples: conversion, fraud detection (flag/not), churn (yes/no).

Interpretation typically uses odds ratios: a one-unit increase in a feature multiplies the odds of “success” by eβe^{\beta}eβ.

Poisson Regression (Poisson + Log Link)

Used for event counts over a fixed exposure window: tickets per day, clicks per session, failures per machine-hour.

Coefficients are interpreted as rate ratios: eβe^{\beta}eβ scales the expected count multiplicatively.

Variants and Practical Extensions

In real projects, you will often meet complications such as overdispersion (variance greater than mean in count data). When that happens, a Negative Binomial model is frequently preferred. Exposure can also be included through offsets (e.g., modelling incidents per kilometre, per hour, or per user). These are the kinds of details that typically come up in capstone-style case studies in data science classes in Bangalore because they mirror what happens in production analytics.

Fitting, Diagnostics, and Common Pitfalls

GLMs are usually fit using maximum likelihood estimation (MLE) rather than least squares. That changes how you evaluate and debug models. Key practices include:

• Check model fit: look at deviance, residual plots, and information criteria like AIC for model comparison.
• Watch for separation (logistic regression): if a feature perfectly predicts the outcome, coefficients can blow up.
• Handle multicollinearity: correlated predictors can make coefficients unstable; regularisation (L1/L2) can help.
• Assess calibration for probabilities: for logistic models, ensure predicted probabilities match observed frequencies.
• Account for overdispersion: Poisson assumptions can fail when counts are “bursty”; consider Negative Binomial or quasi-Poisson approaches.

A good modelling workflow treats GLMs as part of an iterative loop: start with a baseline model, validate assumptions, refine the feature set, and compare alternatives using hold-out performance and interpretability needs.

Conclusion

Generalised Linear Models bridge the gap between elegant theory and messy real-world outcomes. They keep the familiar linear predictor, but replace the “one-size-fits-all normal error” assumption with distributions and link functions that match how data actually behaves. Logistic regression and Poisson regression alone cover a large share of practical industry problems, from conversion modelling to operational forecasting. If your learning path includes data science classes in Bangalore, investing time in GLMs will pay off quickly,because they teach not just how to fit models, but how to choose the right statistical assumptions for the question you are answering.