Michael Brenndoerfer | Data & AI, Private Equity, Technology

Michael Brenndoerfer

Generalized Linear Models › Visualizing GLMs

Michael BrenndoerferApril 1, 20252 min read

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Part 4 of 9Regression Models

Chapter 40Generalized Linear Models › Visualizing GLMs

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The following visualizations demonstrate how different link functions transform the linear predictor to produce the expected response. Each GLM type uses a specific link function that is mathematically appropriate for its target distribution. The identity link maintains linearity for continuous normal data, the logit link produces S-shaped probabilities for binary outcomes, and the log link ensures positive predictions for count data.

Out[7]:

Visualization

Blue diagonal identity-link line across linear predictor eta from minus four to four and expected response mu on the same unbounded scale. — Identity link function for linear regression. The linear predictor η maps directly to the expected response μ without mapping (μ = η), maintaining a one-to-one linear relationship suitable for continuous, unbounded outcomes.

Coral S-shaped inverse-logit curve across eta from minus four to four, with expected response constrained from zero to one. — Logit link function for logistic regression. The inverse logit (logistic sigmoid) maps the unbounded linear predictor η into probabilities between 0 and 1 using μ = 1/(1 + e^(-η)), creating the characteristic S-shaped curve.

Teal exponential inverse-log curve across eta from minus four to four, with the displayed expected-response range retained from zero to ten. — Log link function for Poisson regression. The exponential function maps the linear predictor η into strictly positive expected counts using μ = e^η.