18. Generalised Linear Models

Extending Regression Beyond Normal Responses

1 Introduction

Linear regression assumes a normally distributed response with constant variance. Many biological data do not satisfy that structure. Counts, proportions, and binary outcomes require a broader framework.

Generalised linear models (GLMs) provide that framework by combining:

• a response distribution,
• a linear predictor, and
• a link function.

2 Key Concepts

The GLM framework rests on a few core components.

• GLMs extend linear-model logic to non-normal responses.
• Response distributions should match the data-generating structure, such as counts or proportions.
• Link functions connect the linear predictor to the expected response scale.
• Overdispersion is a practical warning sign that the simplest count model may be inadequate.
• Interpretation still depends on biological question and design, not only on family choice.

3 Common Biological GLMs

• Binomial GLM for presence/absence or success/failure data.
• Poisson GLM for count data.
• Negative binomial models when count data are overdispersed.

4 Why GLMs Matter

GLMs let us keep the logic of regression while matching the model more closely to the data-generating process.

5 Source

This chapter will draw primarily on the material in:

• /Users/ajsmit/Documents/R_local/BCB_Stats/generalised_linear_models.qmd