19. Nonlinear and Flexible Regression

When Straight Lines Are Not Enough

1 Introduction

Some relationships are curved because the biology is curved. Growth saturates, rates asymptote, thresholds appear, and effects change across the predictor range.

This chapter groups together approaches that relax the strict straight-line form of simple linear regression.

2 Key Concepts

The central ideas are these.

• Nonlinearity often reflects real biological structure rather than nuisance variation.
• Flexible regression can improve fit when straight-line assumptions fail.
• Polynomial, mechanistic, quantile, and additive models answer different kinds of questions.
• Greater flexibility increases interpretive demands and the risk of overfitting.
• Model choice should follow biological form, not only statistical convenience.

3 Families Covered

• polynomial regression,
• nonlinear mechanistic models,
• quantile regression,
• generalised additive models.

4 Practical Principle

Use flexible regression when the biological process or the residual structure makes a straight line inadequate. Greater flexibility can improve fit, but it also increases interpretive demands.

5 Sources

This chapter will draw primarily on:

• /Users/ajsmit/Documents/R_local/BCB_Stats/non-linear_regression.qmd
• /Users/ajsmit/Documents/R_local/BCB_Stats/quantile_regression.qmd
• /Users/ajsmit/Documents/R_local/BCB_Stats/generalised_additive_models.qmd