17. Dependence and Mixed Models

When Observations Are Not Independent

1 Introduction

Many datasets contain dependence that simple regression and ANOVA do not handle well. Repeated measures, nested sampling, temporal autocorrelation, and spatial clustering all violate the assumption that observations contribute fully independent information.

This chapter links that problem to the logic of mixed-effects models.

2 Key Concepts

These ideas explain why mixed models enter the workflow.

• Dependence means observations share structure and are not fully independent.
• Nested and repeated-measures data are common sources of dependence.
• Mixed-effects models separate fixed effects from group-level random variation.
• Ignoring dependence often produces overconfident inference.
• Model structure should reflect sampling structure as well as the biological question.

3 Main Ideas

• Dependence can arise from time, space, hierarchy, or repeated measurement.
• Pseudoreplication can occur at the analysis stage when dependence is ignored.
• Mixed-effects models allow part of the variation to be modelled at the group level rather than forcing all observations into a single independent structure.

4 Common Cases

• quadrats within sites,
• repeated measures on the same individual,
• observations nested within years, bays, or transects,
• temporal or spatial autocorrelation.

5 Why Mixed Models Help

Mixed models separate:

• fixed effects, which represent the systematic effects of interest, and
• random effects, which capture structured variation among groups or units.

They are often the right next step when dependence is real and biologically meaningful.

6 Links

This chapter consolidates:

• 22-data-dependence.qmd
• 23-mixed-models.qmd