Module M.5 Linear mixed-effects models

Introduction to Primate Data Exploration and Linear Modeling with R

Introduction: Linear mixed-effects models (LMMs), also known as hierarchical models, are another extension of simple linear models used when there is clustering (i.e., nested data structures) or non-independence (i.e., repeated measurements) among observations. These models are called “mixed-effects” because they incorporate both fixed and random effects. Fixed effects are variables with a constant effect on the response variable, while random effects are variables whose values or levels are assumed to be drawn randomly from a larger population of levels. Given the natural clustering in biological data (e.g., genetic groups, geographic locations), as well as the longitudinal monitoring of the same individuals over time, LMMs represent another essential tool in modern population biology.

In this module, you will expand your skills on linear models (Modules M.4) to LMMs while testing associations between Cayo Santiago rhesus macaque social cognition and age.

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Upon completion of this module, you will be able to:

• Fit linear mixed-effects models in R;
• Interpret model output;
• Plot model predictions;
• Visualize random effects.

References:

• ggplot2
• lmerTest: Tests in Linear Mixed Effects Models
• RStudio
• Tidyverse R packages for data science

Extra training:

• Freeman 2017. An introduction to hierarchical modeling
• Oskolkov 2020. How linear mixed model works

Associated literature:

• Rosati et al. 2018. Developmental shifts in social cognition: socio-emotional biases across the lifespan in rhesus monkeys

• Rosati et al. 2018. Data from: Developmental shifts in social cognition: socio-emotional biases across the lifespan in rhesus monkeys

Expand for R Notation and functions index

Notation:

• [] for subsets by columns.

Functions:

• Base R:

  • class() and str() for data structure;
  • predict() for extracting model predictions;
  • summary() for model output.

• ggeffects:

  • ggpredict() for plotting model predictions.

• lmerTest:

  • lmer() for fitting linear mixed-effects models.

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Testing associations between social cognition and age

Rhesus macaques represent an excellent comparative system to study the evolutionary origins of cognitive development in primates. However, comparative developmental research on cognition is often challenging to implement due to low sample sizes or no access to populations of individuals that vary with age. Cayo Santiago rhesus macaques provide the rare opportunity to address questions on the evolution of cognition, given that experimental tasks can be performed in many individuals in the field. Cayo Santiago monkeys are habituated to human observers, and thus researchers can generate relatively large amounts of data of socioemotional cognitive traits of individuals with known age (Fig 1).