Module M.7 Generalized linear mixed-effects models

Introduction to Primate Data Exploration and Linear Modeling with R

Introduction: Generalized linear mixed-effects models (GLMMs) are an extension of linear mixed-effects models (Module M.5) used when there is clustering (i.e., nested data structures) or non-independence (i.e., repeated measurements) among observations and the response variable is not normally distributed. As generalized linear models (Module M. 6), GLMMs consider distributions from an exponential family (e.g., binomial, Poisson) but can also incorporate random effects.

In this module, you will expand your skills on linear models (Modules M.4) to GLMMs while testing associations between Cayo Santiago rhesus macaque male social dispersal and population density.

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

• Center predictor variables;
• Test correlations among predictor variables;
• Fit generalized linear mixed-effects models;
• Interpret model output;
• Plot model predictions.

References:

• lme4: Linear Mixed-Effects Models using ‘Eigen’ and S4
• MuMIN: Multi-Model Inference
• RStudio
• sjPlot: Data Visualization for Statistics in Social Science
• Tidyverse R packages for data science

Extra training:

• Freeman, 2017. An Introduction to Hierarchical Modeling
• Grace-Martin, 2021. Interpreting regression coefficients
• Quantifying Health, 2023

Associated literature:

• Weiß et al. 2016. Individual dispersal decisions affect fitness via maternal rank effects in male rhesus macaques

Expand for R Notation and functions index

Notation:

• [] for subsets by columns;
• : for generating regular sequences;
• $ for accessing or creating a variable in a dataset.

Commands:

• Base R:

  • as.numeric() for changing variable class to numeric;
  • cor() for testing correlations between variables;
  • exp() for exponential function;
  • install.packages() for installing packages;
  • names() for extracting/changing column names;
  • summary() for model output.

• lmer4:

  • glmer() for fitting generalized linear mixed-effects models.

• MuMIn:

  • model.sel() for model selection table.

• sjPlot:

  • plot_model( ) for plotting model effects.

• tidyverse:

  • mutate() for modifying and creating new columns.

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Testing associations between social dispersal and population density

Rhesus macaque populations are socially organized into multi-male, multi-female social groups (Fig 1). At Cayo Santiago, these groups formed naturally and most females remain in their natal groups their entire life. However, males migrate out of their natal social group at puberty (social dispersal; Fig 1). This behavior likely evolved to avoid inbreeding. Although natal social group dispersal is expected, individual males show high variability in the timing of migration. One important factor driving annual social dispersal in males could be high population density due to increased competition. As Cayo Santiago is an 15.2 ha island, metrics of population density are accurately estimated.