Generalised linear mixed-effects models (GLMMs)

Session-9

R-Peer-Group

What is a GLMM?

• Contains both 'fixed' and 'random' effects

• This allows us to make the most of our data (better statistical power),
  while also accounting for pseudoreplication and non-independence of data

• GLMMs are most useful for correlation structures relating to discrete
  data types (e.g. site), rather that continuous variables (e.g. time or distance)

Some questions you might ask.

Table 1

Formula structures in lmer

model.names <- lmer(response ~ fixed.effects + (random.effects),
                    data, family, ...)

Some common random effect structures:

• (1|site) - site as a random factor

• (1|site/quadrat) - quadrants nested within sites

• (1|site) + (1|year) - two random factors (unnested)

Model checking

• Plot residuals (“Pearson” or “Deviance”)
  • against fitted values
  • against each explanatory variable
  • Cooks distance/leverage plots
  • residuals against time or spatial coordinates (if relevant)

Model simplification by AIC

• The search for the most parsimonious models
• Models must be nested
• Lower AIC = more parsimonious model

AIC values in difference packages may not be directly comparable
due to differences in model fitting procedures (e.g. lme4 vs glmmADMB)

Note:

In the packages lme4 or nlme:

• To compare difference fixed effects structures, models must be fitted by ML
• To compare random effects structures you can use models fitted by REML

Use the package MuMln for automated model selection by AIC

What other options are there?

• For non-linear responses, consider Generalised Additive Models (GAM/GAMM)

• For specific temporal or spatial autocorrelation structures, consider:

  • Generalised Least Squares
  • Generalised Estimation Equations

Both covered in Zuur et al., 2009

Resources

• Crawley, M. J. (2013) The R book (2nd Ed) Wiley and sons: London
• Zuur et al. (2009) Mixed effects models and extensions in Ecology.
  Springer: New York
• Bolker et al. (2009)Generalized linear mixed models: a practical
  guide for ecology and Evolution. Trends in ecology and evolution,
  24, 3, 127-135
• http://glmm.wikidot.com/
• http://glmmadmb.r-forge.r-project.org/glmmADMB.html