Session 1 – 01:00:00 – What Are Multilevel Models?
We begin by introducing multilevel models as ‘models of models,’ where random effects are used to capture variation among groups. Using data on breeding success in Scottish seabird colonies, we highlight how grouping structures arise naturally in ecological research.
Session 2 – 01:00:00 – Random Intercepts in Binomial Models
This session introduces random intercepts in binomial models, where the response is binary and clustered by group. Frog presence or absence across Irish wetland sites serves as a motivating example for how random effects improve inference over fixed-effect-only models.
Session 3 – 01:00:00 – Partitioning Variance in Grouped Data
We explore how multilevel models partition variance into within-group and between-group components. Visualising this structure helps us understand how differences across ecological groups like nesting sites or habitats are captured statistically.
Session 4 – 01:00:00 – Normality and Shrinkage in Random Effects
Random effects are often assumed to follow a normal distribution. In this session, we explore what this means in ecological contexts where group-level effects vary. We use pollinator data from pan traps across the UK to show how estimates for individual sites are informed not just by local observations but also by the overall dataset. This leads us to the concept of statistical shrinkage, or partial pooling, where site-level estimates are “shrunk” toward the global average—especially for sites with limited data—highlighting how multilevel models balance group-specific and population-wide information.
Session 5 – 01:00:00 – Intraclass Correlation (ICC)
Intraclass correlation (ICC) quantifies the proportion of total variance attributable to grouping structure. We compute and interpret ICC in ecological settings, showing how it reflects similarity within clusters, such as repeated measures from the same location.
Session 6 – 01:00:00 – Fitting Basic Models in R
To consolidate the day’s material, we fit binomial and normal random effects models using R. We will walk through examples, examine model output, and interpret the effects of grouping on estimated parameters.
Session 7 – 01:00:00 – Introducing Liner Mixed Effects Models (LMEMs) for Continuous Outcomes
We transition from binary responses to continuous data using linear mixed effects models. Tree height measurements collected from multiple forest plots provide a motivating example for incorporating random intercepts, allowing us to account for differences in average tree height across plots while examining how individual-level factors like soil nutrients influence growth.
Session 8 – 01:00:00 – Random Intercepts in LMEMs
This session focuses on fitting and interpreting random intercept models, allowing each group to have a different baseline level. We examine site-level variability in simulated plant trait data and discuss implications for ecological inference.
Session 9 – 01:00:00 – Allowing Slopes to Vary Across Groups
We extend the model by allowing regression slopes to vary by group. Using an extended version of the Palmer Penguins dataset, we explore how the relationship between flipper length and body mass differs across penguin species. By fitting a model with random slopes, we show how multilevel models can capture this ecological heterogeneity and reveal species-specific growth patterns.
Session 10 – 01:00:00 – Correlated Random Intercepts and Slopes
Here we fit models with both random intercepts and slopes and examine the correlation between them. This provides insight into how group-specific responses differ not just in level but also in relationship to predictors.
Session 11 – 01:00:00 – Evaluating Model Fit and Complexity
We introduce model selection tools including AIC and likelihood ratio tests, and discuss when to use restricted maximum likelihood (REML). Residual diagnostics and random effect plots help us assess model adequacy.
Session 12 – 01:00:00 – Visualising and Interpreting LMEMs
We visualise fitted models using group-specific lines and predicted values. We interpret shrinkage and assess how multilevel models improve understanding of ecological patterns across groups.
Session 13 – 01:00:00 – Hierarchical Data and Nested Models
Ecological data often exhibit nested structure, such as trees within plots within forests. We explore how to represent these structures in multilevel models and what nesting means for interpretation and variance.
Session 14 – 01:00:00 – Implementing Nested Random Effects in R
We demonstrate how to code nested models in R and interpret the resulting variance components. A biodiversity dataset with multiple nested spatial levels helps illustrate the hierarchy in practice.
Session 15 – 01:00:00 – Variance Partitioning in Nested Structures
We explore how to extract and interpret variance at each nested level, and how this informs our understanding of group-level effects. We also revisit ICC in the context of more complex groupings.
Session 16 – 01:00:00 – Crossed Random Effects: Concepts and Examples
Not all grouping structures are hierarchical. We introduce crossed random effects using examples such as species abundance recorded by multiple observers at different sites, where groupings overlap rather than nest.
Session 17 – 01:00:00 – Fitting Crossed Random Effects Models
Participants learn how to implement crossed random intercept models in R and distinguish them from nested models. We interpret variance and model outputs in the context of observer bias and site-level variability.
Session 18 – 01:00:00 – Comparing Nested and Crossed Models
We compare nested and crossed structures. We discuss how the choice of model affects inference, and which structure best reflects the data-generating process.
Session 19 – 01:00:00 – Adding Group-Level Predictors
Multilevel models can include predictors at both individual and group levels. We use simulated fish size data across multiple lakes to demonstrate how both fish age (individual) and lake depth (group) influence outcomes.
Session 20 – 01:00:00 – Centring Predictors for Clearer Interpretation
We explain why centring predictors—either around the grand mean or group mean—is important for interpretability and model performance. Ecological examples show how centring affects coefficient interpretation and variance partitioning.
Session 21 – 01:00:00 – Cross-Level Interactions
This session explores how predictors at different levels can interact to influence ecological outcomes. Using simulated data on invertebrate richness across multiple sites, we examine how the effect of local flowering plant richness on invertebrate species richness varies with site-level land use intensity. This example highlights how ecological relationships may strengthen or weaken depending on broader environmental context and illustrates the value of modelling cross-level interactions in multilevel analysis.
Session 22 – 01:00:00 – Introducing Generalised Linear Mixed Models
We now extend mixed models to non-normal outcomes using GLMMs. Count and binary data are common in ecology; we demonstrate how GLMMs can be used for pollinator counts and presence-absence data.
Session 23 – 01:00:00 – Dealing with Overdispersion in Count Models
Overdispersion is a common issue in ecological count data. We discuss diagnostics, model remedies, and how to incorporate individual-level random effects to capture unobserved heterogeneity in animal counts.
Session 24 – 01:00:00 – Fitting and Evaluating GLMMs in R
We walk through fitting Poisson and binomial GLMMs in R using ecological datasets. Emphasis is placed on understanding model output, visualising predictions, and identifying overdispersion or convergence issues.
Session 25 – 01:00:00 – Why Bayesian? An Introduction for Ecologists
We introduce Bayesian multilevel models and discuss how they differ from frequentist approaches. Key concepts—such as priors, posteriors, and uncertainty—are presented with ecological examples that benefit from incorporating prior knowledge.
Session 26 – 01:00:00 – Specifying Models with brms
This session focuses on using the brms package in R to fit Bayesian models. We fit a hierarchical model for tree growth, showing how familiar syntax translates into a Bayesian framework.
Session 27 – 01:00:00 – Interpreting Posterior Output
We learn how to interpret Bayesian model output, including posterior means, credible intervals, and diagnostic metrics. Ecological examples are used to demonstrate the difference between posterior and frequentist summaries.
Session 28 – 01:00:00 – Model Checking and Posterior Predictive Checks
Good model checking is essential in Bayesian analysis. We explore convergence diagnostics (R-hat, ESS) and use graphical posterior predictive checks to assess model fit using the bayesplot package.
Session 29 – 01:00:00 – Case Study: Bayesian vs. Frequentist Models
We apply both Bayesian and frequentist models to the same ecological dataset—species counts across locations—and compare their estimates, uncertainty, and interpretability. This highlights the advantages of the Bayesian approach for certain ecological questions.
Session 30 – 01:00:00 – Final Review
We conclude the course with a summary of key concepts, discussing when and why to use multilevel models, how to select appropriate structures, and what tools are available in R. We close with Q&A and suggestions for packages, vignettes, and readings.
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