Week 03 — Linear Models and GLM’s

Week: 3

Topic: Linear Models and GLM’s

1 Background

Review the following topics if you don’t fully understand them:

  • Inference

  • Linear Models

  • Generalized Linear Models

  • Distributions

    • Normal

    • Binomial

    • Poisson

    • Negative Binomial

Again, you can use AI or a quick search to help you understand these concepts, but make sure you understand them somewhat

2 Learning Objectives

Explain how linear models, generalized linear models, and mixed models share a common structure

Identify when normal-error linear models are inappropriate and how GLMs address these limitations

Interpret regression coefficients under different link functions and error distributions

Critically evaluate modeling choices in published ecological and natural resource studies

Implement and compare LMs and GLMs in R while articulating underlying assumptions

2.1 Session A:

2.1.1 Part 1: Paper discussion (~45 minutes of the class)

Discussion of: Bolker et al. (2009)

Submit before class: 1) A question of something you had a hard time understanding, and a question you would ask someone to test if they understood the paper (as if you were an instructor testing a student). You can submit both questions in the same section on CANVAS.

I will open with a short lecture (15 minutes) on the paper, then we will have a discussion (15 minutes). Submit: 1 question of something you have a hard time understanding. I will lead the discussion, but be ready to discuss/explain topics. You will then work in groups.

Questions To think about while reading
  • When should a fixed effect be treated as random (and vice versa)?

  • How do you diagnose and handle overdispersion and zero-inflation?

  • Tradeoffs between lme4, glmmTMB, and Bayesian approaches for complex data?

2.1.2 Part 2: Working in pairs (or trios) (~30 Minutes)

Half of you will read chapter 2 of Zuur et al. (2009) (Mixed Effects Models and Extensions in Ecology with R) and the other half chapter 3.

Each Student gets 8 minutes to give a lecture + 2 minutes for questions.

Following this, students will answer 1) the most important concept, and 2) one question given by me.

After this, they will switch roles.

2.1.3 Exit ticket

What was the most challenging thing about today?

2.2 Session B

Methods workshop — hands-on coding

2.2.1 Objectives

  • Fit a GLM, GAM, and a GLMM to count and binomial response data.
  • Interpret fixed-effect estimates and random-effect variances.

  • Diagnose model fit (residuals, overdispersion, zero‑inflation) and fix common problems.

  • Compare two model fits and write a concise ecological interpretation.

2.2.2 Preparation:

Install the following packages:

  • lme4

  • glmmTMB

  • DHARMa

  • broom.mixed

  • ggplot2

  • performance

Class schedule

  • 5 minutes –> Discussion about overdispersion

  • 10 minutes –> Demo by me

  • 30 minutes –> Paired work:

    • Task A (15 min): Fit Poisson GLM and GLMM on y; extract fixed effect, random variance, compute AIC.

    • Task B (15 min): Run DHARMa simulateResiduals on GLMM and inspect plot; note any issue (overdispersion, zero inflation, non-uniform residuals).

    • Work in pairs. You can decide how to work

    • Figure out issues/problems in the data

  • 10 minutes –> Discussion part 2

  • Students present results –> 5 minutes

  • Submit data

References

Bolker, Benjamin M., Mollie E. Brooks, Connie J. Clark, Shane W. Geange, John R. Poulsen, M. Henry H. Stevens, and Jada-Simone S. White. 2009. “Generalized Linear Mixed Models: A Practical Guide for Ecology and Evolution.” Trends in Ecology & Evolution 24 (3): 127–35. https://doi.org/10.1016/j.tree.2008.10.008.
Zuur, A., E. N. Ieno, N. Walker, A. A. Saveliev, and G. M. Smith. 2009. Mixed Effects Models and Extensions in Ecology with R. Statistics for Biology and Health. Springer New York.