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Course syllabus

Overview

This is a 6-session workshop, developed with the goal of giving you enough GAM knowledge to feel comfortable fitting and working with GAMs in your day-to-day modelling practice. We will be covering a basic intro to GAM theory, with the rest focused on practical applications and a few advanced topics that we think might be interesting.

Learning Goals

  • Understand the basic GAM model, basis functions, and penalties
  • Fit 1D, 2D, and tensor-product GAMs to normal and non-normal data
  • Plot GAM fits, and understand how to explain GAM outputs
  • Diagnose common mispecification problems when fitting GAMs
  • Use GAMs to make predictions about new data, and assess model uncertainty
  • See how more complicated GAM models can be used as part of a modern workflow

Syllabus

1. What is a GAM, and 1d smoothers

Lead instructors: Eric

  • Example data: temperature with depth

  • refresher on GLMs (regression, parameters, link functions)

  • why smooth?

  • simple models with s()

  • introduction to the data

  • what's going on behind the scenes here?

    • interpolation vs. linear models
    • wiggles/penalties (non-technical)

  • adding more than one smooth to your model

  • summary and plot

2. "twiddling knobs in gam"

Lead instructors: David

  • moving beyond normal data (richness, shrimp biomass)

    • exponential family and conditionally exp family (i.e., family + tw + nb)

  • more dimensions (Shrimp biomass)

    • thin-plate 2d (Shrimp biomass with space)

    • what are tensors? (Shrimp biomass as a function of depth and temperature)

      • ti vs te

    • spatio-temporal modelling

      • te(x,y,t) constructions

  • centering constraints

    • what does the intercept mean?

3. model checking and selection (follow-up on temperature, richness, and shrimp data sets)

Lead instructors: Noam

  • gam.check is yr pal

    • 4 plots
    • checking k
    • limitations with count data

  • quantile residuals

  • diagnostic: DHARMa

  • fitting to the residuals

  • AIC etc.

  • shrinkage and select=TRUE

4. predictions and variance

Lead instructor: Gavin

  • predict (exclude=?)
  • what are those bands
  • getting summaries (abundance estimates?)
  • posterior simulation

5. Connections, Q&A

**Lead instructor: David, all **

  • GAMs in context with other methods

    • INLA/hierarchical modelling/lme4/etc.
    • Connection to covariance matrices in regression for dependent data
    • Bayesian views of GAMs

  • links to other software

    • utility: mgcvUtils
    • fitting: jagam/brms/TMB

  • Q&A

6. more complex models for fisheries and aquatic ecology

**Lead instructor: Eric **

  • other smoothers

    • random effects
    • cyclic smoothers
    • Gaussian Markov Random Fields
    • factor-smooths
    • geographically weighted regression

  • other responses:

    • twlss/betar

Other things we've collectively taught

Other useful GAM resources:

  • Simon Wood's book "Generalized Additive Models: An Introduction with R, Second Edition", is an incredibly useful tool for learning about GAMs, and covers all of this material in depth.

  • Hefley et al. (2017). "The basis function approach for modeling autocorrelation in ecological data". This is a great paper laying out how basis functions are used to model complex spatially structured systems.

  • The mgcVis package has more tools for plotting GAM model outputs. See Fasiolo et al.'s paper 2019 "Scalable visualization methods for modern generalized additive models".