About me

What to expect during this workshop

The workshop will run for 2 hours.

• Combines slides, live coding examples, and exercises for you to participate in.

• Ask questions in the chat throughout!

What to expect during this workshop

What you need for this workshop

• You are comfortable with simple operations in R.

• You know how to perform linear regression.

Workshop resources

GitHub: github.com/nrennie/f4sg-gams

Slides: nrennie.github.io/f4sg-gams

Data

We’ll be modelling Covid-19 data during the workshop. The data is from the {COVID19} R package.

• For Great Britain and France between January 2021 and January 2022.

• For each day, data on cases, tests, vaccines, deaths, …

Guidotti, E., Ardia, D., (2020), “COVID-19 Data Hub”, Journal of Open Source Software 5(51):2376, doi: 10.21105/joss.02376.

Data

How to download:

covid <- readr::read_csv(
  "https://raw.githubusercontent.com/nrennie/f4sg-gams/main/data/covid.csv"
  )

• See data/ folder on GitHub for pre-processing.

Sometimes relationships are easy to spot…

Sometimes relationships are easy to spot…

Other times not so much!

What are generalised additive models?

Let’s start with linear models…

What are generalised additive models?

Generalised additive models are essentially just a sum of smooth functions of the explanatory variables.

What are generalised additive models?

Generalised additive models in R

There are several packages for fittings GAMs in R. The two main packages are:

• {gam}

• {mgcv}

We’ll be using {mgcv}.

Hint: don’t load both packages at the same time!

Live demo!

Exercise 1

Open exercises/exercise_01.R for prompts.

• Load the packages required for this workshop.

• Load the data for the exercises. Subset it to look at France only.

• Split the data into training and testing sets.

• Create a plot of confirmed cases over time.

• Fit a linear model using the gam() function in {mgcv} with confirmed as the outcome, and date_obs as the explanatory variable.

Fitting smooth functions

We want to fit some sort of smooth function to each predictor. We can add together basis functions.

Fitting smooth functions

gam_0 <- gam(confirmed ~ date_obs, data = gbr_train)
gam_1 <- gam(confirmed ~ s(date_obs), data = gbr_train)

There are different smooth classes available: s(), te(), ti(), and t2(). Smooth classes are invoked directly by s() terms, or as building blocks for tensor product smoothing via te(), ti() or t2() terms.

There are also different types of splines, specified by the bs argument. See ?smooth.terms for details.

Multiple terms

fit <- gam(y ~ s(x1) + s(x2) + x3, data = data)

• You can include multiple predictors in gam().

• You can use different types of smoothing for each one.

• You can include non-smooth terms (esp. categorical) variables as well.

How smooth is smooth enough?

Additional arguments

• Level of smoothing can be controlled with sp in gam() or s().

• You can choose the dimension of the basis function using k in s().

Hint: look at ?gam and ?s to see the wide range of arguments.

Live demo!

Exercise 2

Open exercises/exercise_02.R for prompts.

• Fit a GAM using s() and gam() to the confirmed cases in France.

• Try adding different additional terms.

• Try varying the smoothing parameter sp for each variable.

• Plot the smooth functions for the predictors, and the outcome.

After you’ve fitted a GAM…

Live demo!

Exercise 3

Open exercises/exercise_03.R for prompts.

• Run gam.check() on your GAM from Exercise 2. Do you need to refit?

• Obtain the fitted values.

• Make a forecast for the range of the test data.

• Inspect the contribution of different terms.

Common problems

• Unstable estimates: when a smooth term can be approximated by some combination of the others.

• Computationally expensive for large data sets: see bam().

• Lack of independence between observations: see gamm().

• Unstable predictions outside the range of training data: see {mvgam}

Are observations independent?

acf(gbr_data$confirmed, main = "ACF plot of confirmed cases")

Generalized additive mixed effect models (GAMMs)

• Like GAMs, GAMMs allow for non-linear relationships between predictors and the response variable by fitting smooth functions to each predictor.

• GAMMs also allow for the inclusion of random effects, which capture the variability of observations within groups or clusters.

• This includes adding correlation structures.

Live demo!

Exercise 4

Open exercises/exercise_04.R for prompts.

• Look at the ACF and PACF plots of the residuals from your previous GAM.

• Try fitting a GAMM model instead.

Additional resources

• GAMs resource list: github.com/noamross/gam-resources

• {mgcv} course: noamross.github.io/gams-in-r-course

• GAMMs: r.qcbs.ca/workshop08/book-en/introduction-to-generalized-additive-mixed-models-gamms.html

• DGAMs for forecasting: doi.org/10.1111/2041-210X.13974

Useful links

GitHub: github.com/nrennie/f4sg-gams

Slides: nrennie.github.io/f4sg-gams

Posit Cloud: posit.cloud/content/7637971