This course will be largely practical, hands-on, and workshop based. For each topic, there will first be some lecture style presentation, i.e., using slides or blackboard, to introduce and explain key concepts and theories. Then, we will cover how to perform the various statistical analyses using R. Any code that the instructor produces during these sessions will be uploaded to a publicly available GitHub site after each session. For the breaks between sessions, and between days, optional exercises will be provided. Solutions to these exercises and brief discussions of them will take place after each break.

The course will take place online using Zoom. On each day, the live video broadcasts will occur between (British Summer Time, UTC+1, timezone) at:
• 12pm-2pm
• 3pm-5pm
• 6pm-8pm

All sessions will be video recorded and made available to all attendees as soon as possible, hopefully soon after each 2hr session.

Attendees in different time zones will be able to join in to some of these live broadcasts, even if all of them are not convenient times. By joining any live sessions that are possible, this will allow attendees to benefit from asking questions and having discussions, rather than just watching prerecorded sessions.

At the start of the first day, we will ensure that everyone is comfortable with how Zoom works, and we’ll discuss the procedure for asking questions and raising comments.

Although not strictly required, using a large monitor or preferably even a second monitor will make the learning experience better, as you will be able to see my RStudio and your own RStudio simultaneously.

All the sessions will be video recorded, and made available immediately on a private video hosting website. Any materials, such as slides, data sets, etc., will be shared via GitHub.

Assumed quantitative knowledge

We assume familiarity with linear regression analysis, and the major concepts of classical inferential statistics (p-values, hypothesis testing, confidence intervals, model comparison, etc). Some familiarity with common generalized linear models such as logistic or Poisson regression will also be assumed.

Assumed computer background

R experience is desirable but not essential. Although we will be using R extensively, all the code that we use will be made available, and so attendees will just to add minor modifications to this code. Attendees should install R and RStudio on their own computers before the workshops, and have some minimal familiarity with the R environment.

Equipment and software requirements

A computer with a working version of R or RStudio is required. R and RStudio are both available as free and open
source software for PCs, Macs, and Linux computers. R may be downloaded by following the links here https://www.r-project.org/. RStudio may be downloaded by following the links here: https://www.rstudio.com/. All the R packages that we will use in this course will be possible to download and install during the workshop itself as and when they are needed, and a full list of required packages will be made available to all attendees prior to the course.

UNSURE ABOUT SUITABLILITY THEN PLEASE ASK oliverhooker@prstatistics.com

Wednesday 16th – Classes from 10:00 to 19:00

Topic 1: Regression modelling overview. We begin with a brief overview and summary of regression modelling in general. The purpose of this is to provide a brief recap of general and generalized linear models, and to show how nonlinear regression fits into this very widely practiced framework.

Topic 2: Polynomial regression. Polynomial regression is both a conceptually and practically simple extension of linear modelling and so provides a straightforward and simple means to perform nonlinear regression. Polynomial regression also leads naturally to the concept of basis function function regression and thus is bridge between the general or generalized linear models and nonlinear regression modelling using generalized additive models.

Topic 3: Spline and basis function regression: Nonlinear regression using splines is a powerful and flexible non-parametric or semi-parametric nonlinear regression method. It is also an example of a basis function regression method. Here, we will cover spline regression using the splines::bs and splines::ns functions that can be used with lm, glm, etc. We also look at regression using radial basis functions, which is closely related to spline regression. Understanding basis functions is vital for understanding Generalized Additive Models.

Thursday 17th – Classes from 10:00 to 19:00

Topic 4: Generalized additive models. We now turn to the major topic of generalized additive models (GAMs). GAMs generalize many of concepts and topics covered so far and represent a powerful and flexible framework for nonlinear modelling. In R, the mgcv package provides a extensive set of tools for working with GAMs. Here, we will provide an in-depth coverage of mgcv including choosing smooth terms, controlling overfitting and complexity, prediction, model evaluation, and so on.

Topic 5: Interaction nonlinear regression: A powerful feature of GAMs is the ability to model nonlinear interactions, whether between two continuous variables, or between one continuous and one categorical variable. Amongst other things, interactions between continuous variables allow us to do spatial and spatio-temporal modelling. Interactions between categorical and continuous variables allow us to model how nonlinear relationships between a predictor and outcome change as a function of the value of different categorical variables.

Topic 6: Generalized additive mixed models. GAMs can also be used in linear mixed effects, aka multilevel, models where they are known as generalized additive mixed models (GAMMs). GAMMs can also be used with the mgcv package.