Tutorial on modelling circular data

Instructors: Professor Mario Cortina Borja (PPP/ICH) and Professor Marco Geraci (MEMOTEF/Sapienza Università di Roma)

Description: Circular data can be represented as points on the circumference of the unit circle. Examples of circular variables include movement direction of animals in ecology, protein structure in biology, neuronal activity and circadian rhythm in physiology, human sense of direction and visual perception of space in cognitive psychology, as well as variables related to time of the day or dates in the year. In general, variables that have a periodic nature fall into this category. Statistical methods for data measured using linear metrics (e.g. Euclidean) do not apply to circular data. The reason is due to the periodic nature of this type of data: while linear data have a meaningful zero, circular data do not. On the circle, measurements at 0° and 360° represent the same direction whereas on a linear scale they would be located at opposite ends of the scale. Importantly, distances on the circle require trigonometric rather than Euclidean calculations. On the one hand, this means that the analyst must be careful with the calculation of even the most basic statistics such as a sample mean or standard deviation as their formulas differ from those applied to linear random variables. On the other hand, the application of circular statistics provides unique information about the distribution of events that cyclically recur over space or time.

This short tutorial is divided into two parts. In the first part, we will introduce some of the tools for exploratory data analysis, such as basic circular statistics, distributions and visualisations. In the second part, we will discuss regression modelling of circular data, from the standard case of cross-sectional observations to the more advanced case of repeated measurements. These methods will be illustrated with applications of interest to public health practitioners. R code to reproduce the tutorials’ examples will be made available to the participants.

Date: Thursday 21st March, 2pm-4pm (tea afterwards)

Location: Room E (ground floor) UCL ICH Wolfson Centre