Short Course: Multivariate Statistics using R

Course Overview

This workshop extends on the Fundamentals of Regression course and introduces multivariate statistics in a model based framework. While particularly relevant to ecologists, these methods have valuable applications across multiple disciplines. We move beyond a single response variable to visualising and analysing a collection of correlated response variables. In this course, many of the motivating applications come from ecology, though the methods do generalise to multivariate data in other settings. Methods available to you depend on the number of responses relative to your sample size; and like in univariate regression we also need to think about the response variable type (binary, count etc). There is emphasis on understanding the concepts of statistical procedures (with a minimum of mathematics, although some will be discussed) and on interpreting computer output. It is designed to help you, the researcher. There will be plenty of practical work.

Regression, with normal and non normal responses, and basic R skills are assumed knowledge. These are covered in our R course, Fundamentals of Regression Course and Mixed Models Course. Please note - this course is NOT about regression with multiple predictor variables - for example when many predictor variables might be correlated with your outcome variable. Our brief pre-enrolment questionaire is designed to help you decide if you are ready for this course (https://unswstatscentral.shinyapps.io/Multivariate_Preenrolment).

Course outline

Introduction to multivariate data – with fewer response variables

• What is a multivariate research question
• Why use multivariate methods
• Covariance matrices
• Analysis with manova
• Checking model assumptions

Multivariate data – with lots of response variables

• Reducing the rank of the covariance matrix
• Reduced Rank Analysis with PCA 
• Reduced Rank Analysis with generalised latent variable models (glmmTMB)
• Visualising high dimensional data 

Multivariate data – hypothesis testing with LOTS and LOTS of response variables

• Design based inference in mvabund
• Analysing Compositional data – row effects and offsets
• Correlation types

Multivariate data – extensions and challenges

• Fourth-corner: For trait-environment relationships
• And More...

Accessibility

This is an in person course. Slides are in PDF format, exercises are in R markdown, and both will be downloadable in advance. If HTML slides and alt text are needed to assist accessibility we will make every effort to provide these, please let us know well in advance. Please email Eve (eve.slavich@unsw.edu.au) with any questions or requests.

Prerequisites: RStudio and Regression (with a single response variable) are assumed knowledge. 

Course requirements: You will need to bring and use your own computer during the workshop.

Date: 21 Thursday to Friday 22 August 2025

Duration:  9.30am - 4:00pm each day

Delivery Mode: This course will be delivered in-person ONLY!

Location: TBA

You will receive a certificate of completion for the course.

Note: If you have a funding support and would like to pay by "Internal Funding Payment", please contact us stats.central@unsw.edu.au

FAQs

How can I contact the organiser with any questions?

Please send us an email at: stats.central@unsw.edu.au