Skip to content

Introduction to Multilevel (hierarchical, or mixed effects) Models using R

  • Level(s) of Study: Short course
  • Start Date(s): 7 June 2023
  • Duration: Wednesday to Thursday 9.30 am - 5.30 pm
  • Study Mode(s): Short course
  • Campus: City Campus
  • Entry Requirements:
    More information


On this two-day course, you will obtain a practical and theoretical introduction to doing multilevel or mixed-effects regression modelling using R. We will particularly focus on multilevel or mixed effects linear models, which are very widely used throughout the social and biological sciences. We will use the popular `lme4` R package, as well as the acclaimed `brms` R package for Bayesian analyses.

This course is aimed at scientific researchers and data analysts who are interested in advancing their level of statistical knowledge and techniques beyond standard regression analysis to regression methods that are suitable for modelling clustered or hierarchical data sets, which are very common in the social and biological sciences.

Level: CPD, Advanced / Professional

The course will cover these key topics:

  • Random effects models. The defining feature of multilevel models is that they are models of models. We begin by using so-called random effects model to illustrate this. Here, we also cover the key concepts of statistical shrinkage and intraclass correlation.
  • Linear mixed effects models. Next, we turn to multilevel linear models, also known as linear mixed effects models. We specifically deal with the cases of varying intercept and/or varying slope linear regression models.
  • Multilevel linear models for nested data structures. We will consider multilevel linear models for nested, as in groups of groups, data. As an example, we will look at multilevel linear models applied to data from children within schools that are themselves within different cities, and where we model the variability of effects across the schools and across the cities.
  • Multilevel linear models for crossed data structures. In some multilevel models, each observation occurs in multiple groups, but these groups are not nested. For example, children may be members of different schools and different social clubs, but the clubs are not subsets of schools, nor vice versa. These are known as crossed or multiclass data structures.
  • Bayesian multilevel models. All of the models that we have considered can be handled, often more easily, using Bayesian models. Here, we provide an brief introduction to Bayesian models and how to perform examples of the models that we have considered using Bayesian methods and the `brms` R package.

The course will take 6 contact hours per day plus two 2-hour breaks.

The sessions will be as follows:

  • Session 1: 9:30am-11:30am;
  • Session 2: 12:30am-2:30pm;
  • Session 3: 3:30pm-17:30pm

Tutor Profile: Mark Andrews is an Associate Professor at Nottingham Trent University whose research and teaching is focused on statistical methodology in research in the social and biological sciences. He is the author of 2021 textbook on data science using R that is aimed at scientific researchers, and has a forthcoming new textbook on statistics and data science that is aimed at undergraduates in science courses. His background is in computational cognitive science and mathematical psychology.

Other available online CPD courses in this series include

Introduction to statistics using R and Rstudio

Introduction to Data Wrangling using R and tidyverse

Introduction to Data Visualization with R using ggplot

Introduction to Generalised Linear Models in R

Introduction to Bayesian Data Analysis with R

Any questions?  Contact, Commercial Manager, School of Social Sciences.

Great explanations of the R output and linking them with theory in an accessible way. I enjoyed the sequential nature of the course, allowing us to follow the tutor step by step. The interpretation of the tests and the results they produce was excellent.

What you’ll study

During the course you’ll:

  • Gain a practical and theoretical introduction to multilevel and mixed effects regression models, with a particular focus on multilevel and mixed effects linear models.
  • Learn how to use the widely used `lme4` R package for multilevel and mixed effects regression.
  • Learn how to apply Bayesian approaches to multilevel modelling using the brms R package.
  • Learn how multilevel models are models of models and understand how random effects models serve as a solid basis for understanding multilevel and mixed effects models generally.
  • Explore the basic and general principles of multilevel and mixed effects linear models, focusing on varying intercept and / or varying slopes regression models
  • Further explore aspects of multilevel and mixed effects linear models, including multilevel models for nested and crossed data
  • Explore Bayesian approaches to multilevel and mixed effects linear models using the acclaimed `brms` software.

What will I gain?  

By the end of the course, you’ll have acquired the know-how to model statistical data that is grouped, clustered, or hierarchically structured, and understand the general concepts of fixed, random, and mixed effects variables and how they are used in multilevel models.  You’ll have the capability to analyse complex and hierarchically arranged datasets using popular multilevel modelling software in the R language, compare competing models, and choose suitable model structures depending on the nature of the data.

  • On completion of at least 80% of the course, you’ll receive a certificate of attendance.

Where you'll learn 

The course is delivered through interactive online workshops via Zoom. It 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. Throughout the course, we will use real-world data sets and coding examples.

Staff Profiles

Mark Andrews

Associate Professor

School of Social Sciences

Mark Andrews

Campus and facilities

Fees and funding

The fee for this course is £360 (VAT Inclusive) - £300 (VAT Exclusive)

Payment is due at the time of booking.

The fee for this course is £360 (VAT Inclusive) - £300 (VAT Exclusive)

Payment is due at the time of booking.

How to apply

You can book your place via the NTU online store:

Book your spot here.

You can book your place via the NTU online store:

Book your spot here.