Course N/T Mixed Models


Course leader: Rodrigo Labouriau

Language: English

Graduate school: Course collaboration

Course fee: 3,600.00 DKK

Max seats: 15

Applicants: 13

Status: Course is finished

Semester: Fall 2021

Application deadline: 15/07/2021

Start date: 17/08/2021

Administrator: Thilde Møller Risgaard

The course Mixed Models is being offered by the Graduate School of Natural Sciences/GSNS and Graduate School of Technical Sciences/GSTS, Aarhus University, fall 2021.

No. of contact hours/hours in total incl. preparation, assignment(s) or the like:
12h of lectures distributed in two lecture days (9:00-12:00, 13:00-16:00); 40h for working in homework, self-study and consultations and interviews with the instructor(s); 28 h for writing a repor. The total work load is of 80h (12h+39h+28h).

Capacity limits:
Minimum 5 and maximum 15

Criteria for participation: The PhD student must masters some basic statistical techniques and the software R as described below.

Regarding the statistical knowledge, it is assumed that the PhD student knows basic inference theory for parametric models, including: estimation, confidence interval and hypothesis testing, linear models and basic generalized linear models. These skills can be obtained in the courses “Basic Statistical Analysis in Life and Environmental Sciences” (see

The course will use the software R as a tool, but it is NOT a course on R. It will be assumed that the PhD students have the software R installed on their computers, and that they know the basic notions of R programming. This includes knowing to: read and write data in R, perform basic operations with variables and vectors, make simple tabulations, use simple functions, use repeated and conditional calculations and draw simple graphs. These skills can be obtained in the course “Introduction to R” (see ).

Aim: The course aims to provide the basic tools to use Mixed Models (including Gaussian Linear Mixed Models, Models for Repeated Measures, Generalized Linear Mixed Models and simple Multivariate Generalized Linear Mixed Models).

Learning outcomes: At the end of the course, the student should be able to:

1) Describe and discuss the use and applicability of classic statistical models for dependent responses based on random components, including: Gaussian linear mixed models, generalized linear mixed models and simple multivariate generalized linear mixed models.
2) Conduct (under supervision) statistical analysis of data with dependence structure using the models abovementioned, including: a) the identification of pertinent models for answering the biologic/scientific question of interest, b) identification of the key assumptions related to those statistical models, c) conduction of the analysis using modern software ( R ), d) model control and verification of the key assumptions, and e) draw reasonable conclusions from those analyses and report written and orally the results obtained.

Content: The course starts by revising the basic theory of Gaussian Linear Models (i.e., linear models based on the normal distribution); these models are extended to the class Gaussian Linear Mixed Models that incorporate random components representing structures of dependency commonly found in dependent experimental and observational studies. Next, the class of generalized linear models are presented, which allow to model non-Gaussian responses (e.g. binomial, Poisson, Gamma and Inverse Gaussian distributed responses) and non-linear relationships with explanatory variables. Finally, simple multivariate generalized linear mixed models, which are presented and discussed. These last models are models allow to model several responses (possibly of different nature) simultaneously. In all cases emphasis is put in applications; mathematical and theoretical details will not be emphasised but instead the conscientious use of the models studied will be aimed.

A written report of the final assessment related to a concrete mini-project should be delivered at the end of the course and discussed with the course lecturer.

Teaching methods:  Lectures alternated with supervised exercise, homework and self-study including the elaboration of an internal seminar based on a simple concrete mini-project.

Instructors: Rodrigo Labouriau 

Tentative time schedule: 2 lecture days from 9:00am (sharp) to 12:00am and 2 practical lectures from 13:00 to 16:00 supplied by office hours. Tentative schedule:

Tuesday 17 August (week 33)

Lecture 1:
Introduction, Practical Matters and Gaussian Linear Mixed Models

  1. a) Introduction and overview of the course the course (carrousel of examples)
    b) Short review of Gaussian Linear Models (GLM): model definition, fitting GLM, inference and model control of GLM
    c) Gaussian linear models with random components: estimation and inference of random effects, prediction of random effects, techniques for investigating the covariance structure, repeated measures and longitudinal data

Practical Lecture 1: Simulation of linear and generalized linear mixed models

  1. a) Simulation of simple linear and generalized linear mixed models
    b) Monte Carlo power calculations for tests involving linear and generalized linear mixed models
    c) Case studies

Homework 1: Tutorials on simulations, case studies, literature reading (including strategic chosen articles and chapters of classic and modern books).

Tuesday 24 August (week 34)

Lecture 2: Generalized Linear Mixed Models

  1. a) Short review of Generalized Linear Models (GLIM): Binomial, Poisson, Gamma and Inverse Gaussian models, basic theory of GLIM, inference and model control of GLM
    b) Basic theory of Generalized Linear Mixed Models (GLIMM, i.e. GLM with random components: Definition of GLIMMs, estimation and hypothesis tests for GLIMM (via parametric bootstrap)

Practical Lecture 2:

  1. a) Tutorials and discussion on the construction of tests for GLMM via parametric bootstrap
    b) Tutorials and discussion on model control techniques for GLMM
    c) Case studies.
    d) Course evaluation

Homework 2: Elaboration of a report on a mini project based on three concrete cases.

Venue: Online

Participation in the course is without cost for PhD students from Aarhus University.

Due to an Agreement between Danish Universities coming into force as of 1 January 2011, participants from other universities than Aarhus University will have to pay DKK 1,200 per ECTS. In principle this also applies to external parties, but exemption can be granted under specific circumstances.

Please be aware that your registration for the course not necessarily equals your admission for the course. You will receive an e-mail after the registration deadline regarding whether you are admitted for the course or if you are registered on the waiting list. Please note that seats are allocated on a first-come-first-served basis.

Course dates:

  • 17 August 2021 09:00 - 16:00
  • 24 August 2021 09:00 - 16:00