Linear Mixed Models STATS4045

  • Academic Session: 2023-24
  • School: School of Mathematics and Statistics
  • Credits: 10
  • Level: Level 4 (SCQF level 10)
  • Typically Offered: Semester 1
  • Available to Visiting Students: Yes

Short Description

To introduce students to Gaussian linear mixed effects modelling in general and to the active use of modern mixed effects modelling software through R and through SAS.


20 lectures (two lectures each week for 10 weeks)

5 tutorials (fortnightly)

2 two-hour laboratory sessions

Requirements of Entry

The normal requirement is that students should have been admitted to an Honours- or Master's-level programme in Statistics.

Excluded Courses

STATS5054 Linear Mixed Models (Level M)


90-minute, end-of-course examination (100%)

Main Assessment In: April/May

Are reassessment opportunities available for all summative assessments? Not applicable

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below. 

Course Aims

To introduce students to Gaussian linear mixed effects modelling in general and to the active use of modern mixed effects modelling software.

Intended Learning Outcomes of Course

By the end of the course students will be able to:

■ explain the notion of a random effect, why and when it is useful and, in particular, how it differs from a fixed effect;

■ demonstrate detailed understanding of the theory underpinning simple mixed effects models for balanced designs;

■ demonstrate general understanding of the theory underpinning general (e.g. unbalanced) mixed effects models;

■ apply their knowledge of mixed effects modelling to practical situations through the use of general mixed effects modelling software such as nlme;

■ check the assumptions of mixed effects models, both graphically and by hypothesis testing based model comparison;

■ explain when to use restricted maximum likelihood (REML) when fitting mixed-effects models;

■ extend the treatment to cover scenarios involving general covariance structures;

■ describe the basic ideas of multilevel models and of generalised estimating equations as applied especially to models for longitudinal data;

■ translate fluently between verbal, mathematical and computational descriptions of models;
critically interpret analyses based on mixed effect models;

■ interpret the output of R procedures for linear mixed-effects models.

Minimum Requirement for Award of Credits