## MATH3092 Mixed Models

### 10 creditsClass Size: 40

Module manager: Duncan Wilson
Email: D.T.Wilson@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2023/24

### Pre-requisite qualifications

Pre-requisite for this module is either MATH2715 OR MATH2735 - you do not need to have studied both.

### Pre-requisites

 MATH2715 Statistical Methods MATH2735 Statistical Modelling

### This module is mutually exclusive with

 MATH5092M Mixed Models with Medical Applications

This module is not approved as a discovery module

### Module summary

Clustering and hierarchical structures are common in scientific research. For example, in a medical study, patients could be clustered by surgeon, with surgeons clustered by hospital. Patient outcomes within clusters are likely to be correlated, thus violating the independence assumptions of many statistical methods. Mixed models overcome this obstacle, by extending familiar models such as linear regression to include additional random terms that account for variability between clusters. Mixed models are essential tools in the medical, environmental and social sciences. Students undertaking this module will learn how to apply mixed models to a broad range of realistic examples from these sciences.

### Objectives

This module aims to introduce students to mixed models for the analysis of data with complex hierarchical or clustered structures. These models will be demonstrated through real-life examples from the medical, environmental and social sciences.

Learning outcomes
By the end of this module, the student should be able to:
1. Understand and explain mixed models and how they are estimated.
2. Apply appropriate mixed models to problems in the medical, environmental or social sciences.
3. Estimate a variety of mixed models using statistical software.
4. Report and interpret the results of a mixed model analysis.

### Syllabus

1.Basic two-level hierarchical models, including variance components models, random intercept models and random slope models.
2.Three-level hierarchical models and complex variance structures.
3.Parameter and residual estimation for mixed models.
4.Mixed models for longitudinal data.
5.Fitting and checking models using statistical software.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 11 1.00 11.00 Practical 11 1.00 11.00 Independent online learning hours 22.00 Private study hours 56.00 Total Contact hours 22.00 Total hours (100hr per 10 credits) 100.00

### Private study

Each week, to prepare for the computer practicals, students will be expected to independently spend two hours reading through a set of online notes and completing exercises on material not introduced in the lectures. Students should arrive at the practicals fully prepared to discuss this material.

### Opportunities for Formative Feedback

Students will complete and receive written feedback on three homework assignments. Students will receive face-to-face feedback on tasks completed during practical sessions.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Report A short report (< 10 pages) on an analysis of a data set. 20.00 Total percentage (Assessment Coursework) 20.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 80.00 Total percentage (Assessment Exams) 80.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated