# Mathematics

## MTH3012 - Advanced Statistical Modelling (2019)

MODULE TITLE CREDIT VALUE Advanced Statistical Modelling 15 MTH3012 Dr Theo Economou (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 0
 Number of Students Taking Module (anticipated) 37
DESCRIPTION - summary of the module content

Statistical modelling lies at the heart of modern data analysis. Simple statistical models include the techniques of regression and multiple regression familiar from most foundation courses in statistics. This module takes those ideas further placing them in the much broader context of the Generalized Linear Model. It then goes on to consider extensions to that framework involving random effects, Generalized Linear Mixed Models, Generalized Additive Models but also models for failure time data with partially observed information. We will use the statistical software R as the main platform to fit this wide range of models, and will use it in practical sessions so that, as well as a sound theoretical basis, you will develop an understanding of how to apply techniques discussed in the course in practical data analysis.

Pre-requisite Module: MTH2006 Statistical Modelling & Inference, or equivalent

AIMS - intentions of the module

The introduction of Generalized Linear Models (GLMs) by Nelder and Wedderburn in 1972 was a milestone in statistical modelling. It provided a unified framework for many seemingly unrelated data analysis techniques. This module will describe the underlying theory and give you a general introduction to the application of commonly used GLMs. The module then goes on to discuss related developments in modern statistical modelling, including nonparametric and semi-parametric formulations (GAMs), hierarchical modelling and random effects (GLMMs). Lastly the module goes on to discuss models for failure time data, used in medical and engineering applications.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

1 Show understanding of the many different types of statistical data structure that commonly occur and the need to model relationships in such data appropriately;

2 Demonstrate awareness of, and ability to apply, the unifying power and flexibility of the generalised linear model (GLM) as a means of describing relationships in data;

3 Reveal awareness of, and ability to apply, related modern developments in statistical modelling techniques, including nonparametric and semi-parametric formulations (GAMs), hierarchical modelling and random effects (GLMMs), and models for failure time data;

4 Utilise appropriate software and a suitable computer language for advanced modelling of data;

Discipline Specific Skills and Knowledge:

5 Demonstrate understanding and appreciation of, and aptitude in, the advanced mathematical modelling of stochastic phenomena and its usefulness;

Personal and Key Transferable/ Employment Skills and Knowledge:

6 Show advanced data analysis skills and be able to communicate associated reasoning and interpretations effectively in writing;

7 Apply relevant computer software competently;

8 Use learning resources appropriately;

9 Exemplify self-management and time-management skills;

10 Gain experience in problem solving using data analysis.

SYLLABUS PLAN - summary of the structure and academic content of the module

- Introduction to advanced statistical modelling of relationships between variables: the need to move beyond the normal theory linear model (motivation and examples);

- Value of general modelling frameworks and paradigms;

- Generalised linear models (GLMs): definition, maximum likelihood estimation, iteratively reweighted least squares, inference in the GLM, GLM selection, GLM diagnostics;

- Examples of GLMs, normal linear models as GLMs, Bernoulli and binomial data, Poisson count data, contingency tables, multinomial data, other GLMs, mean dispersion relationships and overdispersion, quasi-likelihood;

- Generalised additive models (GAMs): parametric versus nonparametric and semi-parametric models, kernel, spline and local polynomial estimation methods, additive models and generalized additive models;

- Hierarchical models and random effects: the whats and whys of random effects and hierarchical (multilevel) modelling, normal theory linear mixed models, generalised linear mixed models (GLMMs);

- Introduction to the analysis of failure time data using accelerated failure time models.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 33 117
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled Learning and Teaching Activities 33 Lectures/practical classes Guided Independent Study 33 Post lecture study and reading Guided Independent Study 40 Formative and summative coursework preparation Guided Independent Study 44 Exam revision/preparation

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Unassessed Practical Modelling Exercises 1 10 hours 1, 2, 4-10 Verbal, in class
Unassessed Practical Modelling Exercises 2 10 hours 1, 3, 4-10 Verbal, in class

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 40 60
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written Exam – Closed Book 60 2 hours 1-6, 9 Written/verbal on request
Coursework – practical modelling exercises and theoretical problems 1 20 10 hours 1, 2, 4-10 Written and verbal
Coursework – practical modelling exercises and theoretical problems 2 20 10 hours 1, 3, 4-10 Written and verbal

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All Above Written Exam (100%) All August Ref/Def Period

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener