Computer Science

ECMM449 - Advanced Statistical Modelling (2019)

Back | Download as PDF
MODULE TITLEAdvanced Statistical Modelling CREDIT VALUE15
MODULE CODEECMM449 MODULE CONVENERUnknown
DURATION: TERM 1 2 3
DURATION: WEEKS 11
Number of Students Taking Module (anticipated) 35
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: ECM2710 or equivalent (familiarity with linear regression and the statistical language R).

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.
11. Gain experience in independent learning in the context of performing a statistical analysis on real world problems.

 

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 33.00 Guided Independent Study 117.00 Placement / Study Abroad 0.00
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 1,2,4-9 Verbal, in class
Unassessed practical modelling exercises 2 10 hours 1,3,4-9 Verbal, in class
       
       
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 50 Written Exams 50 Practical Exams
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 50 2 hours - Summer Exam Period  1-6, 9 Verbal on specific request
Coursework – practical modelling exercises and theoretical problems 1 15 10 hours 1,2, 4-10 Written and verbal
Coursework – practical modelling exercises and theoretical problems 2 15 10 hours 1,3,4-10 Written and verbal
Individual research project on an advanced topic agreed with the module leader 20 20 hours 1-11 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-assessment
Written exam – closed book Written exam (100%) All August referral/deferral period
Coursework – practical modelling exercises and theoretical problems 1 Written exam (100%) All August referral/deferral period
Coursework – practical modelling exercises and theoretical problems 2 Written exam (100%) All August referral/deferral period
Individual research project on an advanced topic agreed with the module leader Written exam (100%) All August referral/deferral 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 50% 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

Basic reading:

 

ELE: http://vle.exeter.ac.uk

 

Web based and Electronic Resources:

 

Other Resources:

 

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set Krzanowski W.J. An Introduction to Statistical Modelling Arnold 1998 000-0-340-69185-9 [Library]
Set Aitkin, M., Francis, B., Hinde, J. and Darnell, R. Statistical Modelling in R Oxford University Press 2008 9780199219131 [Library]
Set Crawley, M.J. The R Book Wiley 2007 9780470510247 [Library]
Set Faraway J J Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models Chapman & Hall 2006 158488424X [Library]
Set Wood, Simon N Generalized additive models: an introduction with R Chapman & Hall/CRC 2006 978-1584884743 [Library]
Set Gelman, A. and Hill J. Data analysis using regression and multilevel/hierarchical models Campbridge University Press 2007 052168689X [Library]
Set Kalbfleisch, J. D. and Prentice, R. L. The statistical analysis of failure time data 2nd Wiley 2002 047136357X [Library]
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES ECM2710
CO-REQUISITE MODULES
NQF LEVEL (FHEQ) 7 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Tuesday 10 July 2018 LAST REVISION DATE Tuesday 10 July 2018
KEY WORDS SEARCH Generalised linear models; mixed models; additive models