MA317-7-SP-CO:
Modelling Experimental Data
2021/22
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Postgraduate: Level 7
Current
Monday 17 January 2022
Friday 25 March 2022
15
28 October 2021
Requisites for this module
(none)
(none)
(none)
(none)
MA321
MSC G30412 Data Science,
MSC G30424 Data Science,
MSC G304PP Data Science with Professional Placement,
DIP G30009 Statistics,
MSC G30012 Statistics,
MSC G30612 Data Science and its Applications,
MSC G30624 Data Science and its Applications,
MSC G306JS Data Science and its Applications,
MPHDG30048 Statistics,
PHD G30048 Statistics,
MPHDG30448 Data Science,
PHD G30448 Data Science,
MSCIN399 Actuarial Science and Data Science,
MSCIG199 Mathematics and Data Science
This module is concerned with the application of linear models to the analysis of data. The underlying assumptions are discussed and general results are obtained using matrices. The standard approach to the analysis of normally distributed data using ANOVA is introduced. Methods for the design and analysis of efficient experiments are introduced. The general methodology is extended to logistic regression and the analysis of multidimensional contingency tables.
The aim of this module is to provide the essential foundations of linear models by studying important topics of statistical modelling. This is achieved by an in-depth study of the main methods to analyse experimental data.
On completion of the module students should be able to:
- calculate confidence intervals for parameters and prediction intervals for future observations;
- understand how to represent a linear model in matrix form;
- check model assumptions and identify influential observations;
- identify simple designed experiments;
- construct factorial experiments in blocks;
- adapt linear models to fit growth curves;
- carry out logistic regression;
- analyze cross-tabulated data using log linear models;
- analyse linear models using R.
Syllabus
Simple linear regression
1. Link between maximum likelihood and least Squares. OLS for linear regression.
2. Pythagoras and the ANOVA table. The estimation of $rc2 .
3. Confidence intervals for parameters and prediction intervals for future observations
General results using matrices
4. Matrix formulation. Normal equations. Solution. Moments of estimators.
5. Gauss-Markov theorem. Estimability
6. H, Q, V.
7. Generalised and weighted least squares.
Multiple regression
8. Multiple regression. Subdividing the regression sum of squares. Lack of fit and pure error.
9. Regression diagnostics. Leverage, Residual plots. Multicollinearity, Serial correlation
10. Model selection. Stepwise methods. Cp plots.
11. Curvilinear regression. Orthogonal polynomials.
12. ANCOVA
Designed experiments
13. Completely randomised experiment. Replication. ANOVA. Contrasts.
14. Randomized blocks. Latin squares. Multiple comparison tests.
15. ANOVA with random effects
16. Balanced incomplete blocks. ANOVA (relation to bivariate regression)
17. Factorial experiments: notation. ANOVA. Model selection.
18. Factorials and blocks: confounding and partial confounding.
19. Fractional replicates. Aliases.
Non-linear models
20. The Newton-Raphson procedure. Application to growth curves.
21. Estimation, confidence intervals, tests.
Logit and loglinear models
22. Logistic regression
23. Loglinear models. Birch's result. Hierarchy principle. Iterative proportional fitting.
24. Independence. Conditional independence. Multistage analysis.
25. Simpson's paradox. Incomplete tables. Square tables.
Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.
This module does not appear to have a published bibliography for this year.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Individual Submission |
|
25% |
| Coursework |
Group Submission |
|
75% |
| Exam |
Main exam: 240 minutes during Summer (Main Period)
|
| Exam |
Reassessment Main exam: 240 minutes during January
|
Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Stella Hadjiantoni, email: stella.hadjiantoni@essex.ac.uk.
Dr Stella Hadjiantoni & Dr Terry Sithole
Dr Stella Hadjiantoni (stella.hadjiantoni@essex.ac.uk), Dr Terry Sithole (sz21720@essex.ac.uk)
No
No
No
Prof Fionn Murtagh
University of Huddersfield
Professor of Data Science
Dr Yinghui Wei
University of Plymouth
Available via Moodle
Of 2870 hours, 20 (0.7%) hours available to students:
2850 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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