Modelling experimental and observational data
Mathematics, Statistics and Actuarial Science (School of)
Undergraduate: Level 5
Monday 17 January 2022
Friday 25 March 2022
15 July 2021
Requisites for this module
BA Q120 Linguistics with Data Science,
BA Q121 Linguistics with Data Science (Including Foundation Year),
BA Q122 Linguistics with Data Science (Including Placement Year),
BA Q123 Linguistics with Data Science (Including Year Abroad)
This module will introduce the principles for the application of linear modelling methodologies for the analysis of experimental and observational data. The first strand of the module will study the assumptions of the general linear model. Collinearity, influential data, assessing the fitted model and model selection techniques will be discussed. The second strand will introduce statistical methods for the efficient analysis of experiments when the data are normally distributed, for example one-way ANOVA. The methodology will be extended to logistic regression. The third strand of the module will study various multivariate methods for the analysis of large and high-dimensional data sets.
The module will focus on providing the:
1. Fundamental understanding of the underlying statistical methodologies;
2. Capabilities of applying these methodologies to real experimental and observational data
3. Knowledge of conducting a robust statistical analysing of the data
4. Capabilities of interpreting the results effectively.
On completion of the module students will have:
A. knowledge and critical understanding of the well-established principles of estimating a multiple linear regression model using real data;
B. knowledge and critical understanding of the well-established principles of assessing fitted models and validate linear models’ assumptions;
C. knowledge and critical understanding of the well-established principles of identifying and conducting simple designed experiments;
D. knowledge and critical understanding of the well-established principles of employing and assessing the results of discriminant analysis, multiple logistic regression, principal component and clustering to real observational data;
E. the ability to use R for the application and statistical analysis of linear regression and machine learning techniques for the modelling of experimental and observational data.
A. Observational versus experimental data
i. Using matrices to represent data, matrix notation
B. Multiple regression
i. Formulating the model, the estimator and other results using matrix formulation
ii. Assumptions and assessment of the fitted model, coefficient of determination and the sample correlation coefficient
iii. Checking the assumptions of the linear model and other regression diagnostics: Residual plots, multicollinearity, homoskedasticity
iv. Model selection methods and hypothesis testing for variable selection.
v. Factorisation of the regression sum of squares and the ANOVA table.
vi. Missing values and imputation
C. Designed experiments for multiple comparison tests
i. Intuition to multiple comparisons.
ii. One-, two-way ANOVA and the ANCOVA.
iii. Understand and interpret a logistic regression model (categorical response variable)
D. Multivariate methods
i. Multiple logistic regression: odds ratio, log odds
ii. Linear discriminant analysis (LDA): classification between populations, discriminant function and probability of misclassification, multiclass LDA, Quadratic discriminant analysis
iii. Test and training samples, leave-one-out and k-fold cross-validation
iv. Precision, recall, accuracy, Youden index, ROC curves, positive predictive value, negative predictive value, confusion matrix
v. Single or multiple topic classification on articles
vi. Feature engineering on textual data
b. Cluster analysis: similarity measures, single-link and other hierarchical methods, k-means
i. Article topic taxonomy
c. Dimensionality reduction - Principle components analysis: definition, interpretation of calculated components, use in regression
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
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.
Module supervisor and teaching staff
Dr Stella Hadjiantoni, email: firstname.lastname@example.org.
Dr Stella Hadjiantoni
Prof Fionn Murtagh
University of Huddersfield
Professor of Data Science
Dr Yinghui Wei
University of Plymouth
Available via Moodle
Of 1193 hours, 28 (2.3%) hours available to students:
1165 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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