Module Directory

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 aims of this module are:

• To provide the fundamental understanding of the underlying statistical methodologies.


• To provide capabilities of applying these methodologies to real experimental and observational data.


• To provide knowledge of conducting a robust statistical analysing of the data.


• To provide capabilities of interpreting the results effectively.

By the end of this module, students will be expected to have:

1. Knowledge and critical understanding of the well-established principles of estimating a multiple linear regression model using real data.


2. Knowledge and critical understanding of the well-established principles of assessing fitted models and validate linear models’ assumptions.


3. Knowledge and critical understanding of the well-established principles of identifying and conducting simple designed experiments.


4. 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.


5. 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.

Syllabus

• Observational versus experimental data
  
  
  
  • Using matrices to represent data, matrix notation.
  
  
  
  


• Multiple regression
  
  
  
  • Formulating the model, the estimator and other results using matrix formulation.
  
  
  • Assumptions and assessment of the fitted model, coefficient of determination and the sample correlation coefficient.
  
  
  • Checking the assumptions of the linear model and other regression diagnostics: Residual plots, multicollinearity, homoskedasticity.
  
  
  • Model selection methods and hypothesis testing for variable selection.
  
  
  • Factorisation of the regression sum of squares and the ANOVA table.
  
  
  • Missing values and imputation
  
  
  
  


• Designed experiments for multiple comparison tests
  
  
  
  • Intuition to multiple comparisons.
  
  
  • One-, two-way ANOVA and the ANCOVA.
  
  
  • Understand and interpret a logistic regression model (categorical response variable).
  
  
  
  


• Multivariate methods


•  Classification
  
  
  
  • Multiple logistic regression: odds ratio, log odds.
  
  
  • Linear discriminant analysis (LDA): classification between populations, discriminant function and probability of misclassification, multiclass LDA, quadratic discriminant analysis.
  
  
  • Test and training samples, leave-one-out and k-fold cross-validation.
  
  
  • Precision, recall, accuracy, Youden index, ROC curves, positive predictive value, negative predictive value, confusion matrix.
  
  
  • Single or multiple topic classification on articles.Feature engineering on textual data
  
  
  
  


• Cluster analysis - similarity measures, single-link and other hierarchical methods, k-means.
  
  
  
  • Article topic taxonomy
  
  
  
  


• Dimensionality reduction - Principle components analysis: definition, interpretation of calculated components, use in regression

Teaching in the School will be delivered using a range of face to face lectures, classes and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.