Statistics
ST413: Statistical Modelling (5 ECTS)
An advanced course on statistical modelling, building on the regression modelling introduced in MA322/ST313, covering the theory and application of generalized linear models and their fitting in R
Taught in Semester(s) II. Examined in Semester(s) II.
Workload: 40 hours (24 Lecture hours, 6 Tutorial hours, 10 Lab hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Formulate a normal model with continuous and categorical explanatory variables, fit such models in R, interpret model output, make inferences using both parameter estimates and ANOVA tables.
- Check adequacy of normal models using standard model diagnostics and modify models using transformations and link functions.
- Formulate and derive properties of generalized linear models (glms).
- Obtain maximum likelihood estimating equations for glms and derive the 5. Iterative Weighted Least Squares algorithm.
- Formulate and use (in R) binomial regression models to analyse proportion data with both continuous and categorical explanatory variables.
- Formulate and use (in R) Poisson regression models to analyse count and rate data.
- Analyse and test associations in multi-way table using log-linear models. Analyse censored survival data using parametric and non-parametric (Cox proportional hazards) models.
Indicative Content
This course provides an introduction to generalized linear models and their application. A key component of the course will be the use of R (open-source statistical software) for statistical model fitting. The topics covered include
- Revision of the general linear model. Introduction to model fitting in R.
- Generalized linear models (glms): exponential family, link function, variance function.
- Fitting glms: Iterative Weighted Least Squares; analysis of deviance; inference; diagnostics.
- Binomial regression models for proportions; binary regression models; contingency tables.
- Log-linear models for count data; Poisson regression models; multinomial models; multi-way tables.
- Models for time to event data; exponential regression; survival data, censoring; Weibull model; Cox proportional hazards model.
Module Resources
- Statistical Modelling In R by Aitkin, Francis, Hinde & Darnell, Oxford.
- An Introduction to Generalized Linear Models by Dobson & Barnett, CRC Press
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