Statistical Modelling(C)
STATISTICAL MODELLING (C)
Part IB Statistics is essential. About two thirds of this course will be lectures, with the remaining hours as practical classes, using R in the CATAM system. R may be downloaded at no cost via http://cran.r-project.org
Introduction to the statistical programming language R
- Graphical summaries of data, e.g. histograms. Matrix computations. Writing simple functions. Simulation. [2]
Linear models Review of least squares and linear models.
- Characterisation of estimated coefficients, hypothesis tests and confidence regions. Prediction intervals. Model selection. Box–Cox transformation. Leverages, residuals, qq-plots, multiple R2 and Cook’s distances. [5]
Overview of basic inferential techniques
- Asymptotic distribution of the maximum likelihood estimator. Approximate confidence regions. Wilks’ theorem. The delta method. Posterior distributions and credible intervals. [3]
Exponential dispersion families and generalised linear models (glm)
- Exponential families and mean–variance relationship. Dispersion parameter and generalised linear models. Canonical link function. Iterative solution of likelihood equations. Regression for binomial data; use of logit and other link functions. Poisson regression models, and their surrogate use for multinomial data. Application to 2- and 3-way contingency tables. Hypothesis tests and model selection, including deviance and Akaike’s Information Criterion. Residuals and model checking. [8]
Examples in R
- Linear and generalised linear models. Interpretation of models, inference and model selection. [6]
Appropriate books
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- A.J. Dobson An Introduction to Generalized Linear Models. Chapman and Hall 2002
- J. Faraway Practical Regression and Anova in R. http://cran.r-project.org/doc/contrib/FarawayPRA.pdf
- A.C. Davison Statistical Models. CUP 2008
- J. Albert and M. Rizzo R by Example. Springer 2012
- S. Chaterjee and J.S. Simonoff Handbook of Regression Analysis. Wiley 2013
- A. Agresti Foundations of Linear and Generalized Linear Models. Wiley 2015
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