Statistical Modelling

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

    • 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

 

Associated GitHub page

https://jaircambridge.github.io/Statistical-Modelling-C/