Spatial Statistics Project
1 Project overview
In this project, you will estimate the effects of air pollution and socio-economic variables on the risk of admission to a hospital caused by respiratory disease. The data for the project cover the 7 year period spanning 2003 to 2009 and describe annual hospital admissions across 624 electoral wards of Greater London. Each person will be individually assigned both a year and a data set to work with. The data are contained in the file london_x.RData where "x" corresponds to your allocated data set, and once loaded, the data are in the form of an sp object called london_x with geographical attributes included. Further information about the contents of the data can be found in Section 4.
2 Project tasks
1. (a) Create a subset of your assigned data for the year you have been assigned.
(b) Calculate the standardised incidence ratio (SIR) for respiratory disease and add this as a new column to your data subset.
(c) Use a spatial plot to explore SIR.
(d) Use scatterplots to explore the association between SIR and PM25, JSA and Price.(10 marks)
2. (a) Use BUGS and appropriate prior distributions to fit a Poisson regression model for respiratory disease, making use of the columns Observed, Expected, PM25, JSA and Price.
(b) Use the Gelman-Rubin diagnostic (Rhat) and Geweke diagnostic plots to assess whether convergence has been reached.
(c) Calculate the Pearson residuals and use these to check the model assumptions.(10 marks)
3. (a) Extend the model developed in 2. by including spatial random effects φ with a Conditional-autoregressive prior distribution.
(b) Use the Gelman-Rubin diagnostic (Rhat) and Geweke diagnostic plots to assess whether convergence has been reached.
(c) Calculate the Pearson residuals and use these to check the model assumptions.(10 marks)
4. Construct a table with columns for DIC, Moran’s I statistic, variance of the Pearson residuals and the estimated effect of PM25 (and 95% credible interval) to critically compare the models in 2. and 3. Using estimates from the better model, interpret the effect of PM25 on the rate of respiratory hospital admission in Greater London.(10 marks)
3 Report structure, content and submission
The report itself does not need to follow any particular structure, however, you should ensure that any analysis you carry out is clearly interpreted, using full sentences. You should write as though your audience were your statistics classmates who are unfamiliar with the data.
• The report should have a cover page with your name and student ID clearly marked
• The report should be between 4 and 6 A4 pages in length including graphics and tables but excluding cover page and any references
• Graphs should be suitably labelled, sensibly scaled and cropped
• Numerical R outputs used to answer questions should be neatly presented in tables or in the text
• Your R code and BUGS code output should be included in an appendix
• Please submit your report by midday on Wednesday 8th April via the upload link on Myplace.
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