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 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)

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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.

4 Some helpful R commands

You will need to load the following packages

library(spdep)

library(sp)

library(R2WinBUGS)

library(CARBayes)

To load the data and produce a plot of PM25 (for example), use

load("london.RData")

spplot(london, "PM25")

To produce the adjacency matrix required for use in the moran.test function

Wnb <- nb2listw(poly2nb(london))

You will need the adjacency matrix attributes Adj, Num.Adj and SumNumNeigh for use in

OpenBUGS to fit the conditional autoregressive model:

W <- nb2mat(poly2nb(london), style = "B")

inds <- lapply(1:nrow(W), function(i) which(W[i, ] == 1))

# the following 3 objects are needed to fit a conditional-autoregressive model

Adj <- Reduce("c", inds)

Num.Adj <- rowSums(W)

SumNumNeigh <- sum(Num.Adj)

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5 Data description - london.RData

Column name Description

Observed Annual hospital admissions due to respiratory disease

Expected Expected annual hospital admissions due to respiratory disease based on

national average rate

JSA Proportion of electoral ward in receipt of jobseeker’s allowance, an

unemployment benefit

Price Annual average sale price of homes (logged GBP)

PM25 Annual average concentration of fine particulate matter PM2.5 (μgl?1

)

year Year of observation: 2003 to 2009 inclusive

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