Regression analysis of spatial data

Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

Detection of visual-field deterioration by Glaucoma Progression Analysis and Threshold Noiseless Trend programs

BACKGROUND: To compare the ability of Glaucoma Progression Analysis (GPA) and Threshold Noiseless Trend (TNT) programs to detect visual-field deterioration.

METHODS: Patients with open-angle glaucoma followed for a minimum of 2 years and a minimum of seven reliable visual fields were included. Progression was assessed subjectively by four masked glaucoma experts, and compared with GPA and TNT results. Each case was judged to be stable, deteriorated or suspicious of deterioration

RESULTS: A total of 56 eyes of 42 patients were followed with a mean of 7.8 (SD 1.0) tests over an average of 5.5 (1.04) years. Interobserver agreement to detect progression was good (mean kappa = 0.57). Progression was detected in 10-19 eyes by the experts, in six by GPA and in 24 by TNT. Using the consensus expert opinion as the gold standard (four clinicians detected progression), the GPA sensitivity and specificity were 75% and 83%, respectively, while the TNT sensitivity and specificity was 100% and 77%, respectively.

CONCLUSION: TNT showed greater concordance with the experts than GPA in the detection of visual-field deterioration. GPA showed a high specificity but lower sensitivity, mainly detecting cases of high focality and pronounced mean defect slopes.

Spatial and Temporal Changes in Soil Organic Carbon Assessment using an Integrated Geostatistical and Compositional Data Analysis Approach

The Irish and UK governments, along with other countries, have made a commitment to limit the concentrations of greenhouse gases in the atmosphere by reducing emissions from the burning of fossil fuels. This can be achieved (in part) through increasing the sequestration of CO2 from the atmosphere including monitoring the amount stored in vegetation and soils. A large proportion of soil carbon is held within peat due to the relatively high carbon density of peat and organic-rich soils. This is particularly important for a country such as Ireland, where some 16% of the land surface is covered by peat. For Northern Ireland, it has been estimated that the total amount of carbon stored in vegetation is 4.4Mt compared to 386Mt stored within peat and soils. As a result it has become increasingly important to measure and monitor changes in stores of carbon in soils. The conservation and restoration of peat covered areas, although ongoing for many years, has become increasingly important. This is summed up in current EU policy outlined by the European Commission (2012) which seeks to assess the relative contributions of the different inputs and outputs of organic carbon and organic matter to and from soil. Results are presented from the EU-funded Tellus Border Soil Carbon Project (2011 to 2013) which aimed to improve current estimates of carbon in soil and peat across Northern Ireland and the bordering counties of the Republic of Ireland.
Historical reports and previous surveys provide baseline data. To monitor change in peat depth and soil organic carbon, these historical data are integrated with more recently acquired airborne geophysical (radiometric) data and ground-based geochemical data generated by two surveys, the Tellus Project (2004-2007: covering Northern Ireland) and the EU-funded Tellus Border project (2011-2013) covering the six bordering counties of the Republic of Ireland, Donegal, Sligo, Leitrim, Cavan, Monaghan and Louth. The concept being applied is that saturated organic-rich soil and peat attenuate gamma-radiation from underlying soils and rocks. This research uses the degree of spatial correlation (coregionalization) between peat depth, soil organic carbon (SOC) and the attenuation of the radiometric signal to update a limited sampling regime of ground-based measurements with remotely acquired data. To comply with the compositional nature of the SOC data (perturbations of loss on ignition [LOI] data), a compositional data analysis approach is investigated. Contemporaneous ground-based measurements allow corroboration for the updated mapped outputs. This provides a methodology that can be used to improve estimates of soil carbon with minimal impact to sensitive habitats (like peat bogs), but with maximum output of data and knowledge.

Spatial allocation of material flow analysis in residential developments: a case study of Kildare County, Ireland

Studies of urban metabolism provide important insights for environmental management of cities, but are not widely used in planning practice due to a mismatch of data scale and coverage. This paper introduces the Spatial Allocation of Material Flow Analysis (SAMFA) model as a potential decision support tool aimed as a contribution to overcome some of these difficulties and describes its pilot use at the county level in the Republic of Ireland. The results suggest that SAMFA is capable of identifying hotspots of higher material and energy use to support targeted planning initiatives, while its ability to visualise different policy scenarios supports more effective multi-stakeholder engagement. The paper evaluates this pilot use and sets out how this model can act as an analytical platform for the industrial ecology–spatial planning nexus.

Knowledge Exchange, Spatial Analysis & Healthy Urban Environments (KESUE): Project Report

The Knowledge Exchange, Spatial Analysis and Healthy Urban Environments (KESUE) project has extended work previously undertaken by a QUB team of inter-disciplinary researchers engaged with the Physical Activity in the Regeneration of Connswater (PARC) project (Tully et al, 2013). The PARC project focussed on parts of East Belfast to assess the health impact of the Connswater Community Greenway. The KESUE project has aimed to extend some of the tools used initially in East Belfast so that they have data coverage of all of Belfast and Derry-Londonderry. The purpose of this has been to enable the development of evidence and policy tools that link features of the built environment with physical activity in these two cities. The project has used this data to help shape policy decisions in areas such as physical activity, park management, public transport and planning.

Working with a range of local partners who part-funded the project (City Councils in Belfast and Derry-Londonderry, Public Health Agency, Belfast Healthy Cities and Department of Regional Development), this project has mapped all the footpaths in the two cities (covering 37% of the NI population) and employed this to develop evidence used in strategies related to healthy urban planning. Using Geographic Information Systems (GIS), the footpath network has been used as a basis for a wide range of policy-relevant analyses including pedestrian accessibility to public facilities, site options for new infrastructure and assessing how vulnerable groups can access services such as pharmacies. Key outputs have been Accessibility Atlases and maps showing how walkability of the built environment varies across the two cities.

In addition to generating this useful data, the project included intense engagement with potential users of the research, which has led to its continued uptake in a number of policies and strategies, creating a virtuous circle of research, implementation and feedback. The project has proved so valuable to Belfast City Council that they have now taken on one of the researchers to continue the work in-house.

Sector analysis provides additional spatial information on the permanent prostate brachytherapy learning curve

PURPOSE: To evaluate the permanent prostate brachytherapy (PPB) learning curve using postimplant multisector dosimetric analysis and to assess the correlation between sector -specific dosimetry and patient-reported outcome measures (PROMs).

METHODS AND METHODS: First 200 patients treated with (125)I PPB monotherapy (145 Gy) at a single institution were assessed. Postimplant dosimetry (PID) using CT was evaluated for whole prostate (global) and 12 sectors, assessing minimum dose to 90% of prostate (D90) and dose to 0.1 cm(3) of rectum (D0.1cc). Global and sector PID results were evaluated to investigate changes in D90 with case number. Urinary and bowel PROMs were assessed using the International Prostate Symptom Score and the Expanded Prostate Cancer Index Composite questionnaire. The correlation between global and individual sector PID and urinary/bowel PROMs was also evaluated.

RESULTS: Linear regression confirmed a significant improvement in global D90 with case number (r(2) = 0.20; p = 0.001) at a rate of 0.11 Gy/case. Postimplant D90 of base sectors increased at a rate of 0.11-0.15 Gy/case (p = 0.0001) and matched global improvement. The regression lines of midgland and apex sectors were significantly different from global D90 (p = 0.01). Posterior midgland sectors showed a significant reduction in D90 with case number at a rate of 0.13-0.19 Gy/case (p = 0.01). Dose to posterior midgland sectors correlated with rectal D0.1cc dose but not bowel PROMs. Dose to posterior midgland sectors correlated with urinary International Prostate Symptom Score change, which was not apparent when global D90 alone was considered.

CONCLUSIONS: Sector analysis provided increased spatial information regarding the PPB learning curve. Furthermore, sector analysis correlated with urinary PROMs and rectal dose.

Energy efficiency in the Chinese provinces: a fixed effects stochastic frontier spatial Durbin error panel analysis

Energy efficiency improvement has been a key objective of China’s long-term energy policy. In this paper, we derive single-factor technical energy efficiency (abbreviated as energy efficiency) in China from multi-factor efficiency estimated by means of a translog production function and a stochastic frontier model on the basis of panel data on 29 Chinese provinces over the period 2003–2011. We find that average energy efficiency has been increasing over the research period and that the provinces with the highest energy efficiency are at the east coast and the ones with the lowest in the west, with an intermediate corridor in between. In the analysis of the determinants of energy efficiency by means of a spatial Durbin error model both factors in the own province and in first-order neighboring provinces are considered. Per capita income in the own province has a positive effect. Furthermore, foreign direct investment and population density in the own province and in neighboring provinces have positive effects, whereas the share of state-owned enterprises in Gross Provincial Product in the own province and in neighboring provinces has negative effects. From the analysis it follows that inflow of foreign direct investment and reform of state-owned enterprises are important policy handles.