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This incorporation of spatial dependence is important because spatial autocorrelation can reduce the efficiency of the Ordinary Least Squares estimator used in linear regression. Since most features over space have an element of spatial dependence associated with them, it suggests that spatial regression may be a better choice than simple linear regression when modeling features over space, although spatial dependence can be removed using a variety of methods including detrending procedures where spatial trends are evident.
The benefit of using the spatial regression technique is its ability to create a model that can be used to make generalized inferences in an area while accounting for the effects of spatial dependence. A study by Zenk et al. Although spatial regression can account for spatial dependence in a dataset, a recent review states that there is always the possibility of ecological bias when area level data are used to represent individual characteristics within studies Wakefield, Geographically weighted regression GWR is a local regression model that creates unique local coefficients in order to describe the variation in the dependent variable.
This creates local models that are well suited to explore the variation in the data graphically Jetz et al. The weighting matrix used in GWR is dependent on the location of individual points and thus must be recalculated at each point. This is in contrast to the spatial regression method where a single contiguity weighting matrix is used for the entire study area based on the extent of spatial dependence on the dependent variable. In GWR, kernels can be used which associate aspects of density of data into the process Fotheringham et al.
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GWR also has the benefit of being able to evaluate changes in strength of relationships over different scales, which is difficult to do using spatial regression Jetz et al. Previous publications have summarized GWR and local analysis in further detail Brunsdon et al. GWR has been used in a recent study to evaluate the relationship between cold surges and cardiovascular disease CVD mortality. This study found that the CVD mortality rates increased significantly after cold surges and that the tolerance of different populations to these weather changes differed over space Yang et al.
Another study compared the findings from linear regression and GWR when studying access to parks and physical activity sites and found that while OLS regression found weak relationships between park density and physical activity site density, GWR indicated disparities in accessibility that varied over space Maroko et al.
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This study shows the importance of using the appropriate method of analysis for the data that is under study. Yet another study used GWR as a tool to indicate the need for spatial coefficients when linking health and environmental data in geographical analysis Young et al. The main difference between spatial regression and GWR is that one is a global model and one is a local model. Overall, GWR should be used when there is spatial non-stationarity or when relationships between variables differ over space Fotheringham et al. A simple map of the residuals of a model indicate whether a spatial regression method should be employed over a traditional linear regression method; when the residuals are clustered into high and low values over space it is likely necessary to use a spatial regression method.
The residuals of a spatial regression or GWR can also be mapped to assess the areas where the models are under or over estimating Fotheringham et al. The concept of access to health care is a central focus of many health research studies. Spatial accessibility is one aspect of access to health care that can be measured using geospatial methods. Geographic access to a service can be represented as straight line distance, network distance and travel time based on travel along a road network Apparicio et al.
The two methods that we will focus our discussion on in this section are road network analysis and interpolation. Network analysis allows for a more realistic representation of travel times along a road network by accounting for the different travel speeds along the various road links. One UK study found that travel time estimates based on network analysis may be preferred to reported travel times for modeling purposes because the reported times can reflect unusual circumstances and reporter error Haynes et al.
The strength of road network analysis is that it allows for the estimation of travel times between different point locations along a road network. It does not allow for continuous travel time surfaces to be mapped. In order to do this we can use a method referred to as interpolation. The advantage of interpolation over simple network analysis is that it can allow for a comparison between different modes of transportation to health care facilities.
To do this it would be necessary to have point data representing travel times via different modes for this type of analysis. For example, using interpolation, a study conducted by Lerner et al. The goal of that study was to create a map that would show where air or ground ambulance should be preferred to transport patients to a trauma center from a given patient starting location.
One Canadian study used this method to compare where ground, helicopter or fixed-wing transport was faster when transporting patients to a cardiac catheterization facility Patel et al. Figure 3 highlights how interpolation can be used to model travel times via different modes of emergency transport over an area.
There are strengths and limitations to using interpolation as part of a geospatial analysis. One limitation of using this method is that an accurate interpolation requires many points that are evenly distributed over the study area. Another limitation is that depending on the type of interpolation used e. In spite of these limitations, interpolation is a powerful method to compare access via different modes of travel.
This is achieved by evaluating those areas that are served faster by different modes of travel using grid cell comparisons.
Mapping of seismic parameters of the Iberian Peninsula by means of a geographic information system
Both network analysis and interpolation can be used to estimate travel time values that can be used as a measures of geographic access. These measures can then be used to evaluate the associations between spatial access to services and other variables e. These access measures can also be linked with census or patient data to study the populations with access to certain services Nallamothu et al.
It is important to note that because the method of interpolation focuses on creating continuous surfaces from point data, it can also be used to model the concentration of environmental variables from a point source or the spread of an infectious agent over boundaries Kistemann et al. The spatial analysis of health services is based on the principle that populations and their need for healthcare vary across space. People are not located randomly about the earth and it is often observed that different areas are populated by groups with differing characteristics e.
Recent studies have used GIS and the principles of location analysis to evaluate optimal locations for pre-hospital helicopter emergency medical services Schuurman et al. It is beyond the scope of this chapter to discuss the mathematical models that are used for location analysis; this information is available elsewhere de Smith et al. This section will discuss two different approaches for identifying the best location for a new service: coverage and distance problems.
There are two types of coverage problems that are commonly referred to in the operations research literature: the location set covering problem LSCP and the maximal covering location problem MCLP. In this model, each demand point is covered at least once. Given these constraints this model seeks to provide the best possible coverage with the limited available resources and does not guarantee service.
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Geospatial tools available within GIS software can be used to assemble the needed data to address both types of coverage problems. Ambulance and fire department response are two examples of services that require complete coverage of an area and thus a LSCP approach to coverage. Other services may strive for as much coverage as possible based on the resources available.
One example is the placement of public health care facilities. By creating catchment areas within GIS, the best possible locations for new facilities can be evaluated based on the most area and population covered Murad, The strength of using these types of coverage models is that they provide a spatial-standard based framework for siting new health service facilities that considers population needs and available resources.
While these frameworks can be used to study the best locations based on the coverage of a facility over a given area, in other instances a distance based approach may be required. There are two common approaches to finding an optimal location based on distance for a new facility: p-median and p-centre approaches. In order to deal with this limitation, heuristic algorithms are employed that use systematic procedures to trade off the quality of the solution with processing speed de Smith et al.
While these methods are founded theoretically in the mathematical modeling and operations research literature, there are a number of components to these strategies that can be evaluated using GIS Church, For example, previous studies have used geospatial methods to evaluate the suitability of selected sites as possible locations for a new facility Cinnamon et al. Both the coverage approach and the distance based approach to the placement of new facilities are important.
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They provide a framework for optimizing the solution to the best location for a new facility. The coverage model focuses on ensuring the population is best served in terms of the placement of a new facility. Spatial dependence violates the assumption of independence needed for standard linear regression Legendre, Spatial regression is a valuable method in situations where spatial autocorrelation exists because it considers the spatial dependence between variables by giving weights to them based on distance.
The weighting matrix used in the spatial regression process accounts for the spatial dependency in the dependent variable Fotheringham et al. In order to determine accurately the weights used within this matrix it is necessary to first determine the range distance of the spatial dependence on the dependent variable using a semivariogram, a graph that visually provides a description of how the data are related correlated with distance.
Beyond the range defined by the semivariogram there is no longer spatial dependence Fotheringham et al. This incorporation of spatial dependence is important because spatial autocorrelation can reduce the efficiency of the Ordinary Least Squares estimator used in linear regression.