5.10 Spatial Pattern Analyses
Spatial pattern analyses were carried out on the existing HCFs and a set of selected solutions from the Spatial-ABM optimization to assess the adherence of the HCF agents to rules for selecting their locations. These analyses investigate:
1. the spatial distribution of the HCFs
2. the relationship of HCF locations with their neighbouring features
Spatial autocorrelation statistical technique was employed to provide an index for determining the spatial dependence or independence of a feature using the geomet-ric and non-geometgeomet-ric attributes of the feature. Unlike the traditional statistics where independence of observation is anticipated, spatial statistical analyses consider that geographical observations are effected by the geographic space and observations are related to other things. According to Tobler’s first law of geography - "everything is re-lated to everything else, but near things are more rere-lated than distant things." (Tobler, 1970). The absence of spatial autocorrelation is an indication of a random distribution of the data over the focused area. If random distribution is established, there will be no need for further statistical spatial autocorrelation analyses.
Two types of spatial autocorrelation measures are:
i Global autocorrelation: This aggregates the spatial association with respect to an entire region and does not indicate where the association is most obvious or where there are no associations.
ii Local autocorrelation: This measures the index based on the location of a feature with respect to a specified neighbourhood proximity. If a clustered pattern is iden-tified, the local spatial autocorrelation helps to identify the local features that are strongly responsible for the general spatial pattern in the region. This measure is applied in this analysis considering the differing characteristics of the different region in Lagos State.
Positive autocorrelation indicates that similar data values of features are within the neighbourhood, while negative autocorrelation is an indication that the values within the neighbourhood are dissimilar. The spatial statistics that describe such local relationships are called Local Indicators of Spatial Association (LISA) among which is the Morans’ I proposed by Anselin (1995), and is employed for this thesis using the Open Geoda spatial statistical version 1.12.1.161 software.
The questions that will be answered in the spatial analyses include:
• Do HCFs have a clustered, random or dispersed pattern?
• If there is clustering, what is the significance of the clustering?
O. Olowofoyeku 5.10. SPATIAL PATTERN ANALYSES
• What are some of the contributing factors to the selection of HCF locations?
• Why are there many or less HCFs in some places?
• Is there an association between the features in the region?
• What spatial processes are responsible for the spatial pattern?
The following sections explain the procedure for answering theses questions.
5.10.1 Data Preparation
As an initial step for point data, the observations are aggregated within a polygon fea-ture which may be the geographic boundary or a grid of cells drawn to cover the study area. The point feature variables within each polygon feature are then aggregated. For this thesis, the Lagos State boundary map was covered with a grid of polygons so that each polygon grid has variables such as number of HCFs, population size, and area of water body coverage that intersects with the grid. Grid polygons that fell outside the Lagos State boundary and grids with zero values of HCF for the focused variable were removed prior to analysis. The distribution of existing HCFs, the newly located HCFs and a combination of new and existing HCFs were compared.
5.10.2 Exploring HCFs Distribution
The next step is to investigate the location of the datasets for variance and outliers. This was done using the box plot in Geoda. The box plot graphics in Figure 5.19 show that the estimated average number of existing HCFs, new HCFs and the combined sets of HCFs are 2, 5 and 7 respectively (indicated by the green circle); and the median values are 1, 4 and 5 respectively (indicated by the orange line). The datasets for all sets of HCFs reveal slight skewness.
A box map was also created for visual exploration of the datasets and the outliers.
The box maps are presented in Figure 5.20. The outliers are also revealed in the maps, including the cells with a high and low number of HCFs. For example, linking the outliers on the box graph to the map shows that the lowest outliers (small number of HCFs within a cell) in the new HCFs data (Figure 5.19b) and the combined new and existing HCFs (Figure 5.19c) are much located on the outskirts and rural areas of the study area. The upper outliers (large number of HCFs within a cell) for the new HCFs (Figure 5.19b) are located towards the south-east and south-west, while the existing HCFs data (Figure 5.20a) has upper outliers around the Lagos metropolis.
For each dataset, most of the values are within the 25% - 75% range. Compared to the newly located HCFs that has most number of HCFs ranging from two to eight, the existing HCFs only has between zero and two values. Upper outliers were revealed in all the datasets, however the existing HCFs have more outliers. These outliers offer valuable information about the distribution of the data. In this case, the number of
O. Olowofoyeku 5.10. SPATIAL PATTERN ANALYSES
HCFs within a grid in each dataset that deviates so much from other values can be investigated further to understand the processes responsible for such high variance in their respective locations.
Figure 5.19: Box graphics of healthcare facilities distribution
(a) Existing HCFs box map
(b) New HCFs box map
(c) New and existing HCFs box map
Figure 5.20: Box plot maps for exploratory analysis of aggregated HCFs in grid polygons