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Jim Kompanek
Global Autocorrelation
The first portion of this lesson involved Global Moran's Spatial Autocorrelation analysis to examine the spatial distribution of Pacific Islanders in Auckland, New Zealand based upon the akCity_MB01_ethnic shapefile. This shapefile divides the city into Census "Mesh Blocks" (MB), which are the smallest census units used in New Zealand, with only a few hundred people in each. Figure 1 represents a choropleth map of Auckland with each MB symbolized based upon a percentile classification scheme, with lighter hues of blue indicating a below 50 percent Pacific Islander population, and red hues indicating an above 50 percent Pacific Islander population. Based upon a cursory examination of the map, the areas of the city with high percentages of Pacific Islanders appear to be to the east and west.
Figure 1. Choropleth map of Auckland, New Zealand indicating the percent of Pacific Islanders in each census "Mesh Block".
The Univariate Moran tool of GeoDA was used to generate the Moran's I value and subsequent scatter plot of results (Figure 2). The value of Moran's I equals 0.6475 and the slope of the regression line is positive, which indicates an overall strong positive global autocorrelation. The slope of the regression line indicates a global correlation exists within the dataset (a downward slope would indicate global correlation does not exist). The type of spatial correlation of each point on the scatter plot is determined by the quadrant of which it is placed: Spatial clusters (positive autocorrelation) are plotted in the northeast and southwest quadrants and outliers (negative spatial autocorrelation) in the northwest and southeast quadrants. The strength of correlation can be determined by the distance between each point and the center of the scatter plot (0,0).
Figure 2. Moran Scatter plot for the percent of Pacific Islanders in each MB within Auckland, New Zealand.
Figure 3 represents the same choropleth map as Figure 1 but with the spatial outliers (negative spatial autocorrelation) hatched in yellow. These hatched areas represent MB's that were located in the northwest and southeast quadrants of the Figure 2.
Figure 3. Choropleth map of Auckland, New Zealand indicating the percent of Pacific Islanders in each census "Mesh Block" with hatched outliers (click on image for full size graphic).
Local Indicators of Spatial Association (LISA)
The following analyses are based upon the akcity_CAU01_ethnic shapefile for Auckland, New Zealand. This shapefile depicts the Census Area Units (CAU's) of the central Auckland "City" region. For this portion of the lesson, I examined the distributed of the Maori population within this area. The first step involved generating a choropleth map to examine the population distribution throughout the study area (Figure 4). A cursory examination indicates the CAU's with the highest Maori population appear to be located in the eastern portion of the study area.
Figure 4. Choropleth map of the Auckland "City" region indicating the percent of Maori in each CAU.
The Univariate LISA tool of GeoDA was used to generate the Moran's I value and associated scatter plot of results (Figure 5). The Moran's I equals 0.5723 and the slope of the regression line is positive. This indicates an overall strong positive autocorrelation.
Figure 5. Moran Scatter plot for the percent of Maori population in Auckland, New Zealand.
A cluster map was also generated using the Univariate LISA tool of GeoDA. The cluster map depicts how each quadrant of the scatter plot (Figure 5) influence the global pattern. The dark red regions depict a "High-High" area, which have high values of Maori population (greater than mean) and significantly effect the global correlation pattern. These areas are entirely located along the southeast portion of the study area. In the case of the dark blue areas which depict "Low-Low" areas, these depict CAU's which have low values of Maori population (lower than mean) but still significantly effect the global correlation pattern. The light blue ("Low-High") and light red ("High-Low") areas depict CAU's with both low and high numbers of Maori (respectively) but represent areas with no spatial correlation but still influence the global correlation pattern. These four options, "High-High", "Low-Low", "Low-High", and "High-Low" correspond to the four quadrants in Figure 5. The white CAU's are not significant and do not significantly effect the global spatial autocorrelation.
Figure 6. Choropleth map of the Auckland "City" region indicating the global correlation pattern of the of the Maori population within Auckland, New Zealand.
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