Table 1.
A comparison of form and structure between Moran’s index, I, and Getis-Ord’s index, G.
Fig 1.
A flow chart of data processing, parameter estimation, and autocorrelation analysis based on Getis-Ord’s indexes.
The analytical process is similar to that based on Moran’s index and Geary’s coefficient. However, the measurements and conclusions are different.
Table 2.
Comparison of the advantages and disadvantages of different approaches to global and local Getis-Ord’s indexes.
Table 3.
The main computational results of spatial autocorrelation and spatial interaction based on Getis-Ord’s indexes (2000 & 2010).
Fig 2.
The scatterplots of spatial auto-correlation based on Getis-Ord’s measurement for the main cities of China ((A) 2000 & (B) 2010). The trend line is added to the trend points based on the outer product correlation, yyTWy, and we have perfect fit, R2 = 1. This implies that the connection line of the scattered points yielded by the linear relation between y and yyTWy is just the trend line.
Table 4.
The computational results of spatial autocorrelation for Getis-Ord’s scattered plots (2000 & 2010).
Fig 3.
The alternative forms of the scatterplots of spatial auto-correlation based on Getis-Ord’s measurement for the main cities of China ((A) 2010 & (B) 2010). This scatter plot is equivalent to the ones display in Fig 4, but the variable y used as a horizontal axis is replaced by the new variable f* = yyTWy. In this case, the original trend line is replaced by a diagonal line.
Fig 4.
The normal parameter values and abnormal goodness of fit in the scatterplots of spatial auto-correlation based on Getis-Ord’s indexes for the main cities of China ((A) 2000 & (B) 2010). The trend line is added to the scattered points based on inner product correlation, λWy, and the intercept is set as 0. The slope of the trend line give the global Getis-Ord’s index, and the value of goodness of fit, R2, is defined by cosine instead of Pearson correlation. The horizontal line represent absolute average line.
Table 5.
Chinese city classification based on conditional mean (trend line) and absolute mean (average line) (2000 & 2010).
Fig 5.
The potential energy indexes and local Getis-Ord’s indexes of the main cities in Mainland China (2000 & 2010).
Fig 6.
The mutual energy indexes based on census population of the main cities in Mainland China (2000 & 2010).