Abstract
This paper focuses on the spatial autocorrelation parameter ρ of the simultaneous autoregressive model, and furnishes its sampling distribution for nonzero values, for two regular square (rook and queen) tessellations as well as a hexagonal case with rook connectivity, using Monte Carlo simulation experiments with a large sample size. The regular square lattice directly relates to increasingly used, remotely sensed images, whereas the regular hexagonal configuration is frequently used in sampling and aggregation situations. Results suggest an asymptotic normal distribution for estimated ρ. More specifically, this paper posits functions between ρ and its variance for three adjacency structures, which makes hypothesis testing implementable and furnishes an easily-computed version of the asymptotic variance for ρ at zero for each configuration. In addition, it also presents three examples, where the first employed a simulated dataset for a zero spatial autocorrelation case, and the other two used two empirical datasets—of these, one is a census block dataset for Wuhan (with a Moran coefficient of 0.53, allowing a null hypothesis of, e.g., ρ=0.7) to illustrate a moderate spatial autocorrelation case, and the other is a remotely sensed image of the Yellow Mountain region, China (with a Moran coefficient of 0.91, allowing a null hypothesis of, e.g., ρ=0.95) to illustrate a high spatial autocorrelation case.
Highlights
Spatial autocorrelation (SA) is a common phenomenon of spatial data analyses, where there is a common naive hypothesis that Spatial Autocorrelation (SA) is zero (e.g., [1,2,3]) for datasets involving, for example, georeferenced demographic, social economic, and remotely sensed image variables
There are two indexes appearing in this table to indicate the level of SA: the MC, and the SAR model estimated ρ (i.e., ρ), both of which represent the same level of SA, but with different values; the MC is directly calculated with the observations, and ρis the ML estimate for the pure SAR model in which the neighborhood was defined by rook adjacency
The main contribution of this paper is furnishing the sampling distribution of the nonzero SA parameter of the SAR model, which is frequently employed in a wide range of disciplines whose study observations are connected with geographical attributes or locations
Summary
Spatial autocorrelation (SA) is a common phenomenon of spatial data analyses, where there is a common naive hypothesis that SA is zero (e.g., [1,2,3]) for datasets involving, for example, georeferenced demographic, social economic, and remotely sensed image variables. A main problem hindering the positing of a nonzero SA hypothesis, or varying degrees of SA, is the unknown sampling distribution of the SA parameter, which may be denoted by ρ of the simultaneous autoregressive
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