## 3 Research Model Design
### Measurement of China's Agricultural Green Development Level
#### 3.2.1 Spatial Autocorrelation Test  
(1) Global spatial autocorrelation  
Global spatial autocorrelation is an index that measures the spatial correlation of research objects from a global perspective. This article uses the global Moran's index to measure the global spatial pattern of agricultural technological innovation and green agricultural development, and its value range is \([-1,1]\), with 0 as the dividing line. Whenthe value is greater than 0, this indicates that the variable has a positive spatial correlation--that is, spatial agglomeration; when the value is less than 0, it indicates that the variable has a negative spatial correlation--that is, spatial dispersion; when the value is equal to 0, it indicates that the variables are not spatially correlated and are randomly distributed.  
\[Moran^{\prime}sI=\frac{n\sum\limits_{i=1}^{n}\sum\limits_{j=1}^{n}W_{ij}(X_{i}- \overline{X})(X_{j}-\overline{X})}{\sum\limits_{i=1}^{n}\left(X_{i}-\overline{ X}\right)\sum\limits_{i=1}^{n}\sum\limits_{j=1}^{n}Wij}=\frac{\sum\limits_{i=1}^{n} \sum\limits_{j=1}^{n}W_{ij}(X_{i}-\overline{X})(X_{j}-\overline{X})}{S^{2}\sum \limits_{i=1}^{n}\sum\limits_{j=1}^{n}Wij} \tag{7}\]  
Here, \(S^{2}=\frac{\sum\limits_{i=1}^{n}\left(X_{i}-\overline{X}\right)^{2}}{n}\) is the variance of the observation unit, \(n\) is the number of observation units, \(W_{ij}\) is the spatial weight matrix, and \(X_{i}\) and \(X_{j}\) are the values of variable \(X\) on spatial units \(i\) and \(j\).  
(2) Local spatial autocorrelation  
Local spatial autocorrelation is an index to measure the spatial correlation of research objects from a local perspective. In this paper, [PERSON]'s index is used to identify the local spatial pattern characteristics of agricultural science and technology innovation and agricultural green development, which can be divided into four types of agglomeration. The first type is high-value agglomeration (HH), which indicates that the innovation level of agricultural science and technology in the province is high, and that of the neighboring provinces is also high, presenting a high-level mean spatial correlation agglomeration state of \"high in the center, high in the surrounding areas\". The second type is low-value collapse (LH), which indicates that the innovation level of agricultural science and technology in the province is low, but the innovation level of agricultural science and technology in the neighboring provinces is high, presenting a spatial disequilibrium correlation agglomeration state of \"low in the center, high in the surrounding areas\". The third type is low-value agglomeration (LL), which indicates that the innovation level of agricultural science and technology in this province is low, and that of its neighboring provinces is also low, presenting a low-level mean spatial correlation agglomeration state of \"low in the center, low in the surrounding areas\". The fourth type is high-value bulge (HL), which indicates that the agricultural science and technology innovation level of the province is high, but that of the neighboring provinces is low, presenting a spatial disequilibrium correlation agglomeration state of \"high in the center, low in the surrounding areas\". The specific calculation formula of the local Moran's index is as follows:  
\[Moran^{\prime}sI_{i}=\frac{n(X_{i}-\overline{X})\sum\limits_{j=1}^{n}W_{ij}(X_ {j}-\overline{X})}{\sum\limits_{i=1}^{n}\left(X_{i}-\overline{X}\right)^{2}}= \frac{(X_{i}-\overline{X})\sum\limits_{j=1}^{n}W_{ij}(X_{j}-\overline{X})}{S^{ 2}} \tag{8}\]