## 3 Research Model Design
### Measurement of China's Agricultural Green Development Level
#### 3.2.2 Spatial Measurement Model  
(1) Spatial panel measurement model setting  
Spatial panel measurement models are classified into different categories due to the similarities and differences between the lag and error terms, and they mainly include three types: spatial lag model (SLM), spatial error model (SEM) and spatial Dubin model (SDM). The expressions of the three spatial panel measurement models constructed in this paper are as follows:  
Spatial lag model (SLM):  
\[Y=\rho wY+\beta X+\varepsilon,\varepsilon\sim N(0,\sigma^{2}I_{n}) \tag{9}\]  
Spatial error model (SEM):  
\[Y=\beta X+\mu,\mu=\lambda w\mu+\varepsilon,\varepsilon\sim N(0,\sigma^{2}I_{n}) \tag{10}\]Spatial Dubin model (SDM):  
\[Y=\rho wY+\beta X+\varsigma wX+\varepsilon,\varepsilon\sim N(0,\sigma^{2}I_{n}) \tag{11}\]  
Spatial effect decomposition (partial differential equation):  
\[Y=\left(1-\rho w\right)^{-1}ni_{n}+\left(1-\rho w\right)^{-1}(\beta X+\varsigma wX )+\left(1-\rho w\right)^{-1}\varepsilon \tag{12}\]  
\[\left(\frac{\partial Y}{\partial X_{1k}}\frac{\partial Y}{\partial X_{2k}} \cdots\frac{\partial Y}{\partial X_{nk}}\right)=\left( \begin{array}{cccc} \frac{\partial Y_{1}}{\partial X_{1k}}&\frac{\partial Y_{1}}{\partial X_{2k}}& \cdots&\frac{\partial Y_{1}}{\partial X_{2k}}\\ \frac{\partial Y_{2}}{\partial X_{1k}}&\frac{\partial Y_{2}}{\partial X_{2k}}& \cdots&\frac{\partial Y_{2}}{\partial X_{nk}}\\ \vdots&\vdots&\ddots&\vdots\\ \frac{\partial Y_{n}}{\partial X_{1k}}&\frac{\partial Y_{n}}{\partial X_{2k}}& \cdots&\frac{\partial Y_{n}}{\partial X_{nk}}\\ \end{array} \right)=\left(1-\rho w\right)^{-1}\left( \begin{array}{cccc} \beta_{k}&w_{12}\varsigma_{k}&\cdots&w_{1n}\varsigma_{k}\\ w_{21}\varsigma_{k}&\beta_{k}&\cdots&w_{2n}\varsigma_{k}\\ \vdots&\vdots&\ddots&\vdots\\ w_{n1}\varsigma_{k}&w_{n2}\varsigma_{k}&\cdots&\beta_{k}\\ \end{array} \right) \tag{13}\]  
In the formulas, \(Y\) is the explained variable (agricultural green development level), \(X_{ik}\) is the \(K\)th explanatory variable, \(w\) is the spatial weight matrix, \(\rho\) is the spatial autoregression coefficient of the explained variable, \(\lambda\) is the spatial regression coefficient of the error term, \(\varsigma_{1-6}\) is the spatial regression coefficient of the error term, \(\beta_{1-6}\) is the spatial regression coefficient of the explanatory variable, \(\alpha\) is the constant term, and \(\varepsilon\) is the random error term. In partial differential equations, the mean value of each element on the diagonal of the matrix on the right side of the equation represents the direct effect of the \(k\)th explanatory variable \(X_{ik}\), while the mean value \(\frac{1}{n^{2}}\sum\limits_{i=1}^{n}\sum\limits_{j=1}^{n}w_{ij}\varsigma_{k}\) of other elements not on the diagonal is an indirect effect. In addition, when \(\varsigma=0,\rho\
eq 0\), the SDM model will degenerate into SLM; when \(\varsigma+\rho\beta=0\), the SDM model will degenerate into SEM. (2) Construction of spatial weight matrix  
The spatial weight matrix can reflect the correlation degree between spatial units, and it is very important to select it appropriately for the study of the spatial spillover effect between agricultural science and technology innovation and agricultural green development. Since agricultural science and technology innovation activities will inevitably be affected by a variety of other nongeographical proximity factors, and since there is a spatial correlation between the economic development levels of various provinces, science and technology innovation activities in underdeveloped provinces have little impact on developed provinces, while scientific and technological innovation activities of developed provinces have a great impact on the space of neighboring provinces. Therefore, this article adopts the spatial economic matrix (hereinafter referred to as the \"economic matrix\") for quantification. The setting formula is:  
\[W_{ij}=\left\{