## 3 Materials and Methods
### Methods
#### 3.3.3 Variable Explanation and Description  
1. Dependent variable: ADR. Based on existing research and theoretical analysis [59; 21; 54], an indicator system, including agricultural production resilience, economic resilience, and ecological resilience, was established as Table 1.  
The effective irrigation area, total power of agricultural machinery, and fixed-asset investment reflect the role of agricultural infrastructure and the production factors' quality in improving the agricultural production resilience. The pesticide and fertilizer inputs and agricultural water use reflect the efficiency of water resources use and the effects of chemical inputs on agricultural ecological environment. The total agricultural output value per farmer, total agricultural output value per cultivated land area, output value of fixed-asset per cultivated land area are to deal with agricultural finance and other risks and agricultural economic development efficiency measurement. 2. Explanatory variable: NGCL. In the threshold effect model, from the perspective of planting system, data availability, and allocation of agricultural production factors in the study area, the rate of \"non-grain\" of cropland (\(rngc_{1}\)) was taken as the explanatory variable and the \"non-agricultural crop sown area/crop sown area\" was used to characterize the NGCL level. In the spatial lag model, according to the influence of farmers' planting inertia, planting experience, and rural social network relationship, the NGCL trend was taken as the explanatory variable; the change rate of NGCL was adopted to measure it. \[rngc_{2}=\left|\frac{S_{nt}}{S_{t}}-\frac{S_{nt-1}}{S_{t-1}}\right| \tag{4}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Object Level** & **System Level** & **Weights** & **Indicators** & **Calculation Method** & **Weights** \\ \hline \hline \multirow{8}{*}{Agricultural production resilience} & \multirow{8}{*}{0.3070} & Proportion of effective irrigation area & Effective irrigation area/ cultivated land area & \multirow{2}{*}{0.1910} \\  & & & Total power of agricultural machinery per area & Total power of agricultural machinery/Sown area & \multirow{2}{*}{0.1278} \\  & & & Fixed-asset investment per agricultural labor & Fixed-asset investment/Number of agricultural labor & \multirow{2}{*}{0.6812} \\ \cline{1-1} \cline{3-5}  & & & Pure amount of chemical fertilizers applied per area & Pure amount of chemical fertilizers/Sown area & \multirow{2}{*}{0.3171} \\ \cline{1-1} \cline{3-5}  & & & Amount of pesticides applied per area & & \\ \cline{1-1} \cline{3-5}  & & & Agricultural water consumption per area & & \\ \cline{1-1} \cline{3-5}  & & & Agricultural water consumption per area & & \\ \cline{1-1} \cline{3-5}  & & & & \\ \cline{1-1} \cline{3-5}  & & & & & \\ \cline{1-1} \cline{3-5}  & & & & & \\ \cline{1-1} \cline{3-5}  & & & & & \\ \cline{1-1} \cline{3-5}  & & & Total agricultural output value per agricultural labor & \multirow{2}{*}{0.2877} \\ \cline{1-1} \cline{3-5}  & & & agricultureultural labor & & \\ \cline{1-1} \cline{3-5}  & & & Total agricultural output value  
where, \(S_{nt}\) and \(S_{nt-1}\) are the sown area of crops in year \(t\)th and year (\(t-1\))th, respectively, and \(S_{t}\) and \(S_{t-1}\) are the non-grain crops (cereals, tubers, etc.) sown area in year \(t\)th and year (\(t-1\))th, respectively. 3. Control variables: to promote the robustness of the estimation result, the industrial structure _is_, local general public budget expenditure lg_p_be_, and grain output \(gp\) were selected as control variables in the models referring to existing studies [54,60]. The industrial structure refers to the structure of regional tertiary industries, which is represented by the proportion of the added value of the primary industry to the gross regional product. All other variables except the ratio were treated with logarithms. 4. Sample overview: the 35-prefecture-level cities in the study area formed a sample of 350. The mean and standard deviation of relevant indicators for samples are shown in Table 2.