Data
Basic information of the survey
The data we used in this paper were obtained from a household survey conducted by the research team in Minqin, China. The basic information about the research area is as follows:
Minqin is located in northwest China, with low hills, plains and deserts in the region. It has a temperate continental arid climate with a very fragile ecological environment. Precipitation is low and unevenly distributed, evaporation is high, the climate is dry, and drought disasters occur frequently. The special natural environment causes farmers in the region to suffer from drought; therefore, the government attaches great importance to water conservancy construction work in Minqin. Currently, three groundwater drip irrigation demonstration areas, two agricultural precision irrigation demonstration areas, two solar greenhouse drip irrigation demonstration areas and one comprehensive watersaving irrigation demonstration garden have been built in the region, with a demonstration area of 15,700 mu. The region is mainly dominated by droughttolerant crops such as corn and cotton, with corn sowing area accounting for 34% of the cultivated land area. The cultivation ratio of fruits and vegetables is low, accounting for 14% of the main arable land area, among which honeydew melon accounts for more than 84%. Minqin honeydew melon is famous nationwide.
The survey used a stratified sampling method, selecting samples in three layers: county, township/town, and village. Approximately 10% of households were randomly selected in each village for the questionnaire survey, with a total of 500 households from 20 villages being sampled. The survey returned 500 completed samples, achieving a 100% response rate. After excluding incomplete or inconsistent questionnaires, 443 valid responses were obtained, resulting in a validity rate of 88.60%. The data used in this article is derived from these 443 valid samples.
The sample size formula is typically used to determine the reasonableness of the sample size. This formula provides a sample estimate that does not take population size into account, making it particularly suitable for large populations, as sample size is less affected by population size when the population is very large.
The sample size formula is as follows:\(\:\:N\left(Sample\:Size\right)=\fracZ^2\times\:P\times\:(1P)e^2\)
In this formula, \(\:N\left(Sample\:Size\right)\) represents the required sample size for the survey, \(\:Z\) is the Zscore corresponding to the confidence level, \(\:P\) is the expected effect size, and \(\:e\) is the confidence interval.
Based on the formula, when the confidence level is 95%, the expected effect size is 0.5, and the acceptable margin of error is 5, the required sample size is approximately 384.16. In this study, the sample size is 443, which is greater than 384.16, indicating that the sample size is reasonable.
The selection of the sample should follow the principles of representativeness, randomness, and validity. Representativeness means that the sample can represent the overall characteristics of the research object. The research object is farmers in Minqin, and the sample includes farmers of different ages, genders, education levels, and years of farming experience (see Table 1), ensuring the representativeness of the sample. Randomness means that the sample selection must be random. The survey was conducted using a random sampling method, ensuring the fairness and objectivity of the sample. Validity means that the quality of the sample should be guaranteed. In this survey, indepth oneonone interviews with farmers were conducted, and all questionnaires were personally filled out by the research team members, ensuring the authenticity and accuracy of the data collection.
The basic information of the sample is shown in Table 1:
Descriptive statistics
Table 2 reports the descriptive statistics of some important characteristics between adopters and nonadopters. According to the survey data, 131 farmers did not adopt WSIT, accounting for 29.57% of the survey sample. The main reasons why farmers are not willing to adopt WSIT include the following: 46.12% of farmers think that the land area is small and the plots are scattered, so it is difficult to bring scale benefits to farmers with highcost WSIT equipment inputs; 21.97% of farmers believe that there are problems after the installation and use of WSIT equipment, and no one follows up and repairs the equipment; and 77.65% of farmers think that there are no demonstration households around for technical guidance.
A total of 312 households adopted WSIT, accounting for 70.43% of the total interviewed farmers. Among them, 92.52% of the farmers adopted WSIT mainly due to promotion by agricultural extension staff or the demonstration role of government model villages. When making the adoption decision, 79.05% of farmers thought that the investment in WSIT facilities should be borne by the government, and they were more willing to invest in labor. A total of 80.67% of the farmers noted that they valued the economic benefits of the use of the technology. Government subsidies were also an important factor in farmers’ adoption decisions. A total of 52.9% of farmers said they received government subsidies for equipment after adoption, and 47.68% said they also received technical subsidies. For the postadoption maintenance of WSIT, 37.01% of farmers stated that the Irrigation District Administration was responsible for maintenance, 49.13% of farmers stated that individuals were responsible for followup equipment maintenance, and a small number of farmers stated that no one was responsible for maintenance of the equipment.
Variables
Social interaction
Social interaction has a rich connotation, and using a single indicator to measure farmers’ social interaction may lead to biased results^{27}. Therefore, this paper draws on the definition of social interaction from socioeconomics and classifies it into four dimensions based on the types and social functions of interaction^{19,20}: depth of social interaction (depth of SI), frequency of social interaction (frequency of SI), direction of social interaction (direction of SI) and breadth of social interaction (breadth of SI), forming an indicator system for social interaction.
Depth of SI reflects the degree of social interaction and determines the degree of interdependence between the interacting parties. Specifically, farmers’ technology adoption behavior can be expressed by whether they join agricultural cooperatives, and information acquisition and screening can be characterized by judging the number of WSIT adopters, such as whether many of their neighbors and friends and relatives adopt WSIT.
Frequency of SI refers to the number of social interactions that occur between individuals within a certain period of time. The frequency of SI is often related to good interpersonal relationships. For example, how can we tell which people in a class are good friends? It is those students who interact frequently, have many interactions, and are together often. The adoption of WSIT for farmers can be expressed in terms of the frequency of contact with friends and relatives, which can usually be expressed in terms of the frequency of spending time with friends and relatives, the frequency of visiting neighbors, and whether there are many people who try to help them solve problems when they encounter difficulties.
The direction of SI is the direction of social interaction, reflecting the good or bad relationship between the two sides of the interaction, including emotional relationships (Is it affectionate or repulsive? Is it harmonious or antagonistic? ), interest relationship (Is it aligned or conflicting, and to what extent? ), and status relations (Are they equal or unequal? What is the pattern of power distribution? )^{43}. Specifically, in terms of farmers’ WSIT adoption behavior, the emotional relationship can be characterized by whether the relationship between villagers is cordial, the interest relationship can be characterized by the number of water use disputes, and the operation of rules and regulations can measure whether status is equal and whether power is properly distributed.
Breadth of SI refers to the scope and field of social interaction. In terms of the scope of interaction, the more comprehensive the scope involved, the more extensive the interaction. For the field of interaction, the clearer the behavioral norms in the field, the more extensive the interaction. Specifically, the scope of interaction for farmers’ WSIT adoption behavior can be characterized by the breadth of external contacts and the number of sources of information, and the field of interaction can be measured by the amount of expenditure on human gifts.
The specific index definitions and descriptions are shown in Table 3:
Scholars adopt the idea of dimensionality reduction to measure multidimensional indicators. In this paper, the entropy value method is used to measure the four dimensions of social interaction and the comprehensive indicators of social interaction. The measurement results are as follows:
$$\:\left\{\beginarraycf_1=0.9356*v_1+0.0644*v_2\\\:f_2=0.7208*v_3+0.2147*v_4+0.0645*v_5\\\:f_3=0.2401*v_6+0.4509*v_7+0.3090*v_8\\\:f_4=0.1495*v_9+0.8505*v_10\\\:SI=0.6615*f_1+0.1746*f_2+0.0479*f_3+0.1160*f_4\endarray\right.$$
(1)
In Eq. (1), \(\:v_1\)…\(\:v_10\) are the variables of social interaction, \(\:f_1\)…\(\:f_4\) represent the depth of SI, the frequency of SI, the direction of SI and the breadth of SI, respectively, and SI is the value of the comprehensive index of the social interaction of farmers.
Control variables
The influence of farmers’ individual factors^{44,45}, household factors^{46,47}, and policies^{48,49} on farmers’ WSIT adoption decisions has been generally recognized by many scholars. Therefore, in this paper, the factors of gender^{50}, age^{51}, farming experience^{52}, risk preference^{53}, dry crop acreage^{54}, water expenditure^{55}, and water price^{56} were selected as control variables for inclusion in the model.
In addition, other control variables are selected in this paper, including personal influence. Leaders can guide and drive their subordinates to accomplish their target tasks through their own influence^{57}. When promoting technology, as village cadres with strong personal influence in the village, they can establish a demonstration effect by being the first to adopt a new technology, thereby motivating other farmers to adopt it. Based on this, this paper characterizes personal influence by the position held in the village and includes it as a control variable in the model.
Cognitive attitude is another key factor that influences farmers’ WSIT adoption decisions. Farmers’ WSIT cognition is an important prerequisite for the emergence of farmers’ propensity to adopt WSIT and has a significant impact on WSIT adoption^{58}. Weak cognition can hinder the adoption of WSIT^{1}. WSIT can promote technological progress in food production, increase total factor productivity, improve food production conditions, and increase farmers’ farming returns^{59}, so the clearer the perception of the importance of WSIT is, the more farmers tend to adopt it. The more knowledge farmers have about the income increase and adoption effect produced by the new technology, the more actively they will adopt the new technology^{10}. Therefore, the cognitive attitudes of farmers (Cognition of WSIT, Cognition of WSIT adoption importance, Cognition of WSIT adoption effect) are included in the control variable system. The specific descriptive statistics of the variables in this paper are shown in Table 4.
3.3 Empirical model
To test Hypothesis 1, the following technology adoption decisionmaking model for farmers was constructed:
$$TA_i=I(\alpha+\sum\nolimits_j=1^k\beta_ijX_ij+\gamma_m1\mathrmSI+\varepsilon_i)\varepsilon_i\simN(0,1)i=1,2,3\cdots\ N$$
(2)
In the above equation, \(\:TA_i\:\)denotes the adoption decision of the ith farmer, which is 1 if adopted and 0 otherwise. \(\:X_i\) denotes the control factors affecting the adoption of farmer i, and SI is the social interaction index of farmers determined by the entropy method. \(\:\upalpha\:\) is the constant term, \(\:\beta\:_i\) and \(\:\gamma\:_m1\) are the regression coefficients, and \(\varepsilon_i\) denotes the random error term. \(\:\textI\) is the indicative function, which means that \(\:TA_i\) takes the value of 1 when the latter condition is satisfied; otherwise, it is 0.
On the basis of the above equation, the indicators of the four dimensions of social interaction were incorporated into the model. The farmers’ technology decisionmaking model is shown below:
$$TA_i=I(\alpha+\sum\nolimits_j=1^k\beta_ijX_ij+\gamma_t1f_1+\gamma_t2f_2+\gamma_t3f_3+\gamma_t4f_4+\varepsilon_i)\varepsilon_i\simN\left(0,1\right)i=1,2,3\cdots\ N$$
(3)
In the above equation, \(\:f_1\), \(\:f_2\), \(\:f_3\), and \(\:f_4\) represent the depth of SI, frequency of SI, direction of SI and breadth of SI, respectively, and \(\:\gamma\:_t1\), \(\:\gamma\:_t2\), \(\:\gamma\:_t3\), and \(\:\gamma\:_t4\) are the regression coefficients of the corresponding dimensions.
For the testing of the three interaction mechanisms proposed in Hypotheses 2 to 4, indicator variables representing the three interaction mechanisms were designed and incorporated into the model. The three interaction mechanisms in farmers’ WSIT adoption behavior were verified by observing the changes in their coefficients.
Since the differences in farmers’ subjective evaluations are the key factors that influence the effect of social interaction, the subjective evaluations of farmers on different aspects are taken as the core characterizing variables of the interaction mechanism. The test model of the interaction mechanism is constructed by adding interaction terms.

A.
Endogenous interaction mechanism test:
$$TA_i=I(\alpha\sum_j=1^k\beta_ijX_ij+\gamma_m1SI+\gamma_n1Participation+\gamma_k1SI*Participation+\varepsilon_i)\varepsilon_i\simN\left(0,1\right)i=1,2,3\cdots\ N$$
(4)

B.
Situational interaction mechanism test:
$$TA_i=I(\alpha\sum\nolimits_j=1^k\beta_ijX_ij+\gamma_m2SI+\gamma_n2Earning+\gamma_k2SI*Earning+\varepsilon_i)\,\varepsilon_i\simN0,1)\;i=1,2,3\cdots\ N$$
(5)

C.
Social norm mechanism test:
$$TA_i=I(\alpha+\sum\nolimits_j=1^k\beta_ijX_ij+\gamma_m3SI+\gamma_n3Incomegap+\gamma_k3SI*Incomegap+\varepsilon_i)\varepsilon_i\simN\left(0,1\right)i=1,2,3\cdots\ N$$
(6)
In the above three equations, participation is the core variable for the endogenous interaction mechanism (“I will adopt if others adopt”), which indicates farmers’ evaluation of the adoption of WSIT by others in their area/village, with 1 if the number is large and 0 otherwise. Earnings is the core variable of the situational interaction mechanism (“I will adopt if others have high adoption benefits”), which indicates farmers’ evaluation of the benefits of adopting WSIT for others in their area/village, with 1 if the benefits are high and 0 otherwise. Income gap is the core variable for the social norm mechanism (the greater the intragroup variation, the more likely it is that group identity can be achieved by referring to group adoption decisions) and represents farmers’ evaluation of income differences in their area/village, with 1 for large income differences and 0 otherwise.
$$\frac\partial\:TA\partial\:SI=\gamma_m+\gamma_k*Participation/Earning/Incomegap$$
(7)
The above equation implies that \(Participation/Earning/Incomegap\) influences the bias effect of SI. The interaction mechanisms of social interaction on farmers’ WSIT adoption are verified.
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