# Mobile Internet Technology Adoption for Sustainable Agriculture: Evidence from Wheat Farmers
## 4 Material and Methods  
### Model Specification  
The dependent variables can be divided into two different sections. The first section is the MDs adoption (selection stage), which is the binary result of deciding whether the farmer adopts MDs that support the internet (\(y_{1}=1\); otherwise, \(y_{1}=0\)); the second section (outcome stage) is the binary result, which determines whether the farmer adopt MIT (\(y_{2}=1\); otherwise \(y_{2}=0\)). The probit method is a common econometric model which contains dependent variables and obtains binary results through maximum probability assessment [74]. By estimation, the two probit models for MDs adoption and MIT disregard the apparent association between the two. The bivariate probit method considers this association, which expands the probit technique [75]. However, the bivariate probit approach does not fully consider the predictable association between MDs adoption and MIT. More specifically, the MDs' adoption ultimately determines the probability of adoption of the MIT. Therefore, the selection stage result can only be observed if the farmers adopt the MDs. Hence, selection of sample bias may appear if the second result observation is not a random sample from the population [76]. The econometric model used to solve this issue is the bivariate probit method for sample selection. This model is based on the well-known Heckman selection model [77]. [PERSON] et al. [78,79] utilized the bivariate probit method with sample selection to examine smartphone use and mobile broadband adoption in Sweden. The following three types of outcomes were observed in this study [80]:  
(i) Wheat farmers do not adopt MDs (\(y_{1}=0\));  
(ii) Wheat farmers adopts MDs but do not use MIT (\(y_{1}=1\); \(y_{2}=0\));  
(iii) Wheat farmers adopts MDs and use MIT (\(y_{1}=1\); \(y_{2}=1\)). Therefore, the following probabilities apply to all three categories of potential findings in the sample:  
\[Y_{1}=0,\,\Pr\left(Y_{1}=0\right)=\Phi\left(-X_{1}\beta_{1}\right) \tag{1}\]  
\[Y_{1}=1,\,Y_{2}=0,\,\Pr\left(y_{1}=1,\,y_{2}=0\right)=\Phi\left(x_{1}\beta_{1 }\right)-\Phi_{2}\left(x_{1}\beta_{1},\,x_{2}\beta_{2},\,\rho\right) \tag{2}\]  
\[Y_{1}=1,\,Y_{2}=1,\,\Pr\left(y_{1}=1,\,y_{2}=1\right)=\Phi_{2}\left(x_{1}\beta _{1},\,x_{2}\beta_{2},\,\rho\right) \tag{3}\]  
The following log-likelihood function can be created by taking these probabilities into account:  
\[\text{InL}=\sum_{i=1}^{N}Y_{i1}Y_{i2}\text{In}\Phi_{2}(X_{1}\beta_{1},X_{2} \beta_{2},\rho)+\ Y_{i1}(1-Y_{i2})\ \text{In}[\Phi(X_{1}\beta_{1})-\Phi_{2}(X_{1}\beta_{1},X_{2}\beta_{2},\rho)] +(1-Y_{i1})\ \text{In}\Phi(-X_{1}\beta_{1}) \tag{4}\]  
where \(\Pr\) represents the probability that the farmer makes a binary decision, \(Y\) denotes the dependent variable of the selection and outcome equation, \(X\) denotes the independent variable vector for both farms, \(\beta\) is the estimated coefficient of each independent variable, and \(\Phi\) is the unit normal distribution function. \(\rho\) represents the association between the two equation errors. Figure 2 shows the sample collection method of the proposed model. According to [PERSON] [81], the instrumental variable is usually used to estimate the Heckman model in the selection phase, and this variable is not used in the outcome phase. No additional variables are required to determine the coefficients in the model. However, since the identification is based only on the parameter assumptions of bivariate normality and there are no missing variable deviations, [PERSON] [81] emphasizes that estimation techniques with similar descriptive variables are not recommended in the two equations. Therefore, researchers have no other options other than to unblock an additional explanatory variable for the select equation or just classify it from the distribution hypothesis regarding the residuals [81].