## 2 Collected Data and Research Method
### Data Collection and Dimensionality Reduction
\begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt}} \hline
**Latent Variable** & **Manifest Variable** & **Survey Statement** \\ \hline Product Design & \(p_{d1}\) & Our company replaces toxic and/or polluting materials in product design \\ (\(P_{D}\)) & \(p_{d2}\) & Our company makes modifications to the product design in order to improve/adapt the environment \\ (\(P_{D}\)) & \(p_{d3}\) & Our company empowers employees to develop cleaner products \\ \hline  & \(p_{p1}\) & Our company cleans and organizes the production/shop floor environments \\  & \(p_{p2}\) & Our company systematically manages stocks (raw materials/inputs/final products) \\  & \(p_{p3}\) & Our company performs equipment maintenance periodically \\  & \(p_{p4}\) & Our company improves and standardizes the equipment of the production process \\  & \(p_{p5}\) & Our company standardizes work instructions in the production processes \\ Production & \(p_{p6}\) & Our company separates waste and waste from production processes \\ Processes & \(p_{p7}\) & Our company has mechanisms for collecting all types of tailings (including spills and burrs) \\ (\(P_{p}\)) & \(p_{f8}\) & Our company empowers employees to carry out cleaner production processes \\  & \(p_{f9}\) & Our company replaces toxic and/or polluting materials in production processes \\  & \(p_{p10}\) & Our company controls the production processes \\  & \(p_{p11}\) & Our company makes changes in the production processes \\  & \(p_{p12}\) & Our company makes technological changes in production processes \\ \hline  & \(r_{1}\) & Our company reuses waste and residues from a production process as byproducts for the same production process \\  & \(r_{2}\) & Our company reuses water used in a production process as a resource for the same production process \\ Reuse (\(R\)) & \(r_{3}\) & Our company uses energy from a production process as a resource for the same production process \\ \hline \end{tabular}
\end{table} 
Table 1: Latent input variables, alongside their associated manifest variables and the corresponding survey statement. Once the manifest variables were combined and related to the latent variables, their consistency and reliability were evaluated by the three tests proposed by [35]: Cronbach's alpha (CA), Composite Reliability (CR), and Average of Variance Extracted (AVE). Regarding CA, for a certain latent variable, the value is given by [35]:  
\[\text{CA}=\frac{k}{k-1}\left(\frac{\sigma_{\text{r}}^{2}-\sum_{i=1}^{k}\sigma_{ i}^{2}}{\sigma_{\text{r}}^{2}}\right), \tag{1}\]  
where \(k\) is the number of manifest variables associated with the latent variable, \(\sigma_{\text{r}}^{2}\) is the variance of all the \(k\) manifest variables, and \(\sigma_{i}^{2}\) represents the variance of each manifest variable individually. A value of \(\text{CA}>0.5\) indicates an acceptable consistency. On the other hand, the CR of a latent variable can be calculated as [35]:  
\[\text{CR}=\frac{\left(\sum_{i=1}^{k}\lambda_{i}\right)^{2}}{\left(\sum_{i=1}^{ k}\lambda_{i}\right)^{2}+\left(\sum_{i=1}^{k}\delta_{i}\right)^{2}}, \tag{2}\]  
where \(\lambda_{i}\) and \(\delta_{i}\) are the completely standardized factor loading and the error of the i-th manifest variable, respectively. A value of CR above 0.7 suggests a significant internal consistency of the sample under study. Finally, for a latent variable, the AVE can be computed according to [35]:  
\[\text{AVE}=\frac{\sum_{i=1}^{k}\lambda_{i}^{2}}{k}. \tag{3}\]  
Values of AVE above 0.5 correspond to samples with a significant representativeness. The obtained values for the three latent variables are presented in Table 3, revealing that most of the input and output variables meet the three criteria. The exception is \(P_{Prod}\), which falls in two out of the three metrics. This indicates that \(P_{Prod}\) may present problems in the model.