# The Role of Advanced Manufacturing Technologies in Production Process Performance: A Causal Model
## 3 Materials and Methods
### Structural Equation Model  
If latent variables qualified for the validation process, they were integrated into the model. In order to evaluate the model in Figure 1, structural equation model (SEM) technique was selected, which was used to explore and test the relationship between variables [66] that include regression analysis, factor analysis, multiple correlations, and route analysis of route. In addition, SEM was chosen since it allowed the analysis of second-order variables, which are latent variables where indicators are other latent variables, in other words, SEM allows the measurement of not only the direct effect, but also the indirect and total effects [67], such as the proposed model in Figure 1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Indexes** & **Measurement** & **Suggested Value** \\ \hline R\({}^{2}\) & Predictive parametric validation & \(\geq\)0.20 \\ Adjusted R\({}^{2}\) & \(\geq\)0.20 \\ Composite Reliability & Internal consistency & \(\geq\)0.70 \\ Cronbach’s Alpha & Internal consistency & \(\geq\)0.70 \\ Average Variance Extracted & Discriminant validity & \(\geq\)0.50 \\ Full Collin. VIIF & Collinearity & \(\leq\)3.30 \\ Q\({}^{2}\) & Predictive non-parametric validity & \(>\)0.00 and similar to R\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Questionnaire validation indexes.  
According to [PERSON], et al. [68], the partial least squares can be estimated according to Equations (1) and (2) from a matrix point of view:  
\[X=TP^{T}+E \tag{1}\]  
\[Y=UQ^{T}+F \tag{2}\]  
where  
\(X\) is an \(nxm\) matrix of predictors or independent variables,  
\(Y\) is a matrix of responses or dependent variables,  
\(T\) and \(U\) are matrices that are, respectively, projections of \(X\) (the \(X\) score, component or factor matrix), and projections of \(Y\) (the \(Y\) scores),  
\(P\) and \(Q\) are, respectively, \(mxl\) and \(pxl\) orthogonal loading matrices,  
\(E\) and \(F\) matrices are the error after calculus.  
The main idea in PLS is to generate a regression equation for the dependent latent variable \(Y\) as a function of the standardized variable \(X\), generating an equation as follows:  
\[Y=\beta X \tag{3}\]  
Observe that in Equation (3), the term \(\beta_{0}\) is absent and that is because the PLS technique uses standardized values. However, it is possible that a dependent variable is explained by \(n\) independent variables and then Equation (3) is converted into Equation (4).  
\[Y=\beta_{1}X_{1}+\beta_{2}X_{2}+\cdots\beta_{n}X_{n} \tag{4}\]  
In this paper, the model was evaluated by the software WarpPLS 6(ScriptWarp Systems, Laredo, TX, USA) that is based on partial least squares (PLS), which is recommended in cases where there is no normality or the values are expressed in ordinal scales [69], which has been used in multiple works, for instance, in [PERSON], et al. [70] where an SEM was presented to examine the use of social networking sites by members of an organization, as well as its effect on job satisfaction, organizational commitment, and job performance. Before interpreting the model, the following efficiency indexes were analyzed:  
1. Average path coefficient (APC) acceptable if \(p<0.05\)
2. Average R-squared (ARS) acceptable if \(p<0.05\)
3. Average adjusted R-squared (AARS) acceptable if \(p<0.05\)
4. Average block VIF (AVIF) acceptable if \(\leq\)5, ideally \(\leq\)3.3
5. Average full collinearity VIF (AFVIF) acceptable if \(\leq\)5, ideally \(\leq\)3.3
6. Tenenhaus Goodness of Fit (GoF) small \(\geq 0.1\), medium \(\geq 0.25\), large \(\geq 0.36\)