## 3 Results
### Validation of the Ordinal Instrument
This evaluation was carried out by implementing the function _mahalanobis_ in \(R\), setting a cut-off threshold at 45.3147, which was determined based on the distribution \(\chi^{2}\). For this, 99.9% of the distribution was considered to accept distances, thus excluding 0.1% of the most distant observations considered atypical. This process identified ten outlier observations, which were eliminated from the database, resulting in a final database composed of 214 multivariate observations. Using the refined database, we verified its parametric assumptions, a critical element given that the chosen instrument validation technique was Confirmatory Factor Analysis (CFA). This method requires adherence to additivity, normality, linearity, homogeneity, and homoscedasticity assumptions. In this context, the first assumption tested was additivity, for which the multivariate correlation matrix applied to each pair of possible ordinal variables was used. The resulting correlation matrix for the sample in question is shown in Figure 3.  
As shown in Figure 3, the bivariate correlation obtained for each pair of items showed adequate correlation values, with no combination of items having correlation values equal to one. This allowed us to confirm that the additivity assumption was met. A false regression analysis was chosen to test the normality, linearity, homogeneity, and homoscedasticity assumptions. This multivariate technique uses a set of theoretical random quantiles derived from the distribution \(\chi^{2}\) to compare with the parameters and quantiles observed in the sample. The results derived from the false regression analysis were evaluated using a histogram, a QQ Plot quantile plot, and a scatterplot, as shown in Figure 4 [28]. Figure 3: Multivariate correlation matrix for all pairs of variables in the instrument. As can be seen in Figure 4a, where the histogram of the standardized quantiles from the regression model was plotted, a uniform distribution was observed, showing a remarkable similarity to the normal distribution. This finding allowed us to validate the assumption of normality. In Figure 4b, the QQ plot plotted the quantiles of the sample against the theoretical quantiles, showing an alignment close to an ideal straight line of 45 degrees, which led to the acceptance of the assumption of linearity. In addition, the scatterplot shown in Figure 4c plots the standardized residuals of the sample against the residuals fitted by the spurious regression model. This graphical representation showed an even distribution of quantiles in all quadrants, with distances from the horizontal axis remaining constant in the range of \(-2\) to \(2\), with no remarkable patterns or groupings. Therefore, the assumptions of homogeneity and homoscedasticity were validated. After confirming the assumptions in the sample, we proceeded with the application of Confirmatory Factor Analysis (CFA), configuring its factor structure through the library _lavaan_ and the statistical programming language \(R\). The results obtained from the CFA are presented in Figure 5 and Table 3.  
Figure 4: Results of the fake regression analysis: (**a**) Histogram; (**b**) QQ Plot; (**c**) ScatterPlot. As seen in Figure 5 and Table 3, the factor loadings of each item in its corresponding factor exceeded the threshold of 0.5, and the correlation between factors did not show a perfect correlation, which led to the conclusion that the factor structure did not present signs of disability. When examining the goodness of fit indices of the model, it was found that the CFI (Comparative Fit Index), TLI (Tucker-Lewis Index), and NNFI (Non-Normed Fit Index) indices exhibited values above 0.9, which, of course, according to [29], classifies the model as excellent. Likewise, when evaluating the SRMR (Standardized Root Mean Square Residual) and RMSEA (Root Mean Square Error of Approximation) indices, values of 0.0317 and 0.0451, respectively, were obtained, which demonstrates the validity and reliability of the designed instrument.