## 3 Results  
### Data Analysis and Dimensionality Reduction  
In order to analyze the effect of the dimensionality reduction discussed in Section 2.1, in Figure 3, we show the histograms of the input manifest and latent variables. In particular, Figure 3a represents the histograms of the manifest variables associated with the latent variable of Product Design, whose histogram is shown in Figure 3b; Figure 3c,d correspond  
Figure 2: Block diagram showing the relation between input and output latent and manifest variables.  
to the manifest and latent variables associated with Product Process; Figure 3e,f represent the Reuse-related manifest and latent variables.  
Generally speaking, we can see that each latent variable follows the same tendency as its corresponding manifest variable. For instance, the Product Design and Product Process variables are loaded toward high values, which is similar to the behavior of their respective manifest variables. The Reuse latent variables and their associated manifest variables, on the other hand, show a more flattened distribution. The reader can also perceive that the frequency at the highest scores is reduced in the latent variables, in all three cases. This effect can be explained by noting that, in the histograms of the manifest variables, shown in Figure 3a,c,e, the represented data are integers ranging from one to seven. However, after dimensionality reduction, the corresponding latent variables assume real values, so the histograms in Figure 3b,d,f were built considering seven beams, uniformly spaced, between zero and seven. This explains the apparent reduction of the frequency for high values of the latent variables. In Figure 4, we show similar histograms for the output manifest and latent variables. It should be noted that the manifest variables \(p_{p8}\) and \(e_{p5}\), both associated with environmental accidents (see Tables 1 and 2), seem to present an anomalous behavior. However, this fact can be attributed to the low number of declared accidents and the relation between this number of accidents and the fines. Once the dimensionality was reduced, both the input and output data were normalized by subtracting the average value of each variable and dividing by the standard deviation. Therefore, each variable has zero mean and unity variance.  
Figure 3: Histograms of input manifest variables and the derived latent variables. (**a**) Histogram of the manifest variables associated with Product Design, \(P_{\text{D}}\), and (**b**) histogram of the Product Design. (**c,d**) Histograms of the manifest and latent variables of Product Process, \(P_{p}\), and (**e,f**) Reuse (R).  
Before building the ANN, it is important to perform correlation analysis, in order to quantify the correlation between the different input variables and the correlation between the input and output variables. The calculated correlation matrix is graphically shown in Figure 5. As can be observed, considering the input variables, \(P_{D}\) and \(P_{P}\) present some correlation, whereas they are quite uncorrelated with \(R\). In regards to the correlation between the input and output variables, the most relevant point is the low correlation between \(E_{P}\) and all three input variables. Consequently, it is expected that \(E_{P}\) will not be related to the input variables when the ANN is implemented.  
Figure 4: Histograms of output manifest variables and the derived latent variables. (**a**) Histogram of the manifest variables associated with Product Performance, \(P_{PROD}\), and (**b**) histogram of the latent variable Environment Product Performance (**c,d**) Histograms of the manifest and latent variables of Process Performance, \(P_{PROC}\), and (**e,f**) Economic Performance (\(E_{P}\)).  
Figure 5: Correlation analysis.