# New Models Used to Determine the Dioxins Total Amount and Toxicity (TEQ) in Atmospheric Emissions from Thermal Processes

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## Abstract

**:**

^{2}) for the models are 0.9711 ± 0.0056 and 0.9583 ± 0.0085; its root mean square errors (RMSE) are 0.2115 and 0.2424, and its mean absolute errors (MAE) are 0.1541 and 0.1733 respectively.

## 1. Introduction

## 2. Experimental

#### 2.1. Data Sources

_{OLD}matrix (130 × 17) since it was used in a previous publication [29].

_{NEW}matrix (64 × 17). From this set, a subset was defined discarding the analyses whose values of total PCDD/F amount or TEQ were outside the range of the 𝕏

_{OLD}set. This subset, comprising all new data within the range of 𝕏

_{OLD}set, was named as 𝕏

_{NEW,INT}(28 × 17).

#### 2.2. Methodology

_{NEW}has been used to evaluate the linear dependence between all congeners using the variance inflation factors (VIFs). This methodology has been explained in a previous publication [29]. It is expected that the more independent congeners are similar for both datasets, 𝕏

_{NEW}and 𝕏

_{OLD}. If so, this process is repeated considering all datasets as a unique one.

_{NEW,INT}has been used to check two linear models that determine the total PCDD/F amount and the TEQ of an atmospheric emission using only the amount of three PCDD/Fs congeners. For this purpose, a graph was constructed whose ordinates were the total amount or TEQ from the analysis and whose abscissae were the amount or TEQ determined by the model. In the best-case scenario, it was supposed to obtain a correlation with a strong linear trend, with its slope equal to one and its intercept equal to zero.

_{NEW,INT}, a new linear regression was performed using 𝕏

_{NEW}and 𝕏

_{OLD}together. The methodology used to adjust a model to data, where the total dioxins’ amount was a linear combination of the independent congeners, was Ordinary Least Squares [36].

_{j}was the amount of each congener j,

_{CTOT}was the total PCDD/F amount in the sample, T

_{TOT}was the total TEQ of the sample, b′

_{0}or b

_{0}were the intercepts of the linear adjustment, and b′

_{j}or b

_{j}were the parameters of the models related to each regressor (where k is the number linearly independent regressors).

_{NEW}and 𝕏

_{OLD}are used to adjust the models. Since the total amount of analyses will remain constant, some analyses may be used more than once in each adjustment. This process is iterated a large number of times (3000 iterations in this case) and all the parameters of each fit are collected in order to determine the confidence interval of the regression parameters. The value of the parameter of the model is equalled to the average of that parameter through all the iterations, and the standard error of that parameter is associated to its standard deviation. The confidence intervals are determined using the percentiles related to the selected statistical significance (95% in this case).

#### 2.3. Software

## 3. Results

#### 3.1. Multicollinearity and VIFs

^{2}of the 17 congeners from both datasets 𝕏

_{OLD}and 𝕏

_{NEW}. The right half side of the table, which is used for comparison purposes only, reflects the same parameters but only using 𝕏

_{OLD}[29].

_{OLD}dataset, the formation of the congeners 2,3,7,8-TCDF, OCDF and 1,2,3,6,7,8-HxCDD was determined as linearly independent since its R

^{2}value, which is related to its VIF value following VIF

_{i}= 1/(1 − R

_{i}

^{2}), is significantly below 0.90. R

^{2}value related to OCDD is 0.89 but it is not significantly below 0.90 and is to be treated as linearly independent.

_{OLD}+ 𝕏

_{NEW}dataset, it can be observed that all VIFs are lower. This may be caused by the fact that the 𝕏

_{OLD}dataset comes from industrial processes and 𝕏

_{NEW}dataset comes from laboratory scale and experimental research. Despite these lower values, it is noticeable that the seven more independent congeners are the same in both datasets, although in a different order, as shown in Table 1. This fact reflects that the correlation between the formation of all 17 congeners is similar enough in both datasets, even considering the differences that may occur between industrial processes and laboratory scale processes.

#### 3.2. Testing Previous Models Using 𝕏_{NEW,INT}

_{NEW,INT}. As explained above, this dataset comprises a number of 28 new PCDD/F analyses from laboratory experiments whose total amount and TEQ fall within the range of the 𝕏

_{OLD}set. Figure 1 shows the interrelationship between the calculated dioxins total amount and TEQ using previous models 1 and 2 and the values from dataset 𝕏

_{NEW,INT}. In these graphs, it is worth mentioning that the linear trend is still strong, even acknowledging that the slope is not close to 1 and the intercept is not close to zero. This fact suggests that a new adjustment of the model may be needed.

#### 3.3. Readjusting Previous Models Using 𝕏_{OLD} and 𝕏_{NEW}

_{OLD}and 𝕏

_{NEW}. The R

^{2}of model 1′ was 0.9705, and the Adjusted R

^{2}was 0.9702. The Adjusted R

^{2}takes into consideration the amount of regressors used in the model in order to avoid overfitting. Since both R

^{2}and Adjusted R

^{2}are almost equal, the possibility of overfitting is discarded. The parameters of the model are shown in Table 2. The same table includes the p-value assigned to each parameter when the null hypothesis (H

_{0}) supposes that the tested congener and the total PCDD/F amount are not interdependent at all (H

_{0}: Parameter b′

_{j}= 0). Since the evaluation of p-values gave extremely low quantities, all of the parameters of model 1′ can be considered as significantly different to zero. This fact and the high value of R

^{2}are enough to validate model 1′ for Equation (1).

_{OLD}and 𝕏

_{NEW}, are shown in Table 2. The value of R

^{2}for model 2′ was 0.9575, and the Adjusted R

^{2}was 0.9570. Following the same criteria as for model 1′, the possibility of overfitting is discarded since both R

^{2}and Adjusted R

^{2}are almost equal.

_{0}) supposes that the calculated total PCDD/F amount or TEQ and the results from the chemical analysis are equal (H

_{0}: slope = 1). The p-value assigned to the intercept when the null hypothesis supposes this parameter equal to zero is also included. These values confirm that model 1′ and model 2′ are highly efficient correlations since their slope is significantly equal to one and their intercept is significantly equal to zero.

#### 3.4. Validating Model 1′ and Model 2′ Using Bootstrapping

^{2}and its low standard error it can be concluded that the percent of variability expressed through model 1′ and model 2′ is very stable to changes in the used dataset.

#### 3.5. Comparison with Previous Models

_{OLD}+ 𝕏

_{NEW}), as opposed to the 130 used in our previous work (𝕏

_{OLD}), which represents an increase of almost 50% in the number of considered sources. In addition, the new dataset included data not only from industrial processes, but also from laboratory thermal decomposition experiments, broadening the scope of application of the models.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Total amounts estimated from previous model 1 (

**left**) and total toxicity estimated from previous model 2 (

**right**) using 𝕏

_{NEW,INT}dataset.

**Figure 2.**Total amount determined by model 1′ (

**left**) and total toxicity determined by model 2′ (

**right**), both calculated considering congeners 1, 10 and 14 as linearly independent.

**Table 1.**Results for VIFs of each congener calculated sequentially, discarding the most linearly dependent congener after each iteration. The left half shows the results for both datasets mixed together (𝕏

_{OLD}+ 𝕏

_{NEW}) and the right half shows the results from 𝕏

_{OLD}as a comparison [29].

𝕏_{OLD} + 𝕏_{NEW} | 𝕏_{OLD} | ||||||
---|---|---|---|---|---|---|---|

R^{2} | VIF | Congener | Number | Number | Congener | VIF | R^{2} |

0.9875 | 80.2 | 1,2,3,6,7,8-HxCDF | 5 | 5 | 1,2,3,6,7,8-HxCDF | 639.3 | 0.9984 |

0.9850 | 66.9 | 1,2,3,7,8-PeCDF | 2 | 12 | 1,2,3,7,8-PeCDD | 423.2 | 0.9976 |

0.9745 | 39.2 | 1,2,3,4,7,8-HxCDD | 13 | 16 | 1,2,3,4,6,7,8-HpCDD | 315.2 | 0.9968 |

0.9720 | 35.7 | 1,2,3,4,7,8-HxCDF | 4 | 3 | 2,3,4,7,8-PeCDF | 168.0 | 0.9940 |

0.9682 | 31.5 | 1,2,3,4,6,7,8-HpCDD | 16 | 4 | 1,2,3,4,7,8-HxCDF | 141.0 | 0.9929 |

0.9636 | 27.5 | 1,2,3,4,6,7,8-HpCDF | 8 | 15 | 1,2,3,7,8,9-HxCDD | 121.9 | 0.9918 |

0.9625 | 26.7 | 2,3,4,7,8-PeCDF | 3 | 9 | 1,2,3,4,7,8,9-HpCDF | 99.6 | 0.9900 |

0.9584 | 24.0 | 1,2,3,4,7,8,9-HpCDF | 9 | 2 | 1,2,3,7,8-PeCDF | 81.1 | 0.9877 |

0.9564 | 22.9 | 1,2,3,7,8-PeCDD | 12 | 8 | 1,2,3,4,6,7,8-HpCDF | 64.5 | 0.9845 |

0.9477 | 19.1 | 1,2,3,7,8,9-HxCDD | 15 | 13 | 1,2,3,4,7,8-HxCDD | 52.8 | 0.9811 |

0.9364 | 15.7 | 2,3,4,6,7,8-HxCDF | 6 | 6 | 2,3,4,6,7,8-HxCDF | 31.8 | 0.9686 |

0.9111 | 11.2 | OCDF | 10 | 7 | 1,2,3,7,8,9-HxCDF | 14.1 | 0.9289 |

0.8839 | 8.6 | 1,2,3,6,7,8-HxCDD | 14 | 11 | 2,3,7,8-TCDD | 10.8 | 0.9073 |

0.8039 | 5.1 | 1,2,3,7,8,9-HxCDF | 7 | 17 | OCDD | 9.3 | 0.8925 |

0.7823 | 4.6 | 2,3,7,8-TCDF | 1 | 14 | 1,2,3,6,7,8-HxCDD | 5.2 | 0.8076 |

0.7834 | 4.6 | 2,3,7,8-TCDD | 11 | 10 | OCDF | 3.4 | 0.7096 |

0.5503 | 2.2 | OCDD | 17 | 1 | 2,3,7,8-TCDF | 2.4 | 0.5857 |

**Table 2.**Parameters and statistic data for the readjusted models: model 1′ for predicting PCDD/F amounts (pg) and model 2′ for TEQ values (pg I-TEQ).

Model | Variable | Parameters | ||||
---|---|---|---|---|---|---|

b_{14} | b_{10} | b_{1} | b_{0} | |||

n = 194 | Value | 0.351 | 0.389 | 0.225 | 1.560 | |

1′ | R^{2} = 0.9705 | Std. error | 0.0258 | 0.0207 | 0.0216 | 0.0309 |

p-value for H_{0} : b_{j} = 0 | <0.0000 | <0.0000 | <0.0000 | <0.0000 | ||

n = 194 | Value | 0.349 | 0.182 | 0.378 | 0.762 | |

2′ | R^{2} = 0.9575 | Std. error | 0.0295 | 0.0237 | 0.0247 | 0.0354 |

p-value for H_{0} : b_{j} = 0 | <0.0000 | <0.0000 | <0.0000 | <0.0000 |

Model | 1′ | 2′ | ||
---|---|---|---|---|

Regression Parameters | Slope | Intercept | Slope | Intercept |

Value | 1.000 | 0.000 | 1.000 | 0.000 |

Std. Error | 0.0126 | 0.0482 | 0.0152 | 0.0448 |

p-value for H_{0} : Intercept = 0 | - | 1.0000 | - | 1.0000 |

p-value for H_{0} : Slope = 1 | 1.0000 | - | 1.0000 | - |

Model | Variable | Parameters | ||||
---|---|---|---|---|---|---|

R^{2} | b_{14} | b_{10} | b_{1} | b_{0} | ||

Average | 0.9711 | 0.354 | 0.386 | 0.225 | 1.560 | |

1′ | Std. Error | 0.0056 | 0.0387 | 0.0285 | 0.0316 | 0.0423 |

Percentile 2.5 | 0.9587 | 0.274 | 0.327 | 0.166 | 1.480 | |

Percentile 97.5 | 0.9812 | 0.429 | 0.439 | 0.290 | 1.640 | |

Average | 0.9583 | 0.350 | 0.180 | 0.379 | 0.759 | |

2′ | Std. Error | 0.0085 | 0.0364 | 0.0286 | 0.0356 | 0.0518 |

Percentile 2.5 | 0.9400 | 0.277 | 0.124 | 0.307 | 0.656 | |

Percentile 97.5 | 0.9734 | 0.421 | 0.237 | 0.447 | 0.862 |

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## Share and Cite

**MDPI and ACS Style**

Palmer, D.; Pou, J.O.; Gonzalez-Sabaté, L.; Díaz-Ferrero, J.; Conesa, J.A.; Ortuño, N.
New Models Used to Determine the Dioxins Total Amount and Toxicity (TEQ) in Atmospheric Emissions from Thermal Processes. *Energies* **2019**, *12*, 4434.
https://doi.org/10.3390/en12234434

**AMA Style**

Palmer D, Pou JO, Gonzalez-Sabaté L, Díaz-Ferrero J, Conesa JA, Ortuño N.
New Models Used to Determine the Dioxins Total Amount and Toxicity (TEQ) in Atmospheric Emissions from Thermal Processes. *Energies*. 2019; 12(23):4434.
https://doi.org/10.3390/en12234434

**Chicago/Turabian Style**

Palmer, Damià, Josep O. Pou, Lucinio Gonzalez-Sabaté, Jordi Díaz-Ferrero, Juan A. Conesa, and Nuria Ortuño.
2019. "New Models Used to Determine the Dioxins Total Amount and Toxicity (TEQ) in Atmospheric Emissions from Thermal Processes" *Energies* 12, no. 23: 4434.
https://doi.org/10.3390/en12234434