## 4 Results  
### Model Fit  
The performance of the model was estimated through the global adjustment indicator AUC. This corresponds to the area under the curve ROC (relative operating characteristic), which represents the ratio between the true positives (TPR, true positive ratio) and the false positives (FPR, false positive ratio), as the model predicts values (Figure 4). When the AUC takes a value of 1, the model has perfect prediction. When it takes a value of 0.5, it is a model without explanatory power that does not discriminate between categories. For the model, an AUC value of 0.85 is obtained, which means that it has a high level of fit.  
Another measure of the model's effectiveness is the confusion matrix, which indicates the level of correct and incorrect classifications. In Figure 5, we can observe that 75.8% of values 1 (ignition) and 77.9% of values 0 (not ignition) were correctly classified.  
Figure 4: ROC curve of the fit of the ignition model.  
One of the advantages of decision tree models is that their results show the explicative importance of the variables. This importance represents the prediction model's error increase after the variable's value has been permuted (separated in a branch of the tree). This is the normalized average of how much this variable changes the final classification result. In this model, the importance of the variables is as follows, as we can observe in Table 2.  
\begin{table}
\begin{tabular}{c c c} \hline
**Variable Importance** & **Variable Label** & **Variable Name** \\ \hline
18.9599929 & Proportion of crops in a 500 m radius & Crop\_buff \\  & buffer (proportion) & \\ \hline
15.2302175 & Average distance from the 500 m radius buffer & DistRoad\_buff \\  & to the nearest road (m) & DistCit \\ \hline
15.046572 & Distance from point to the nearest city (m) & DistCit \\ \hline
8.80795483 & Proportion of forest plantation in a 500 m & ForPlan\_buff \\  & radius buffer (proportion) & ForPlan\_buff \\ \hline
7.63480897 & Proportion of grassland in a 500 m radius & Grass\_buff \\  & buffer (proportion) & Grass\_buff \\ \hline
6.82820899 & Proportion of scrubs in a 500 m radius & Scrub\_buff \\  & buffer (proportion) & Scrub\_buff \\ \hline
6.35721698 & Point exposition (indices) & Exposition \\ \hline
5.09869124 & Population density of the point & DensPop \\  & (inhabitants/census district) & DensPop \\ \hline
4.0326676 & Point elevation (m.a.s1.) & Elev \\ \hline
4.01163185 & Point slope (grades) & Slope \\ \hline
2.78965119 & Proportion of impermeable land in a 500 m & Imper\_buff \\  & radius buffer (proportion) & \\ \hline
2.31063774 & Proportion of native forest in a 500 m radius & Nat\_buff \\  & buffer (proportion) & \\ \hline
1.84278487 & Type of land cover predominant in the & LC \\  & point (categorical) & \\ \hline
1.04896344 & Proportion of bare soil in a 500 m radius & Bare Soil\_buff \\  & buffer (proportion) & \\ \hline \end{tabular}
\end{table}
Table 2: Variables’ importance.  
Figure 5: Confusion matrix.  
In order of importance, the variables that best explain the ignition of wildland fire in the Maule region are the proportion of crops, the distance to the nearest road, and the distance to the nearest city. The second group of variables with a medium explanatory capacity integrates the proportion of forest plantations, the proportion of grassland, the proportion of scrub, exposure, and population density.