Model Performance

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Summary statistics suggest superior performance by the GWR model which had an Akaike’s information criterion (AICc) value of 18303 and explained 36.3% of the deviance, compared to the OLS model which had an AICc value of 19818 and explained 28.6% of the deviance (Table 2). Higher percentage deviance explained and lower AICc values reveal greater goodness of fit for the GWR model. Additionally, the adjusted critical t-value of 3.110 signals that the GWR model is statistically significant (Table 3).

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Summary statistics for the OLS Regression show that all explanatory variables are statistically significant except for SHM which has a p-value of 0.391 and a t-score of -0.857 (Table 4). For the GWR analysis,  PB_Kill is observed as having substaintly larger deviance than the other explanatory variables given the standard deviation value of 35.205 (Table 5). PB_Kill and Fire_Den have the largest magnitude mean values of -1.544 and 3.392 respectively (Table 5). The mean parameter estimates for PB_Kill is significantly smaller than the medium, due to extreme outliers as evidence by the minimum of -413.336 and maximum of 161.266. The remainder of the explanatory variables have much narrower distributions and exhibit no irregular behavior.

 

The global Moran’s I was calculated to measure the spatial autocorrelation of the dataset. A k-nearest neighbor-based approach resulted in a Moran’s I of 0.3767, a variance of 0.000011, a z-score of 111.8, and a p-value near zero (Figure 2). The positive Moran’s I indicate that there is positive spatial autocorrelation or clustering; high similarly in target values within the local neighborhoods. The z-score and p-values express statistical significance, meaning that the spatial clustering observed in the fire points is unexpected to have occurred randomly. Moran’s I was also tested using fixed distance and inverse distance methods, both of which resulted in even greater statistically significant p-values and z-scores.

 

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GWR Explanatory Variable Coefficient Maps

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GWR analysis revealed that there is significant spatial variation in relationships for all explanatory variables except PB_Kill. Despite some positive and negative correlations in the far northwest of British Columbia, PB_Kill remains neutral across the vast majority of the province with standard deviations close to zero. This suggests that the volume of trees killed by mountain pine beetle has a fairly constant influence on the spatial distribution of wildfires throughout the province. Fire_Den shows a strong north-south dichotomy, with the majority of southern British Columbia indicating a negative relationship and a small region in the central north having a positive correlation. Similar spatial patterns in the relationship of explanatory variables to fire occurrence points are observed for MSP & SHM and MAT & Elev. The coefficient surface layers for MPS and SHM both have strong positive relationships in the central north and southeast as well as strong negative relationships in the northeast and center of the province. Similarly, MAT & Elev both have strong positive relationships in the northwest and central regions. Negative relationships occur on the southwestern side, portions of the northeast, and portions of the southeast. These similarities were expected based on the moderate collinearity previously identified during the OLS Regression. In the case of Road_Dist, it is clear that positive correlations were greatest the closer to BC’s main highway network. As distance increased the correlation with fire event points quickly became negative. This was also to be expected as fire events are likely to occur closest to sites of human activity, and human development is often the densest along transportation corridors. The results from Road_Den however were quite unexpected, with strong positive relationships in the central north and negative relationships throughout the vast majority of the province. Strangely, Road_Den and Fire_Den appear to have almost opposite relationships. ALR_Dist had positive relationships all along the eastern portion of the province. This makes sense as a considerable amount of agriculture in British Columbia is located to the east in the Okanagan Valley. Tree_Ht has a strong positive relationship along the central west coast and the northeast, while a strong negative relationship in the northwest and southeast. The cause for the considerable east-west dichotomy in the north is unknown, possibly related to forest harvest practices. Lastly, Coast_Dist has quite sporadic spatial variability in its relationship to fire occurrence points. There are numerous local regions of high positive and negative correlation

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OLS Regression and GWR Residuals Maps

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