# Spatial Performance Indicators for Traffic Flow Prediction
## 4 Results
### Comparison Between Different Traffic Prediction Methods  
The Global Moran's I comparison between different methods is summarized in Figure 8. All methods have \(p_{I}\)-values lower than 0.05 and positive \(z_{I}\)-scores, which indicate that the null hypothesis of Global Moran's I can be rejected, and the resulting prediction error has positive spatial autocorrelation (similar values are spatially clustered). STSGCN and ASTGCN, which utilize the predefined adjacency matrix of the network, exhibit higher spatial autocorrelation than DDGCRN and STAEformer. DDGCRN, which learns dynamic graphs for spatial contexts, ranks third, whereas STAEformer, which has no graph modeling, ranks last. The differences between STSGCN, ASTGCN, and DDGCRN were subtle and less informative, whereas STAEformer showed a more apparent difference. A higher Global Moran's I in the context of traffic flow prediction error suggests that the model's prediction error is spatially structured, with nearby locations tending to have more similar values and not being distributed randomly. The value of \(z_{I}\)-score depends on \(I\), \(E[I]\), and \(V[I]\) (Equation (4)). In Global Moran's I, the values of \(E[I]\) and \(V[I]\) depend only on the spatial weight matrix (from the adjacency matrix) and number of nodes. If we compare different methods in the same traffic network, the values of both \(p_{I}\)-value and \(z_{I}\)-score are solely dependent on the value of \(I\). In Figure 6, we can see that some nodes in STAEformer have a lower RMSE (deep blue color) but the remaining nodes are similar to other methods. This finding suggests that the lower RMSE of STAEformer could be caused by sporadic dispersive improvement, rather than global improvement, which reduces spatial autocorrelation. Such an improvement could be beneficial if the improved nodes are located at a critical location. However, if the improvement is in an isolated place, it could be less beneficial even though the average RMSE difference is large. The Getis-Ord General \(G\) comparison between different methods is summarized in Figure 9. All methods except ASTGCN have \(p_{G}\)-values less than 0.05 with positive \(z_{G}\)-scores, indicating that the null hypothesis of Getis-Ord General G can be rejected and suggesting a spatial clustering of high-value nodes. In these methods, some spatially clustered areas have a higher RMSE, forming hotspots, and these methods struggle to predict traffic flow in those areas. As for ASTGCN, the null hypothesis cannot be rejected, suggesting no tendencies to cluster high or low values. The \(G\) value of ASTGCN was the lowest among all the methods by a small margin, but the \(p_{G}\)-value and \(z_{G}\)-score were significantly different. The \(z_{G}\)-score was calculated using \(G\), \(E[G]\), and \(V[G]\) (Equation (7)), as summarized in Table 7. The value of \(E[G]\) is identical for all methods because it is the total sum of all spatial weights divided by the possible number of pairs of nodes, which are determined only by the adjacency matrix. Therefore, the \(z_{G}\)-score is dependent only on the values of \(G\) and \(V[G]\). \(G\) measures the degree of the clustering of high or low values, depending on whether it is larger or smaller than \(E[G]\). From Equation (7), the value of \(V[G]\) determines the magnitude of \(G-E[G]\) required for  
Figure 8: Comparison of Global Moran’s I for different traffic flow prediction methods. the null hypothesis to be rejected. Unlike \(V[I]\), the value of \(V[G]\) depends on the value of the nodes, and the value of each method may differ. Interestingly, the \(V[G]\) values of both STSGCN and ASTGCN are similar, and both utilize the adjacency matrix as their prior knowledge. Both of them had lower \(V[G]\) values, suggesting higher confidence in the observed \(G\) value, compared to DDGCRN and STAEformer. However, the \(G-E[G]\) value of ASTGCN was significantly lower than that of the other methods, resulting in a low \(z_{G}\)-score and insignificant \(p_{G}\)-value.