Evaluating Spatial Interaction Models for Regional Mobility in Sub-Saharan Africa
Fig 5
The utility of each model to describe travel in various settings.
A) For travel between all pairs of locations, we compared the error in the actual versus predicted amount of travel. If this error was not within defined bounds (outside of the dotted black lines) (see Materials and Methods), we determined that both models do not adequately describe this travel (shown in black). For the remaining volumes and routes of travel, we determined if the gravity model (blue) or the radiation model (red) performed better to identify which model should be used in various settings. For example, the radiation model does much better than the gravity model predicting low volumes of travel and vice versa (shown in red versus blue). B) A schematic highlighting the situations when a radiation model is preferred over a gravity model and when caution should be taken using the predicted results of either model. Scenarios to use a gravity model over a radiation model include: travel to and from a major population centre, over short distances, and when predicting large volumes of travel. A radiation model should be used over a gravity model when describing travel between rural areas and low volumes of travel. Caution should be taken using either model if the travel is between locations of intermediate rural population and over short distances. C) We performed a logistic regression to determine when to use each model for various amounts of travel (a gravity factor). As the amount of travel increases, the number of times the gravity model outperforms the radiation model increases. For examples for the lowest amounts of travel 43% of the time a radiation model if preferable to a gravity model. In contrast for the largest amount of travel, all of these routes (100%) were better predicted with a gravity model than a radiation model.