Which distance-decay function for migration and which one for commuting? A case study of Slovenia

The volume of social interactions like migration and commuting between two locations depends significantly on the distance between them. In the paper, we analysed the shape and parameters of several distance-decay functions for commuting and for migration flows, respectively. The analysis was performed for inter-municipal interactions in Slovenia in 2010–2011. The functions considered were power, exponential, normal, square root exponential, hyperbolic, power-exponential, and normalized power-exponential distance-decay functions. Distance was considered in three ways: as the Euclidean distance, as the shortest road distance, and as the fastest road distance between municipal centres under consideration. The analysis was performed for the whole set of interactions in the state, as well as for interactions to specific urban centres. We demonstrate that the power-exponential distance-decay function fits best for all analysed cases. The determination coefficients for this type of function are low when analysing all data together, but they increase significantly when distance-decay functions are modelled for urban centres at different levels of consideration