Comparative models

The production-constrained gravity model, the OPS model⁴³, and the original radiation model^30,36 were employed to compare the performance of the newly proposed model. The conventional production-constrained gravity model is defined as:

where α,β are the parameters to be estimated. Because the distances between regions of the datasets are relatively large, the power function dij-β is preferred in this study^10,53,54. Here, we used the model following generalised linear modelling, in which the dependent variables are assumed to follow a Poisson distribution because this is suitable for count data modelling⁵⁵. The model is shown as:

where T^ij is the mean that is logarithmically linked to a linear combination of the logged independent variables. The gravity model is fitted by maximum likelihood estimation.

The last comparative model is the OPS model⁴³, which is a parameter-free and universal model that assumes the individual at an origin i chooses a destination j when the opportunity benefit of j is higher than the maximum opportunity benefits of i and those of the intervening opportunities sij. Following the derivation of the radiation model, the probability is formulated as:

where PrPi+sijz is the probability that the maximum benefit obtained after Pi+sij samplings is exactly z. The predictive formula is:

Although several parameter-free and universal models for human mobility are proposed^30,38,43,46, we used the OPS model for comparison to the newly proposed model, because the model has the derivation and high predictability regardless of spatial scale such as inter-city and intra-city scales^43,44.