The gravity model (GM) analogous to Newton's law of universal gravitation has
successfully described the flow between different spatial regions, such as
human migration, traffic flows, international economic trades, etc. This simple
but powerful approach relies only on the 'mass' factor represented by the scale
of the regions and the 'geometrical' factor represented by the geographical
distance. However, when the population has a subpopulation structure
distinguished by different attributes, the estimation of the flow solely from
the coarse-grained geographical factors in the GM causes the loss of
differential geographical information for each attribute. To exploit the full
information contained in the geographical information of subpopulation
structure, we generalize the GM for population flow by explicitly harnessing
the subpopulation properties characterized by both attributes and geography. As
a concrete example, we examine the marriage patterns between the bride and the
groom clans of Korea in the past. By exploiting more refined geographical and
clan information, our generalized GM properly describes the real data, a part
of which could not be explained by the conventional GM. Therefore, we would
like to emphasize the necessity of using our generalized version of the GM,
when the information on such nongeographical subpopulation structures is
available.Comment: 14 pages, 6 figures, 2 table