This would be a good question for a regional scientist. I'm modeling flows of students between school districts. A helpful reviewer pointed me to previous work that modeled such flows using spatial interaction models, otherwise known as gravity models.
I am a bit puzzled, because in Chun & Griffith (2019), in Chapter 7 on Spatial Interaction models, the toy data set includes flows of the number of workers among 6 counties in Texas. It also contains rows for the number of workers who worked in the same county with the origin id and the destination id the same county id for a total of 6 * 6 = 36 observations.
On the other hand, in Wolwer, Burgard & BreBlein (2018), the toy data set is one of trade volumes and it excludes the trade within countries.
It seems like since I am modeling students who stay or move, this is more analogous to workers, so I should include rows for students who stay.
I can't find explicitly direction in the literature as to the inclusion or exclusion of this.
I found a set of answers. These two articles goes over the basic history of the problem:
Oshan, T. M. (2020). The spatial structure debate in spatial interaction modeling: 50 years on. Progress in Human Geography, 1. https://doi.org/10.1177/0309132520968134
Oshan, T. M. (2016). A primer for working with the Spatial Interaction modeling (SpInt) module in the python spatial analysis library (PySAL). REGION, 3(2), 11. https://doi.org/10.18335/region.v3i2.175
Oshan (2016) discusses how traditionally researchers left out intra-regional flows (or no flows), but upon investigation this was revealed to bias estimates. Next, Oshan (2016) notes two papers that present possible solutions. The first sets intra-regional flows to zero for simplicity’s sake. The second takes an average distance of various possible origin and destination dyads within the region.
Tsutsumi, M., & Tamesue, K. (2011). Intraregional Flow Problem in Spatial Econometric Model for Origin-destination Flows. Procedia - Social and Behavioral Sciences, 21, 184–192. https://doi.org/10.1016/j.sbspro.2011.07.023
The second takes an average distance of various possible origin and destination dyads within the region.
Kordi M, Kaiser C, Fotheringham AS (2012) A possible solution for the centroid-tocentroid and intra-zonal trip length problems. International Conference on Geographic Information Science, Avignon
Maybe this can help:
Preprint International trade and the gravity model: recent evidence i...
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