Intraregional flow problem in spatial econometric model for origin–destination flows

The gravity model is used in a variety of fields to explain spatial interaction behavior such as transportation, commodity, or migration flows, but the model assumes observed flows to be independent and thus affected by spatial autocorrelation. Recent studies succeeded in modeling origin–destination (OD) flows in a spatial econometric field, implying that considering spatial dependence among flows will improve the accuracy of the model. However, not all OD flow data contain intraregional flows, and no research has been conducted on how to cope with such data. This study focuses on the problem wherein the spatial econometric model for flows proposed by LeSage and Pace (2008 <i>Journal of Regional Science</i> <b>48</b> 941–967) is not feasible when the flow data do not have intraregional flows. We propose the EM algorithm as a method to overcome this problem and show validity of the proposed method through an application to Japanese migration flow data. <br> <b>Keywords:</b> spatial interaction, gravity model, spatial autoregression, EM algorithm, origin–destination flows