{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T20:14:25Z","timestamp":1783023265061,"version":"3.54.6"},"reference-count":43,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T00:00:00Z","timestamp":1695859200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100017414","name":"Beijing Municipal Social Science Foundation","doi-asserted-by":"publisher","award":["22GLC062"],"award-info":[{"award-number":["22GLC062"]}],"id":[{"id":"10.13039\/100017414","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100017414","name":"Beijing Municipal Social Science Foundation","doi-asserted-by":"publisher","award":["KM202010009002"],"award-info":[{"award-number":["KM202010009002"]}],"id":[{"id":"10.13039\/100017414","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Beijing Municipal Education Commission Social Science Project","award":["22GLC062"],"award-info":[{"award-number":["22GLC062"]}]},{"name":"Beijing Municipal Education Commission Social Science Project","award":["KM202010009002"],"award-info":[{"award-number":["KM202010009002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Spatial autocorrelation analysis is essential for understanding the distribution patterns of spatial flow data. Existing methods focus mainly on the origins and destinations of flow units and the relationships between them. These methods measure the autocorrelation of gravity or the positional and directional autocorrelations of flow units that are treated as objects. However, the intrinsic complexity of actual flow data necessitates the consideration of not only gravity, positional, and directional autocorrelations but also the autocorrelations of the variables of interest. This study proposes a global spatial autocorrelation method to measure the variables of interest of flow data. This method mainly consists of three steps. First, the proximity constraints of the origin and destination of a flow unit are defined to ensure similarity of flow units in terms of direction, distance, and position. This undertaking aims to determine the neighborhood of flow units and generate their adjacent matrices. Second, a spatial autocorrelation measurement model for flow data is constructed on the basis of the adjacent matrix generated. Artificial data sets are also employed to test the validity of the model. Finally, the proposed method is applied to the flow data analysis of population migration in central and eastern China to prove the practical application value of the model. The proposed method is universal and can be generalized to the global spatial autocorrelation analysis of any type of flow data.<\/jats:p>","DOI":"10.3390\/ijgi12100396","type":"journal-article","created":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T07:50:26Z","timestamp":1695887426000},"page":"396","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Flow-Data-Based Global Spatial Autocorrelation Measurements for Evaluating Spatial Interactions"],"prefix":"10.3390","volume":"12","author":[{"given":"Shuai","family":"Sun","sequence":"first","affiliation":[{"name":"School of Architecture and Art, North China University of Technology, Rd.5 Jinyuanzhuang, Beijing 100144, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haiping","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Geographic Science, Nanjing Normal University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1111\/j.1538-4632.1995.tb00338.x","article-title":"Local indicators of spatial association\u2014LISA","volume":"27","author":"Anselin","year":"1995","journal-title":"Geogr. Anal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/978-3-319-72553-6_2","article-title":"Spatial Autocorrelation and the p-Median Problem","volume":"51","author":"Griffith","year":"2018","journal-title":"Morphisms Quant. Spat. Anal."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"234","DOI":"10.2307\/143141","article-title":"A computer movie simulating urban growth in the Detroit region","volume":"46","author":"Tobler","year":"1970","journal-title":"Econ. Geogr."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.compenvurbsys.2018.03.008","article-title":"Challenges for social flows","volume":"70","author":"Andris","year":"2018","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s11067-014-9256-4","article-title":"Spatial autocorrelation in spatial interactions models: Geographic scale and resolution implications for network resilience and vulnerability","volume":"15","author":"Griffith","year":"2015","journal-title":"Netw. Spat. Econ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1111\/gean.12069","article-title":"Measuring spatial autocorrelation of vectors","volume":"47","author":"Liu","year":"2015","journal-title":"Geogr. Anal."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"101519","DOI":"10.1016\/j.compenvurbsys.2020.101519","article-title":"BiFlowLISA: Measuring spatial association for bivariate flow data","volume":"83","author":"Tao","year":"2020","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/978-3-642-01976-0_2","article-title":"Spatial interaction and spatial autocorrelation: A cross-product approach","volume":"23","author":"Getis","year":"2010","journal-title":"Perspect. Spat. Data Anal."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/0166-0462(92)90035-Y","article-title":"Spatial autoregressive error components in travel flow models","volume":"22","author":"Bolduc","year":"1992","journal-title":"Reg. Sci. Urban Econ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1080\/09595237400185281","article-title":"Evaluating the friction of distance parameter in gravity models","volume":"8","author":"Cliff","year":"1974","journal-title":"Reg. Stud."},{"key":"ref_11","unstructured":"Haynes, K.E., and Fotheringham, A.S. (2020). Gravity and Spatial Interaction Models, WVU Research Repository."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Cliff, A., Martin, R., and Ord, J. (1976). A Reply to the Final Comment, Taylor & Francis.","DOI":"10.1080\/09595237600185351"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"LeSage, J.P., and Llano, C. (2016). A spatial interaction model with spatially structured origin and destination effects. Spat. Econom. Interact. Model., 171\u2013197.","DOI":"10.1007\/978-3-319-30196-9_9"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1080\/01621459.1975.10480272","article-title":"Estimation methods for models of spatial interaction","volume":"70","author":"Ord","year":"1975","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1068\/a100305","article-title":"Estimating spatial-interaction models","volume":"10","author":"Haining","year":"1978","journal-title":"Environ. Plan. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1177\/0308518X8301500103","article-title":"A new set of spatial-interaction models: The theory of competing destinations","volume":"15","author":"Fotheringham","year":"1983","journal-title":"Environ. Plan. A Econ. Space"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1111\/1467-9701.00074","article-title":"Proper econometric specification of the gravity model","volume":"20","year":"1997","journal-title":"World Econ."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Van Bergeijk, P.A., and Brakman, S. (2010). The Gravity Model in International Trade: Advances and Applications, Wiley.","DOI":"10.1017\/CBO9780511762109"},{"key":"ref_19","unstructured":"Fotheringham, A.S., and O\u2019Kelly, M.E. (1989). Spatial Interaction Models: Formulations and Applications, Kluwer Academic Publishers."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.ijpe.2017.10.018","article-title":"Interactions between flows of human resources in functional regions and flows of inventories in dynamic processes of global supply chains","volume":"209","author":"Bogataj","year":"2019","journal-title":"Int. J. Prod. Econ."},{"key":"ref_21","unstructured":"Anselin, L. (2022). Handbook of Spatial Analysis in the Social Sciences, Edward Elgar Publishing."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1111\/j.1435-5957.2010.00279.x","article-title":"Thirty years of spatial econometrics","volume":"89","author":"Anselin","year":"2010","journal-title":"Pap. Reg. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1111\/j.1538-4632.1992.tb00262.x","article-title":"Network autocorrelation in transport network and flow systems","volume":"24","author":"Black","year":"1992","journal-title":"Geogr. Anal."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1080\/00045608.2011.561070","article-title":"Modeling network autocorrelation in space\u2013time migration flow data: An eigenvector spatial filtering approach","volume":"101","author":"Chun","year":"2011","journal-title":"Ann. Assoc. Am. Geogr."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2980","DOI":"10.1016\/j.jspi.2010.03.045","article-title":"The Moran coefficient for non-normal data","volume":"140","author":"Griffith","year":"2010","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1111\/j.1467-9787.2008.00573.x","article-title":"Spatial econometric modeling of origin-destination flows","volume":"48","author":"LeSage","year":"2008","journal-title":"J. Reg. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Beenstock, M., and Felsenstein, D. (2016). Double Spatial Dependence in Gravity Models: Migration from the European Neighborhood to the European Union. Spat. Econom. Interact. Model., 225\u2013251.","DOI":"10.1007\/978-3-319-30196-9_11"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1007\/s10844-015-0361-8","article-title":"Collective regression for handling autocorrelation of network data in a transductive setting","volume":"46","author":"Loglisci","year":"2016","journal-title":"J. Intell. Inf. Syst."},{"key":"ref_29","unstructured":"Storm, H., and Heckelei, T. (2016, January 28\u201330). Using Multiple Neighboring Interaction Effects in Spatial Regression Specifications to Reduce Omitted Variable Bias. Proceedings of the 56th Annual Conference, Bonn, Germany."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1111\/j.1538-4632.2009.00773.x","article-title":"Network autocorrelation","volume":"41","author":"Peeters","year":"2009","journal-title":"Geogr. Anal."},{"key":"ref_31","first-page":"67","article-title":"Testing spatial autocorrelation in weighted networks: The modes permutation test","volume":"15","author":"Bavaud","year":"2016","journal-title":"Spat. Econom. Interact. Model."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1080\/07350015.2015.1061437","article-title":"Estimating spatial autocorrelation with sampled network data","volume":"35","author":"Zhou","year":"2017","journal-title":"J. Bus. Econ. Stat."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.econlet.2015.10.035","article-title":"Difference-in-differences techniques for spatial data: Local autocorrelation and spatial interaction","volume":"137","author":"Delgado","year":"2015","journal-title":"Econ. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s00168-018-0860-y","article-title":"Flow autocorrelation: A dyadic approach","volume":"61","author":"Bavaud","year":"2018","journal-title":"Ann. Reg. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1016\/j.respol.2016.10.008","article-title":"How complex international partnerships shape domestic research clusters: Difference-in-difference network formation and research re-orientation in the MIT Portugal Program","volume":"46","author":"Hird","year":"2017","journal-title":"Res. Policy"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1111\/jors.12114","article-title":"Interpreting spatial econometric origin-destination flow models","volume":"55","author":"LeSage","year":"2015","journal-title":"J. Reg. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/PL00011451","article-title":"A linear regression solution to the spatial autocorrelation problem","volume":"2","author":"Griffith","year":"2000","journal-title":"J. Geogr. Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/s12076-016-0172-8","article-title":"The spatial autocorrelation problem in spatial interaction modelling: A comparison of two common solutions","volume":"10","author":"Griffith","year":"2017","journal-title":"Lett. Spat. Resour. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s10109-015-0225-3","article-title":"Eigenvector selection with stepwise regression techniques to construct eigenvector spatial filters","volume":"18","author":"Chun","year":"2016","journal-title":"J. Geogr. Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1080\/17421772.2015.1076575","article-title":"The gravity model for international trade: Specification and estimation issues","volume":"10","author":"Krisztin","year":"2015","journal-title":"Spat. Econ. Anal."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s10109-008-0068-2","article-title":"Modeling network autocorrelation within migration flows by eigenvector spatial filtering","volume":"10","author":"Chun","year":"2008","journal-title":"J. Geogr. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Patuelli, R. (2016). Spatial autocorrelation and spatial interaction. Encycl. GIS, 1\u20137.","DOI":"10.1007\/978-3-319-23519-6_1522-1"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1111\/gean.12274","article-title":"Detecting colocation flow patterns in the geographical interaction data","volume":"54","author":"Zhang","year":"2022","journal-title":"Geogr. Anal."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/12\/10\/396\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:00:36Z","timestamp":1760130036000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/12\/10\/396"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,28]]},"references-count":43,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["ijgi12100396"],"URL":"https:\/\/doi.org\/10.3390\/ijgi12100396","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,28]]}}}