328:– most of transport studies require directly or indirectly the definition of TAZs. The modifiable boundary and the scale issues should all be given specific attention during the specification of a TAZ because of the effects these factors exert on statistical and mathematical properties of spatial patterns (ie the modifiable areal unit problem—MAUP). In the studies of Viegas, Martinez and Silva (2009, 2009b) the authors propose a method where the results obtained from the study of spatial data are not independent of the scale, and the aggregation effects are implicit in the choice of zonal boundaries. The delineation of zonal boundaries of TAZs has a direct impact on the reality and accuracy of the results obtained from transportation forecasting models. In this paper the MAUP effects on the TAZ definition and the transportation demand models are measured and analyzed using different grids (in size and in origin location). This analysis was developed by building an application integrated in commercial GIS software and by using a case study (Lisbon Metropolitan Area) to test its implementabiity and performance. The results reveal the conflict between statistical and geographic precision, and their relationship with the loss of information in the traffic assignment step of the transportation planning models.
193:. A researcher might correct the variance-covariance matrix using samples from individual-level data. Alternatively, one might focus on local spatial regression rather than global regression. A researcher might also attempt to design areal units to maximize a particular statistical result. Others have argued that it may be difficult to construct a single set of optimal aggregation units for multiple variables, each of which may exhibit non-stationarity and spatial autocorrelation across space in different ways. Others have suggested developing statistics that change across scales in a predictable way, perhaps using fractal dimension as a scale-independent measure of spatial relationships. Others have suggested Bayesian hierarchical models as a general methodology for combining aggregated and individual-level data for ecological inference.
308:
importance of the spatial arrangement and spatial autocorrelation of data values. Reynold’s simulation experiments were expanded by Swift, who in which a series of nine exercises began with simulated regression analysis and spatial trend, then focused on the topic of MAUP in the context of spatial epidemiology. A method of MAUP sensitivity analysis is presented that demonstrates that the MAUP is not entirely a problem. MAUP can be used as an analytical tool to help understand spatial heterogeneity and
149:
calculate upper and lower limits as well as average regression parameters for multiple sets of spatial groupings. The MAUP is a critical source of error in spatial studies, whether observational or experimental. As such, unit consistency, particularly in a time-series cross-sectional (TSCS) context, is essential. Further, robustness checks of unit sensitivity to alternative spatial aggregation should be routinely performed to mitigate associated biases on resulting statistical estimates.
31:
211:
846:
113:(1988). In particular, Openshaw (1984) observed that "the areal units (zonal objects) used in many geographical studies are arbitrary, modifiable, and subject to the whims and fancies of whoever is doing, or did, the aggregating". The problem is especially apparent when the aggregate data are used for cluster analysis for
320:
analytical solution to MAUP is discovered, spatial sensitivity analysis using a variety of areal units is recommended as a methodology to estimate the uncertainty of correlation and regression coefficients due to ecological bias. An example of data simulation and re-aggregation using the ArcPy library is available.
323:
In transport planning, MAUP is associated to
Traffic Analysis Zoning (TAZ). A major point of departure in understanding problems in transportation analysis is the recognition that spatial analysis has some limitations associated with the discretization of space. Among them, modifiable areal units
87:
For example, census data may be aggregated into county districts, census tracts, postcode areas, police precincts, or any other arbitrary spatial partition. Thus the results of data aggregation are dependent on the mapmaker's choice of which "modifiable areal unit" to use in their analysis. A census
196:
Studies of the MAUP based on empirical data can only provide limited insight due to an inability to control relationships between multiple spatial variables. Data simulation is necessary to have control over various properties of individual-level data. Simulation studies have demonstrated that the
144:
causes variation in statistical results between different levels of aggregation (radial distance). Therefore, the association between variables depends on the size of areal units for which data are reported. Generally, correlation increases as areal unit size increases. The zoning effect describes
92:
calculating population density using state boundaries will yield radically different results than a map that calculates density based on county boundaries. Furthermore, census district boundaries are also subject to change over time, meaning the MAUP must be considered when comparing past data to
331:
Research has also identified the modifiable areal unit problem (MAUP) to be a factor in climate action and governance by affecting coordination between national and local actors. Data scaling issues associated with MAUP may result in mismatches in climate priorities and create inequities in the
319:
between variables, making the relationship appear weak or even negative. Conversely, MAUP can cause random variables to appear as if there is a significant association where there is not. Multivariate regression parameters are more sensitive to MAUP than correlation coefficients. Until a more
148:
Since the 1930s, research has found extra variation in statistical results because of the MAUP. The standard methods of calculating within-group and between-group variance do not account for the extra variance seen in MAUP studies as the groupings change. MAUP can be used as a methodology to
307:
Using simulations for univariate data, Larsen advocated the use of a
Variance Ratio to investigate the effect of spatial configuration, spatial association, and data aggregation. A detailed description of the variation of statistics due to MAUP is presented by Reynolds, who demonstrates the
929:
Viegas, J., E.A. Silva, L. Martinez (2009a). “Effects of the
Modifiable Areal Unit Problem on the Delineation of Traffic Analysis Zones” “Environment and Planning B – Planning and Design“, 36(4): 625–643.
992:
662:
Swift, A., Liu, L., and Uber, J. (2008) "Reducing MAUP bias of correlation statistics between water quality and GI illness." Computers, Environment and Urban
Systems 32, 134–148
710:
Viegas, José Manuel; Martinez, L. Miguel; Silva, Elisabete A. (January 2009). "Effects of the
Modifiable Areal Unit Problem on the Delineation of Traffic Analysis Zones".
1061:
456:
Chen, Xiang; Ye, Xinyue; Widener, Michael J.; Delmelle, Eric; Kwan, Mei-Po; Shannon, Jerry; Racine, Racine F.; Adams, Aaron; Liang, Lu; Peng, Jia (27 December 2022).
680:
Reynolds, H. (1998). "The
Modifiable Area Unit Problem: Empirical Analysis By Statistical Simulation." PhD thesis, Department of Geography University of Toronto,
140:
Ecological bias caused by MAUP has been documented as two separate effects that usually occur simultaneously during the analysis of aggregated data. First, the
932:
Viegas, J., E.A. Silva, L. Martinez (2009a). “A traffic analysis zone definition: a new methodology and algorithm” “Transportation“. 36 (5): 6“, 36 (5): 6 .
102:
1031:
332:
outcomes of climate action, potentially undermining the effectiveness of policies designed to address climate change at different governance levels.
650:
Holt D, Steel D, Tranmer M, Wrigley N. (1996). “Aggregation and ecological effects in geographically based data.” “Geographical
Analysis” 28:244{261
861:
Gehlke, C. E.; Biehl, Katherine (March 1934). "Certain effects of grouping upon the size of the correlation coefficient in census tract material".
1260:
346:
1265:
635:
356:
275:
371:
129:
are prone to disregard the MAUP when drawing inferences from statistics based on aggregated data. MAUP is closely related to the topic of
247:
671:
Larsen, J. (2000). "The
Modifiable Areal Unit Problem: A problem or a source of spatial information?" PhD thesis, Ohio State University.
254:
1176:
437:
294:
145:
variation in correlation statistics caused by the regrouping of data into different configurations at the same scale (areal shape).
232:
225:
1199:
351:
261:
153:
1207:
899:
164:-statistic; * denotes statistical significant at level 0.05, ** for 0.001, *** for smaller than 10;(D) subscripts 1, 2, 3 of
172:
denotes the strata Z1+Z2 with Z3, Z1 with Z2+Z3, and Z1 and Z2 and Z3 individually, respectively; (E) subscripts 1 and 2 of
1194:
Wrigley, Neil (1995). "Revisiting the modifiable areal unit problem and the ecological fallacy". In Cliff, Andrew D (ed.).
243:
324:
and boundary problems are directly or indirectly related to transportation planning and analysis through the design of
1134:
818:
51:
341:
1099:
393:
221:
80:. The resulting summary values (e.g., totals, rates, proportions, densities) are influenced by both the shape and
926:
Cressie, N. (1996). “Change of
Support and the Modifiable Areal Unit Problem.” “Geographical Systems“, 3:159–180.
1225:
Zhang, Ming; Kukadia, Nishant (January 2005). "Metrics of urban form and the modifiable areal unit problem".
197:
spatial support of variables can affect the magnitude of ecological bias caused by spatial data aggregation.
376:
309:
101:
The issue was first recognized by Gehlke and Biehl in 1934 and later described in detail in an entry in the
268:
1202:
special publications series. Vol. 31. Oxford; Cambridge, Massachusetts: Blackwell. pp. 123–181.
458:"A systematic review of the modifiable areal unit problem (MAUP) in community food environmental research"
125:, in which misinterpretations can easily be made without realizing it. Many fields of science, especially
424:
812:
361:
325:
1108:
1007:
969:
766:
719:
593:
581:
469:
403:
398:
134:
114:
505:
315:
This topic is of particular importance because in some cases data aggregation can obscure a strong
190:
1151:
1078:
1023:
878:
838:
Spatial data configuration in then statistical analysis of regional economic and related problems
735:
487:
130:
118:
73:
1213:
1203:
1182:
1172:
1164:
905:
895:
850:
800:
782:
631:
433:
141:
81:
530:
1234:
1143:
1116:
1070:
1015:
977:
870:
790:
774:
727:
601:
477:
366:
47:
126:
693:
1112:
1011:
973:
795:
770:
754:
723:
626:
Fotheringham, A. S.; Rogerson, P. A (2008). "The
Modifiable Areal Unit Problem (MAUP)".
597:
473:
982:
388:
122:
110:
89:
55:
34:
An example of the modifiable areal unit problem and the distortion of rate calculations
1255:
1249:
1155:
1129:
1120:
957:
491:
106:
1082:
1027:
739:
943:
Cressie, Noel A (1996). "Change of support and the modifiable areal unit problem".
189:
Several suggestions have been made in literature to reduce aggregation bias during
77:
605:
1074:
1053:
133:
and ecological bias (Arbia, 1988). Stan Openshaw's work on this topic has led to
1049:
316:
210:
30:
1147:
854:
778:
482:
457:
1019:
1091:
786:
1227:
Transportation Research Record: Journal of the Transportation Research Board
1217:
1186:
1092:"The bright side of MAUP: defining new measures of industrial agglomeration"
909:
804:
54:. MAUP affects results when point-based measures of spatial phenomena are
17:
69:
755:"Data Scaling: Implications for Climate Action and Governance in the UK"
180:
denotes the strata Z1+Z2 with Z3+Z4, and Z1+Z3 with Z2+Z4, respectively.
882:
845:
65:
956:
Holt, David; Steel, David; Tranmer, Mark; Wrigley, Neil (July 1996).
916:
Unwin, D. J. (1996). "GIS, spatial analysis and spatial statistics."
1238:
874:
731:
152:
151:
958:"Aggregation and ecological effects in geographically based data"
681:
204:
586:
International Journal of Geographical Information Science
993:"Excess commuting and the modifiable areal unit problem"
137:
suggesting it be referred to as the "Openshaw effect."
1167:. In Fotheringham, A Stewart; Rogerson, Peter (eds.).
694:
https://app.box.com/s/a84w16x7hffljjvkhtlr72eisj4qiene
855:
Creative Commons Attribution 3.0 Unported (CC BY 3.0)
692:Swift, A. (2017). "Crime mapping data simulation",
156:A hand map with different spatial patterns. Note:
1062:Annals of the Association of American Geographers
991:Horner, Mark W.; Murray, Alan T. (January 2002).
506:"MAUP | Definition – Esri Support GIS Dictionary"
863:Journal of the American Statistical Association
712:Environment and Planning B: Planning and Design
1130:"GIS, spatial analysis and spatial statistics"
853:at the GIS Wiki, which is available under the
1196:Diffusing geography: essays for Peter Haggett
50:that can significantly impact the results of
8:
658:
656:
563:
561:
553:
103:Concepts and Techniques in Modern Geography
1165:"The modifiable areal unit problem (MAUP)"
1054:"The uncertain geographic context problem"
981:
794:
481:
295:Learn how and when to remove this message
840:. Dordrecht: Kluwer Academic Publishers.
705:
703:
701:
567:
29:
1171:. Los Angeles: Sage. pp. 105–124.
451:
449:
415:
849:This article contains quotations from
810:
347:Boundary problem (in spatial analysis)
231:Please improve this section by adding
1169:The SAGE handbook of spatial analysis
628:The SAGE handbook of spatial analysis
357:Neighborhood effect averaging problem
7:
372:Uncertain geographic context problem
983:10.1111/j.1538-4632.1996.tb00933.x
531:"Geographic Boundary Change Notes"
25:
892:The modifiable areal unit problem
426:The Modifiable Areal Unit Problem
1200:Institute of British Geographers
1128:Unwin, David J (December 1996).
1121:10.1111/j.1435-5957.2011.00350.x
844:
352:Modifiable temporal unit problem
209:
244:"Modifiable areal unit problem"
1261:Geographic information systems
753:Sudmant, Andrew (2024-09-01).
580:Goodchild, Michael F. (2022).
1:
851:Modifiable areal unit problem
682:http://www.badpets.net/Thesis
606:10.1080/13658816.2022.2102637
529:Geography, US Census Bureau.
233:secondary or tertiary sources
40:modifiable areal unit problem
1266:Problems in spatial analysis
1075:10.1080/00045608.2012.687349
918:Progress in Human Geography.
52:statistical hypothesis tests
1135:Progress in Human Geography
1090:Menon, Carlo (March 2012).
58:into spatial partitions or
1282:
1148:10.1177/030913259602000408
1100:Papers in Regional Science
779:10.1007/s00267-024-01991-5
630:. Sage. pp. 105–124.
483:10.1007/s44212-022-00021-1
394:Red states and blue states
109:(1984) and in the book by
27:Source of statistical bias
1020:10.1080/00420980220099113
201:MAUP sensitivity analysis
84:of the aggregation unit.
836:Arbia, Giuseppe (1988).
759:Environmental Management
342:Arbia's law of geography
890:Openshaw, Stan (1984).
817:: CS1 maint: bibcode (
554:Gehlke & Biehl 1934
423:Openshaw, Stan (1983).
377:Reference class problem
310:spatial autocorrelation
894:. Norwick: Geo Books.
326:traffic analysis zones
220:relies excessively on
181:
160:is the probability of
72:) as in, for example,
35:
962:Geographical Analysis
582:"The Openshaw effect"
362:Representation theory
155:
33:
1163:Wong, David (2009).
945:Geographical Systems
404:Spatial epidemiology
399:Spatial econometrics
135:Michael F. Goodchild
115:spatial epidemiology
1113:2012PRegS..91....3M
1012:2002UrbSt..39..131H
974:1996GeoAn..28..244H
771:2024EnMan.tmp...83S
724:2009EnPlB..36..625V
598:2022IJGIS..36.1697G
474:2022UrbIn...1...22C
191:regression analysis
185:Suggested solutions
105:(CATMOG) series by
182:
131:ecological fallacy
123:choropleth mapping
119:spatial statistics
74:population density
36:
869:(185A): 169–170.
637:978-1-4129-1082-8
462:Urban Informatics
305:
304:
297:
279:
46:) is a source of
16:(Redirected from
1273:
1242:
1221:
1190:
1159:
1124:
1096:
1086:
1058:
1045:
1043:
1042:
1036:
1030:. Archived from
997:
987:
985:
952:
913:
886:
848:
841:
823:
822:
816:
808:
798:
750:
744:
743:
707:
696:
690:
684:
678:
672:
669:
663:
660:
651:
648:
642:
641:
623:
617:
616:
614:
612:
592:(9): 1697–1698.
577:
571:
565:
556:
551:
545:
544:
542:
541:
526:
520:
519:
517:
516:
510:support.esri.com
502:
496:
495:
485:
453:
444:
443:
431:
420:
367:Spatial analysis
300:
293:
289:
286:
280:
278:
237:
213:
205:
48:statistical bias
21:
1281:
1280:
1276:
1275:
1274:
1272:
1271:
1270:
1246:
1245:
1239:10.3141/1902-09
1224:
1210:
1193:
1179:
1162:
1127:
1094:
1089:
1056:
1048:
1040:
1038:
1034:
995:
990:
955:
951:(2–3): 159–180.
942:
939:
937:Further reading
902:
889:
875:10.2307/2277827
860:
835:
832:
827:
826:
809:
752:
751:
747:
709:
708:
699:
691:
687:
679:
675:
670:
666:
661:
654:
649:
645:
638:
625:
624:
620:
610:
608:
579:
578:
574:
566:
559:
552:
548:
539:
537:
528:
527:
523:
514:
512:
504:
503:
499:
455:
454:
447:
440:
429:
422:
421:
417:
412:
338:
301:
290:
284:
281:
238:
236:
230:
226:primary sources
214:
203:
187:
127:human geography
99:
28:
23:
22:
15:
12:
11:
5:
1279:
1277:
1269:
1268:
1263:
1258:
1248:
1247:
1244:
1243:
1222:
1208:
1191:
1177:
1160:
1142:(4): 540–551.
1125:
1087:
1069:(5): 958–968.
1046:
1006:(1): 131–139.
988:
968:(3): 244–261.
953:
938:
935:
934:
933:
930:
927:
924:
914:
900:
887:
858:
842:
831:
828:
825:
824:
765:(3): 414–424.
745:
732:10.1068/b34033
718:(4): 625–643.
697:
685:
673:
664:
652:
643:
636:
618:
572:
557:
546:
535:www.census.gov
521:
497:
445:
438:
414:
413:
411:
408:
407:
406:
401:
396:
391:
389:Gerrymandering
385:
384:
380:
379:
374:
369:
364:
359:
354:
349:
344:
337:
334:
303:
302:
217:
215:
208:
202:
199:
186:
183:
111:Giuseppe Arbia
98:
95:
93:current data.
90:choropleth map
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1278:
1267:
1264:
1262:
1259:
1257:
1254:
1253:
1251:
1240:
1236:
1232:
1228:
1223:
1219:
1215:
1211:
1205:
1201:
1197:
1192:
1188:
1184:
1180:
1178:9781412910828
1174:
1170:
1166:
1161:
1157:
1153:
1149:
1145:
1141:
1137:
1136:
1131:
1126:
1122:
1118:
1114:
1110:
1106:
1102:
1101:
1093:
1088:
1084:
1080:
1076:
1072:
1068:
1064:
1063:
1055:
1051:
1047:
1037:on 2017-04-22
1033:
1029:
1025:
1021:
1017:
1013:
1009:
1005:
1001:
1000:Urban Studies
994:
989:
984:
979:
975:
971:
967:
963:
959:
954:
950:
946:
941:
940:
936:
931:
928:
925:
922:
919:
915:
911:
907:
903:
897:
893:
888:
884:
880:
876:
872:
868:
864:
859:
856:
852:
847:
843:
839:
834:
833:
829:
820:
814:
806:
802:
797:
792:
788:
784:
780:
776:
772:
768:
764:
760:
756:
749:
746:
741:
737:
733:
729:
725:
721:
717:
713:
706:
704:
702:
698:
695:
689:
686:
683:
677:
674:
668:
665:
659:
657:
653:
647:
644:
639:
633:
629:
622:
619:
607:
603:
599:
595:
591:
587:
583:
576:
573:
569:
568:Openshaw 1984
564:
562:
558:
555:
550:
547:
536:
532:
525:
522:
511:
507:
501:
498:
493:
489:
484:
479:
475:
471:
467:
463:
459:
452:
450:
446:
441:
439:0-86094-134-5
435:
428:
427:
419:
416:
409:
405:
402:
400:
397:
395:
392:
390:
387:
386:
382:
381:
378:
375:
373:
370:
368:
365:
363:
360:
358:
355:
353:
350:
348:
345:
343:
340:
339:
335:
333:
329:
327:
321:
318:
313:
311:
299:
296:
288:
277:
274:
270:
267:
263:
260:
256:
253:
249:
246: –
245:
241:
240:Find sources:
234:
228:
227:
223:
218:This section
216:
212:
207:
206:
200:
198:
194:
192:
184:
179:
175:
171:
167:
163:
159:
154:
150:
146:
143:
138:
136:
132:
128:
124:
120:
116:
112:
108:
107:Stan Openshaw
104:
96:
94:
91:
85:
83:
79:
78:illness rates
75:
71:
67:
63:
62:
57:
53:
49:
45:
41:
32:
19:
1230:
1226:
1195:
1168:
1139:
1133:
1104:
1098:
1066:
1060:
1050:Kwan, Mei-Po
1039:. Retrieved
1032:the original
1003:
999:
965:
961:
948:
944:
920:
917:
891:
866:
862:
837:
813:cite journal
762:
758:
748:
715:
711:
688:
676:
667:
646:
627:
621:
609:. Retrieved
589:
585:
575:
549:
538:. Retrieved
534:
524:
513:. Retrieved
509:
500:
465:
461:
425:
418:
383:Applications
330:
322:
314:
306:
291:
282:
272:
265:
258:
251:
239:
219:
195:
188:
177:
173:
169:
165:
161:
157:
147:
142:scale effect
139:
100:
86:
60:
59:
43:
39:
37:
1107:(1): 3–28.
570:, p. 3
317:correlation
285:August 2018
61:areal units
1250:Categories
1209:0631195343
1041:2015-07-05
923:: 540–551.
901:0860941345
611:24 January
540:2017-02-24
515:2017-03-09
410:References
255:newspapers
222:references
97:Background
56:aggregated
18:Areal unit
1233:: 71–79.
1156:129487607
787:1432-1009
492:255206315
468:(1): 22.
70:districts
64:(such as
1218:30895028
1187:85898184
1083:52024592
1052:(2012).
1028:56418131
910:12052482
857:license.
805:38811434
796:11306386
740:54840846
336:See also
1109:Bibcode
1008:Bibcode
970:Bibcode
883:2277827
830:Sources
767:Bibcode
720:Bibcode
594:Bibcode
470:Bibcode
269:scholar
66:regions
1216:
1206:
1198:. The
1185:
1175:
1154:
1081:
1026:
908:
898:
881:
803:
793:
785:
738:
634:
490:
436:
271:
264:
257:
250:
242:
1152:S2CID
1095:(PDF)
1079:S2CID
1057:(PDF)
1035:(PDF)
1024:S2CID
996:(PDF)
879:JSTOR
736:S2CID
488:S2CID
430:(PDF)
276:JSTOR
262:books
82:scale
1256:Bias
1231:1902
1214:OCLC
1204:ISBN
1183:OCLC
1173:ISBN
906:OCLC
896:ISBN
819:link
801:PMID
783:ISSN
632:ISBN
613:2024
434:ISBN
248:news
176:and
168:and
44:MAUP
38:The
1235:doi
1144:doi
1117:doi
1071:doi
1067:102
1016:doi
978:doi
871:doi
791:PMC
775:doi
728:doi
602:doi
478:doi
224:to
121:or
76:or
68:or
1252::
1229:.
1212:.
1181:.
1150:.
1140:20
1138:.
1132:.
1115:.
1105:91
1103:.
1097:.
1077:.
1065:.
1059:.
1022:.
1014:.
1004:39
1002:.
998:.
976:.
966:28
964:.
960:.
947:.
921:20
904:.
877:.
867:29
865:.
815:}}
811:{{
799:.
789:.
781:.
773:.
763:74
761:.
757:.
734:.
726:.
716:36
714:.
700:^
655:^
600:.
590:36
588:.
584:.
560:^
533:.
508:.
486:.
476:.
464:.
460:.
448:^
432:.
312:.
235:.
117:,
1241:.
1237::
1220:.
1189:.
1158:.
1146::
1123:.
1119::
1111::
1085:.
1073::
1044:.
1018::
1010::
986:.
980::
972::
949:3
912:.
885:.
873::
821:)
807:.
777::
769::
742:.
730::
722::
640:.
615:.
604::
596::
543:.
518:.
494:.
480::
472::
466:1
442:.
298:)
292:(
287:)
283:(
273:·
266:·
259:·
252:·
229:.
178:p
174:q
170:p
166:q
162:q
158:p
42:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
