In this paper the examination of the modifiable areal unit problem is extended into multivariate statistical analysis. In an investigation of the parameter estimates from a multiple linear regression model and a multiple logit regression model, conclusions are drawn about the sensitivity of such estimates to variations in scale and zoning systems. The modifiable areal unit problem is shown to be essentially unpredictable in its intensity and effects in multivariate statistical analysis and is therefore a much greater problem than in univariate or bivariate analysis. The results of this analysis are rather depressing in that they provide strong evidence of the unreliability of any multivariate analysis undertaken with data from areal units. Given that such analyses can only be expected to increase with the imminent availability of new census data both in the United Kingdom and in the USA, and the current proliferation of GIS (geographical information system) technology which permits even more access to aggregated data, this paper serves as a topical warning.
Get full access to this article
View all access options for this article.
References
1.
AmrheinC GFlowerdewR, 1989, “The effect of data aggregation on a Poisson regression model of Canadian migration”, in Accuracy of Spatial Databases Eds GoodchildM FGopalS (Taylor and Francis, London) pp 229–238.
2.
ArbiaG, 1989Spatial Data Configuration in Statistical Analysis of Regional Economic and Related Problems (Kluwer, Dordrecht).
3.
BachL, 1981, “The problem of aggregation and distance for analyses of accessibility and access opportunity in location—allocation models”Environment and Planning A13955–978.
BattyM, 1976, “Entropy in spatial aggregation”Geographical Analysis81–21.
6.
BattyMSammonsR, 1978, “On searching for the most informative spatial pattern”Environment and Planning A10747–779.
7.
BattyMSikdarP K, 1982a, “Spatial aggregation in gravity models: 1. An information-theoretic framework”Environment and Planning A14377–405.
8.
BattyMSikdarP K, 1982b, “Spatial aggregation in gravity models: 2. One-dimensional population density models”Environment and Planning A14525–553.
9.
BattyMSikdarP K, 1982c, “Spatial aggregation in gravity models: 3. Two-dimensional trip distribution and location modles”Environment and Planning A14629–658.
10.
BattyMSikdarP K, 1982d, “Spatial aggregation in gravity models: 4. Generalisations and large-scale applications”Environment and Planning A14795–822.
11.
BlairPMillerR E, 1983, “Spatial aggregation in multiregional input—output models”Environment and Planning A15187–206.
12.
BlalockH M, 1964Causal Inferences in Nonexperimental Research Chapel Hill (University of North Carolina Press, Chapel Hill, NC).
ClarkW A VAveryK L, 1976, “The effects of data aggregation in statistical analysis”Geographical Analysis8428–438.
15.
FotheringhamA S, 1989, “Scale-independent spatial anlaysis”, in Accuracy of Spatial Databases Eds GoodchildM FGopalS (Taylor and Francis, London) pp 221–228.
16.
GaleD E, 1984Neighborhood Revitalization and the Postindustrial City: A Multinational Perspective (Lexington Books, Lexington, MA).
17.
GehlkeC EBiehlK, 1934, “Certain effects of grouping upon the size of the correlation coefficient in census tract material”Journal of the American Statistical Association Supplement29169–170.
18.
GoodchildM F, 1979, “The aggregation problem in location—allocation”Geographical Analysis11240–255.
19.
GriffithD A, 1988Advanced Spatial Statistics (Kluwer, Dordrecht).
20.
LiptonS G, 1977, “Evidence of central-city revival”Journal of the American Institute of Planners43136–147.
21.
MasserIBrownP J B, 1975, “Hierarchical aggregation procedures for interaction data”Environment and Planning A7509–523.
22.
MasserIBrownP J B, 1977, “Spatial representation and spatial interaction”Papers of the Regional Science Association3871–92.
23.
MironJ, 1984, “Spatial autocorrelation in regression analysis: A beginner's guide”, in Spatial i$ Statistics and Models Eds GaileG LWillmottC J (Kluwer, Dordrecht) pp 201–222.
NelsonK P, 1988Gentrification and Distressed Cities: An Assessment of Trends in Intrametropolitan Migration (University of Wisconsin Press, Madison, WI).
26.
OpenshawS, 1977, “Optimal zoning systems for spatial interaction models”Environment and Planning A9169–184.
27.
OpenshawS, 1978, “An empirical study of some zone-design criteria”Environment and Planning A10781–794.
28.
OpenshawS, 1984Concepts and Techniques in Modern Geography, Number 38. The Modifiable Areal Unit Problem (Geo Books, Norwich).
29.
OpenshawSTaylorP J, 1979, “A million or so correlation coefficients: Three experiments on the modifiable areal unit problem”, in Statistical Applicaions in the Spatial Sciences Ed. WrigleyN (Pion, London) pp 127–144.
30.
PerleE D, 1977, “Scale changes and impacts on factorial ecology structures”Environment and Planning A9549–558.
31.
PutmanS HChungS-H, 1989, “Effects of spatial systems design on spatial interaction models. 1: The spatial definition problem”Environment and Planning A2127–46.
32.
RobinsonA H, 1956, “The necessity of weighting values in correlation analysis of areal data”Annals of the Association of American Geographers46233–236.
33.
RobinsonW S, 1950, “Ecological correlations and the behavior of individuals”American Sociological Review15351–357.
34.
SawickiD S, 1973, “Studies of aggregated areal data—problems of statistical inference”Land Economics49109–114.
35.
ThomasE NAndersonD L, 1965, “Additional comments on weighting values in correlation analysis of areal data”Annals of the Association of American Geographers55492–505.
36.
USBC, 1980Census ′80: Continuing the Factfinder Tradition US Bureau of the Census, by C P Kaplan, T L Van Valey and Associates, Washington, DC (US Government Printing Office, Washington, DC).
37.
USBC, 1981aCensus of Population and Housing, 1980: Summary Tape File 1 Technical Documentation US Bureau of the Census (US Government Printing Office, Washington, DC).
38.
USBC, 1981bCensus of Population and Housing, 1980: Summary Taype File 1A (New York) (US Bureau of the Census, Washington, DC).
39.
USBC, 1981cCensus of Population and Housing, 1980: Summary Tape File 3A (New York) (US Bureau of the Census, Washington, DC).
40.
USBC, 19831980 Census of Population and Housing, Census Tracts for Buffalo, NY SMSA US Bureau of the Census (US Government Printing Office, Washington, DC).
41.
WrigleyN, 1985Categorical Data Analysis for Geographers and Environmental Scientists (Longman, Harlow, Essex)
