The Modifiable Areal Unit Problem in Pearson’s Correlation Coefficients under the Presence of Bivariate Spatial Autocorrelation: A Simulation Study

Authors: Sang-Il Lee*, Seoul National University, Monghyeon Lee, Samsung Co. Ltd.
Topics: Spatial Analysis & Modeling, Geographic Information Science and Systems, Quantitative Methods
Keywords: modifiable areal unit problem (MAUP), the Pearson’s correlation coefficient, bivariate spatial autocorrelation
Session Type: Paper
Day: 4/6/2019
Start / End Time: 9:55 AM / 11:35 AM
Room: 8217, Park Tower Suites, Marriott, Lobby Level
Presentation File: No File Uploaded

Effects of the modifiable areal unit problem (MAUP) on Pearson’s correlation coefficients have well been documented; the higher the aggregation levels (coarser areal units), the smaller the Pearson’s correlation coefficients. This study examines whether the straightforward generalization can hold under the presence of bivariate spatial autocorrelation. More specifically, this study examines whether the initial level of bivariate spatial autocorrelation makes a substantial difference to the variability of the MAUP effects on the Pearson’s correlation coefficient. A simulation study employs a random spatial aggregation (RSA) procedure which is used to generate different levels of spatial aggregation (the scale effect) and different zonations (the zoning effect). Different pairs with different levels of bivariate spatial autocorrelation as measured by Lee’s L^* statistic are generated at an identical aspatial correlation. A more detailed experimental design is as follows. First, a hypothetical study region composed of 1,024 squares is set. 9 pairs of variables for the square tessellation are generated simulating 9 different levels of correlation. For one particular correlation level, 9 pairs of variables are generated simulating 9 different levels of bivariate spatial autocorrelation. Second, the 1,024 squares are randomly aggregated into 10 different aggregation levels. Third, for each aggregation level, 1,000 different sets of zonations are generated. This simulation study is expected to yield a set of more generalizable results regarding the variability of the MAUP effects on the Pearson’s correlation coefficient due to not only different levels of correlation but different levels of bivariate spatial autocorrelation.

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