Skip to main content

Scale and local modeling: new perspectives on the modifiable areal unit problem and Simpson’s paradox


The concept of ‘spatial scale’, or simply ‘scale’ is implicit in any discussion of global versus local models. The raison d’etre of local models is that a global scale (where here ‘global’ simply refers to all locations within a predefined area of interest) might be the incorrect scale at which to undertake any analysis of spatial processes; the alternative being a local scale (where here ‘local’ refers to individual locations). Here we explore two well-known scale issues in the context of local modeling: the modifiable areal unit problem (MAUP) and Simpson’s paradox. In doing so, we highlight that scale effects play two very different roles in any consideration of local versus global modeling. First, we examine the sensitivity of global and local models to the MAUP and show how the effects of the MAUP in global models are a function of the degree to which processes vary over space. This generates a new insight into the MAUP: it results from the properties of processes rather than the properties of data. Then we highlight the extreme differences that can result when calibrating global and local models and how Simpson’s paradox can arise in this context. In the examination of the MAUP, scale is treated as a measure of the degree to which data are aggregated prior to any form of modeling; in the study of Simpson’s paradox, scale refers to the geographical entity for which a model is calibrated.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18


  1. In this paper, the term ‘process’ is used to describe a sequence of events whereby change in one variable leads to a measurable change in another. These events are unknown so in essence the use of the word ‘process’ is shorthand for a conditioned relationship between two variables.

  2. While MGWR is a truly local model in that it uses subsets of the data to undertake a series of local calibrations, Bayesian SVC and ESF are ‘whole-data’ techniques and as such are not true local models. However, all these models are based on the same premise—that the relationships that produce the observed pattern of the dependent variable might not be stationary over space—and all produce locally varying parameter estimates to reflect this premise. Consequently, we refer to all such models as ‘local’.


Download references


Funding was provided by National Science Foundation (Grant No. 1758786).

Author information

Authors and Affiliations


Corresponding author

Correspondence to A. Stewart Fotheringham.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Fotheringham, A.S., Sachdeva, M. Scale and local modeling: new perspectives on the modifiable areal unit problem and Simpson’s paradox. J Geogr Syst 24, 475–499 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Spatial processes
  • Scale
  • Local modeling
  • MGWR
  • MAUP
  • Simpson’s paradox

JEL Classification

  • C31-Spatial models