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The concept of scale is inherent to, and consequential for, the modeling of geographical processes. However, scale also causes huge problems because the results of many types of spatial analysis appear to be dependent on the scale of the units for which data are reported (measurement scale). Consequently, when the same spatial models are calibrated at different scales of aggregations, the results are often vastly different (the well-known Modifiable Areal Unit Problem or MAUP). With the advent of local models and the fundamental difference in their scale of application compared to global models, this issue is further exacerbated in unexpected ways. For example, a global model and local model calibrated using data measured at the same aggregation scale can also result in different and sometimes contradictory inferences (the classic Simpson's Paradox). Here we provide a geographical perspective on why and how contrasting inferences might result from the calibration of a local and global model using the same data. Further, we examine the viability of such an occurrence using a synthetic experiment and two empirical examples. Finally, we discuss how such a perspective might inform the analyst’s conundrum: when the respective inferences run counter to one another, do we believe the local or global model results? 

Abstract Scale is a central concept in the geographical sciences and is an intrinsic property of many spatial systems. It also serves as an essential thread in the fabric of many other physical and social sciences, which has contributed to the use of different terminology for similar manifestations of what we refer to as ‘scale’, leading to a surprising amount of diversity around this fundamental concept and its various ‘multiscale’ extensions. To address this, we review common abstractions about spatial scale and how they are employed in quantitative research. We also explore areas where the conceptualizations of multiple spatial scales can be differentiated. This is achieved by first bridging terminology and concepts, and then conducting a scoping review of the topic. A typology for spatial scale is discussed that can be used to categorize its multifarious meanings and measures. This typology is then used to distinguish what we term ‘process scale,’ from other types of spatial scale and to highlight current trends in uncovering aspects of process scale. We end with suggestions on how to further build knowledge regarding spatial processes through the lens of spatial scale.