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In 2020, Arizonans approved Proposition 207, the Smart and Safe Arizona Act, which legalized recreational marijuana sales. Previous research has typically used non‐spatial survey data to understand marijuana legalization voting patterns. However, voting behavior can, in part, be shaped by geographic context, or place, which is unaccounted for in aspatial survey data. We use multiscale geographically weighted regression to analyze how place shaped Proposition 207 voting behavior, independently of demographic variations across space. We find significant spatial variability in the sensitivity of voting for Proposition 207 to changes in several of the predictor variables of opposition and support for recreational marijuana legalization. We argue that local statistical modeling approaches provide a more in‐depth understanding of ballot measure voting behavior than the current use of global models. Related Articles: Branton, Regina, and Ronald J. McGauvran. 2018. "Mary Jane Rocks the Vote: The Impact of Climate Context on Support for Cannabis Initiatives." Politics & Policy 46(2): 209–32. https://doi.org/10.1111/polp.12248. Brekken, Katheryn C., and Vanessa M. Fenley. 2020. "Part of the Narrative: Generic News Frames in the U.S. Recreational Marijuana Policy Subsystem." Politics & Policy 49(1): 6–32. https://doi.org/10.1111/polp.12388. Fisk, Jonathan M., Joseph A. Vonasek, and Elvis Davis. 2018. "'Pot'reneurial Politics: The Budgetary Highs and Lows of Recreational Marijuana Policy Innovation." Politics & Policy 46(2): 189–208. https://doi.org/10.1111/polp.12246. [ABSTRACT FROM AUTHOR]

The issue of whether place significantly affects spatial behavior has long created both a philosophical and an operational schism within geography. Here we show how these schisms can be bridged by identifying how place and behavior can be linked through recognizing and incorporating what we term intrinsic and behavioral contextual effects into models of spatial behavior. We argue that spatial modeling frameworks that attempt to relate spatial behavior to aspects of people and places might be seriously misspecified if they do not incorporate both types of contextual effects. We compare three popular statistical modeling frameworks that encompass placed-based contextual effects: spatial error models, multilevel models, and multiscale geographically weighted regression (MGWR). Based on Monte Carlo simulation and empirical analysis, we demonstrate the reassuring similarity of the results from the three frameworks but also the superiority of MGWR. The inclusion of essentially unmeasurable effects within a nomothetic framework provides an important bridge between two previously distinct philosophies within geography and acts as a binding force within the discipline. [ABSTRACT FROM AUTHOR]

A recent addition to the suite of techniques for local statistical modeling is the implementation of the multiscale geographically weighted regression (MGWR), a multiscale extension to geographically weighted regression (GWR). Using a back-fitting algorithm, MGWR relaxes the restrictive assumption in GWR that all processes being modeled operate at the same spatial scale and allows the estimation of a unique indicator of scale, the bandwidth, for each process. However, the current MGWR framework is limited to use with continuous data making it unsuitable for modeling data that do not typically exhibit a Gaussian distribution. This study expands the application of the MGWR framework to scenarios involving discrete response outcomes (count data following a Poisson's distribution). Use of this new MGWR Poisson regression (MGWPR) model is demonstrated with a simulated data set and then with COVID-19 case counts within New York City at the zip code level. The results from the simulated data underscore the superiority of the MGWPR model in effectively capturing spatial processes that influence count data patterns, particularly those operating across diverse spatial scales. For empirical data, the results reveal significant spatial variations in relationships between socio-ecological factors and COVID-19 cases – variations often missed by traditional 'global' models. [ABSTRACT FROM AUTHOR]

The optimal bandwidths produced in the calibration of MGWR models have uncertainty attached to them which can be quantified and a confidence interval placed around each covariate-specific bandwidth. Without data standardization, the optimized covariate-specific bandwidths will be, in part, a function of the data variability and to ensure comparability across bandwidths it is therefore important to make the variability of each covariate the same. The first is that a current bibliography (Fotheringham et al., [7]) lists over 2,500 references for applications of Geographically Weighted Regression (GWR) and Multiscale Geographically Weighted Regression (MGWR) divided into 30 categories so this is clearly a popular research area. GWR is simply MGWR with the unrealistic restriction that the bandwidth is the same for each process being modeled and also for the local intercept. [Extracted from the article]

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). With the advent of local models and the fundamental difference in their scale of application compared to global models, this issue is 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 FROM AUTHOR]

Studies of spatially varying parameter estimates obtained in the calibration of various types of local statistical models are commonplace. The variation in such estimates is typically explained in terms of spatially varying processes. This paper highlights that an alternative explanation for spatially varying parameter estimates, in terms of non‐linearity, should be examined prior to relating such variation to spatially varying processes. This can be achieved by a simple screening procedure which is described and demonstrated and which can easily be applied to the results of any local model. The problem is highlighted, and the solution demonstrated, with a set of simulated data and then with a real‐world data set. The paper also highlights the obverse situation whereby the inappropriate application of a GAM produces spurious nonlinear results when the real relationships are linear but spatially varying. [ABSTRACT FROM AUTHOR]

This article examines the relationship between spatial dependency and spatial heterogeneity, two properties unique to spatial data. The property of spatial dependence has led to a large body of research [...]

Models designed to capture spatially varying processes are now employed extensively in the social and environmental sciences. The main strength of such models is their ability to represent relationships that vary across locations through locally varying parameter estimates. However, local models of spatial processes also provide information on the nature of these spatially varying relationships through the estimation of a 'bandwidth' parameter. This paper examines bandwidth at a conceptual, operational and empirical level within the framework of geographically weighted regression, one of the more frequently employed local spatial models. We outline how bandwidth relates to three characteristics of spatial processes: variation, dependence and strength. [ABSTRACT FROM AUTHOR]

The measurement of spatial dependence within a set of observations or the residuals from a regression is one of the most common operations within spatial analysis. However, there appears to be a lack of appreciation for the fact that these measurements are generally based on an a priori definition of a spatial weights matrix and hence are limited to detecting spatial dependence at a single spatial scale. This paper highlights the scale-dependence problem with current measures of spatial dependence and defines a new, multi-scale approach to defining a spatial weights matrix based on a discrete Fourier transform. This approach is shown to be able to detect statistically significant spatial dependence which other multi-scale approaches to measuring spatial dependence cannot. The paper thus serves as a warning not to rely on traditional measures of spatial dependence and offers a more comprehensive, and scale-free, approach to measuring such dependence. [ABSTRACT FROM AUTHOR]

We discuss the nature of processes relating to human behaviour and how to model such processes when they vary over space. In so doing, we describe the role of local modelling and how the bandwidth parameter, a component of multiscale geographically weighted regression, can inform on the spatial scale over which processes are relatively constant. To do this, we translate properties of spatial data, such as heterogeneity and spatial dependency into the realm of spatial processes. We argue that the modelling of spatially varying processes has important ramifications for how we see the world. [ABSTRACT FROM AUTHOR]

This introduction provides a brief review of the motivation, background, and context of the Forum. It explains the roles of the six papers in the Forum and the importance of reproducibility and replicability across the broad sweep of contemporary geographic research. [ABSTRACT FROM AUTHOR]

The scientific method is predicated on the assumption that research designs and results can be reproduced and replicated. However, recent findings in some disciplines suggest that many studies fail to reach this standard, moving issues surrounding reproducibility and replicability forward into the research agenda of those fields. While the topic has yet to become a point of controversy in geography, the intricacies of geographic phenomena and spatial data analysis make the field vulnerable to criticism. This commentary discusses how uncertainties related to the conception, measurement, analysis, and communication of geographic analyses contribute to difficulties in the reproduction and replication of geographic research. Investigating how these uncertainties collectively impact the reproducibility and replicability of spatial data analyses should be a critical focus of future Geographical Analysis research. A call to action for geographers to improve the reproducibility and replicability of their work and specific recommendations on how Geographical Analysis might facilitate this process conclude the commentary. [ABSTRACT FROM AUTHOR]

This work provides an investigation of the presence of spatial variability in the determinants of mortality rates. Specifically, by using the age‐adjusted mortality rates of the counties of the contiguous United States, this research applies a multiscale geographically weighted regression (MGWR) approach to examine the spatial variations in the relationships between mortality rates and a diverse group of associated determinants. The results demonstrate that the MGWR approach produces a differentiable account of the global, regional, and local effects acting on mortality rates across the United States. Thus, this work lays the groundwork for the consideration of spatial varying effects on mortality rates, which operate at different spatial scales. [ABSTRACT FROM AUTHOR]

Bandwidth, a key parameter in geographically weighted regression models, is closely related to the spatial scale at which the underlying spatially heterogeneous processes being examined take place. Generally, a single optimal bandwidth (geographically weighted regression) or a set of covariate-specific optimal bandwidths (multiscale geographically weighted regression) is chosen based on some criterion, such as the Akaike information criterion (AIC), and then parameter estimation and inference are conditional on the choice of this bandwidth. In this article, we find that bandwidth selection is subject to uncertainty in both single-scale and multiscale geographically weighted regression models and demonstrate that this uncertainty can be measured and accounted for. Based on simulation studies and an empirical example of obesity rates in Phoenix, we show that bandwidth uncertainties can be quantitatively measured by Akaike weights and confidence intervals for bandwidths can be obtained. Understanding bandwidth uncertainty offers important insights about the scales over which different processes operate, especially when comparing covariate-specific bandwidths. Additionally, unconditional parameter estimates can be computed based on Akaike weights accounts for bandwidth selection uncertainty. [ABSTRACT FROM AUTHOR]

Geographically Weighted Regression (GWR) has been broadly used in various fields to model spatially non-stationary relationships. Multi-scale Geographically Weighted Regression (MGWR) is a recent advancement to the classic GWR model. MGWR is superior in capturing multi-scale processes over the traditional single-scale GWR model by using different bandwidths for each covariate. However, the multiscale property of MGWR brings additional computation costs. The calibration process of MGWR involves iterative back-fitting under the additive model (AM) framework. Currently, MGWR can only be applied on small datasets within a tolerable time and is prohibitively time-consuming to run with moderately large datasets (greater than 5,000 observations). In this paper, we propose a parallel implementation that has crucial computational improvements to the MGWR calibration. This improved computational method reduces both memory footprint and runtime to allow MGWR modelling to be applied to moderate-to-large datasets (up to 100,000 observations). These improvements are integrated into the mgwr python package and the MGWR 2.0 software, both of which are freely available to download. [ABSTRACT FROM AUTHOR]

This paper considers what happens when we abandon the concept that models of social processes have global application in favor of a local approach in which context or the influence of 'place' has an important role. A brief history of this local approach to statistical modeling is given, followed by a consideration of its ramifications for understanding societal issues. The piece concludes with future challenges and prospects in this area. [ABSTRACT FROM AUTHOR]