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A conjecture recently began to materialize in the GIScience and spatial statistics literature asserting that many georeferenced attribute random variables (RVs) contain a positive–negative spatial autocorrelation (SA) mixture, rather than the widely recognized purely positive SA based upon routine cursory observation. Another newly emerging supposition maintains that, after controlling for the already well-known tendency for SA to increase with increasingly fine geographic resolutions, georeferenced socio-economic/demographic attribute RVs have roughly the same magnitude of positive SA as that degree frequently computed for remotely sensed pixel data, an extent suppressed in its net amount by the negative SA in a variable's mixture. This article, the first of a two-part series, summarizes research exploring these two propositions using population density as a common georeferenced RV across a diverse set of geographic landscapes. The principal population density findings support these two suppositions. Part II presents parallel analyses for a wide range of georeferenced RVs across the same set of geographic landscapes.
Daniel A. Griffith; Khushboo Agarwal; Meifang Chen; Changho Lee; Emily Ann Panetti; Kyunghee Rhyu; Lasya Venigalla; Xiaohe Yu. Geospatial socio‐economic/demographic data: The existence of spatial autocorrelation mixtures in georeferenced data—Part I. Transactions in GIS 2021, 1 .
AMA StyleDaniel A. Griffith, Khushboo Agarwal, Meifang Chen, Changho Lee, Emily Ann Panetti, Kyunghee Rhyu, Lasya Venigalla, Xiaohe Yu. Geospatial socio‐economic/demographic data: The existence of spatial autocorrelation mixtures in georeferenced data—Part I. Transactions in GIS. 2021; ():1.
Chicago/Turabian StyleDaniel A. Griffith; Khushboo Agarwal; Meifang Chen; Changho Lee; Emily Ann Panetti; Kyunghee Rhyu; Lasya Venigalla; Xiaohe Yu. 2021. "Geospatial socio‐economic/demographic data: The existence of spatial autocorrelation mixtures in georeferenced data—Part I." Transactions in GIS , no. : 1.
The “Urban Economics” section of Frontiers in Sustainable Cities, which lies at the intersection between economics and geography, seeks to address economic analysis applied to urban phenomena from a locational perspective while contributing to a knowledge base (also see Proost and Thisse, 2019) supporting cities whose socio-economic/demographic and environmental impacts foster a resilient urban habitat for existing populations without degrading its quality for future generations [see, e.g., EPS (Economic Planning Systems), 2011]. This journal section's goal is to advance the research frontiers in this sub-field, bolstering its foundation established, in part, by the new urban economics of the 1970s with the more contemporary new economic geography championed by, among others, Glasser (2011) and Economics Nobelist Paul Krugman. This inaugural editorial highlights sustainable urban spatial economics, essentially an interdisciplinary sub-field that studies safeguard reasons for economic activity concentration in and dispersion across networks of cities as well as within individual cities by emphasizing the roles of both spatial autocorrelation and distance factors (e.g., transportation costs), focusing on agglomeration and dispersion tendencies arising from this former georeferenced data property and constrained by these latter friction of distance operators. It interfaces with what has become known as the new science of cities (Batty, 2013) plus the domain of the more technical urban informatics (Shi et al., 2021). Following a somewhat nebulous and more applied inception, urban economics began crystalizing in the 1960s, with the first books devoted exclusively to it appearing in the early 1970s: Mills (1972), Grieson (1973), Leahy et al. (1970), Rasmussen (1973), Richardson (1977), and Hirsch (1984), to name a few. A hallmark of this emergence was the release of Cities (Davis, 1973) by Scientific American, followed by the 1974 appearance of a dedicated subject matter journal; in contrast, its eponymous organization (i.e., the Urban Economics Association) formally founded itself much later, in the early 2000s. Accompanying the initial book publications were ones focusing on geographic aspects of urban economics that underlined its two spatial dimensions: Internal Structure of the City by Bourne (1971), and Systems of Cities by Bourne and Simmons (1978). This combined collection of formative texts is superseded today by far more comprehensive books also containing geographic information systems (GIS) output, such as O'Sullivan (2011/2019). The two geographic dimensions, coupled with state-of-the-art thinking reflected in, for example, O'Sullivan, suggest grand challenges facing modern sustainable urban spatial economics. These themes provide an impetus for the launching of this section; they are neither the sole nor an all-inclusive enumeration of topics, but rather are intended to stimulate the urban economic geography community to fill some of the glaring gaps existing in the literature. O'Sullivan (his 2011 8th and selected earlier editions) proposes five axioms many, if not most, urban economists consider to be well-established rules/principles describing especially the arrangement of within-city economic activities, widely accepted because of their individual intrinsic merits, whose more explicitly spatial versions supplemented with a sixth axiom furnish a conceptual framework upon which the structure of a more abstract sustainable urban economic geography rests: 1. prices adjust to achieve locational equilibrium (in part, relating to bid-rent curve theory) 2. self-reinforcing spatial effects generate extreme production, consumption, and/or transfer of urban wealth outcomes 3. in situ production is subject to economies of scale 4. spatial externalities cause inefficiency 5. spatial competition generates zero excess economic profit 6. public resources provision achieves a(n) (location-) allocation equilibrium in which no individual can be made better off without making at least one other individual worse off In the 9th edition, O'Sullivan effectively translates these postulates into the following key standard economics concepts: opportunity costs (manifested as location rent), the marginal principle, Nash equilibrium (named after the Economics Nobelist), comparative statics, Pareto efficiency [Schumpeter (1952) lists Pareto as one of the 10 great economists to that date; The Best Schools, https://thebestschools.org/features/top-economists-1900-to-present/, ranks him 19th among the top 50 economists from 1900 to the present], and self-reinforcing changes. Ahlfeldt et al. (2015) add another element here by emphasizing equilibrium instead of marginal effects, which is great for measuring externalities (also see Bayer et al., 2007) such as agglomeration economies as well as spatial economic spillovers such as pollution. Linking these axioms and their key concept replacements coupled with shifts from marginal to equilibrium analysis to sustainable urban economics presents an epic challenge. Another overall challenge collectively signaled by these propositions is inculcating a widespread adoption/application of spatial econometric methodologies (i.e., accounting for spatial autocorrelation) when engaging in urban economic data analyses; doing so also fosters a recognition that spatial spillover effects can diminish or reinforce sustainability. The first axiom promotes land use and housing research; sustainability coincides with equitable and affordable housing. The second sanctions agglomeration economies research, with particular reference to localization and urbanization economies; sustainability can exploit geographic cluster-generated synergisms that render beneficial socio-economic/demographic and environmentally benign outcomes. The third axiom encourages research about trade-offs between economies of scale and assembly and distribution transportation costs:...
Daniel A. Griffith. Urban Economics: Geography and Spatial Dependence Matter to the Sustainability of Cities. Frontiers in Sustainable Cities 2021, 3, 1 .
AMA StyleDaniel A. Griffith. Urban Economics: Geography and Spatial Dependence Matter to the Sustainability of Cities. Frontiers in Sustainable Cities. 2021; 3 ():1.
Chicago/Turabian StyleDaniel A. Griffith. 2021. "Urban Economics: Geography and Spatial Dependence Matter to the Sustainability of Cities." Frontiers in Sustainable Cities 3, no. : 1.
Epidemiologists and health geographers routinely use small-area survey estimates as covariates to model areal and even individual health outcomes. American Community Survey (ACS) estimates are accompanied by standard errors (SEs), but it is not yet standard practice to use them for evaluating or modeling data reliability. ACS SEs vary systematically across regions, neighborhoods, socioeconomic characteristics, and variables. Failure to consider probable observational error may have substantial impact on the large bodies of literature relying on small-area estimates, including inferential biases and over-confidence in results. The issue is particularly salient for predictive models employed to prioritize communities for service provision or funding allocation. Leveraging the tenets of plausible reasoning and Bayes’ theorem, we propose a conceptual framework and workflow for spatial data analysis with areal survey data, including visual diagnostics and model specifications. To illustrate, we follow Krieger et al.’s (2018) call to routinely use the Index of Concentration at the Extremes (ICE) to monitor spatial inequalities in health and mortality. We construct and examine SEs for the ICE, use visual diagnostics to evaluate our observational error model for the ICE, and then estimate an ICE–mortality gradient by incorporating the latter model into our model of sex-specific, midlife (ages 55–64), all-cause United States county mortality rates. We urge researchers to consider data quality as a criterion for variable selection prior to modeling, and to incorporate data reliability information into their models whenever possible.
Connor Donegan; Yongwan Chun; Daniel Griffith. Modeling Community Health with Areal Data: Bayesian Inference with Survey Standard Errors and Spatial Structure. International Journal of Environmental Research and Public Health 2021, 18, 6856 .
AMA StyleConnor Donegan, Yongwan Chun, Daniel Griffith. Modeling Community Health with Areal Data: Bayesian Inference with Survey Standard Errors and Spatial Structure. International Journal of Environmental Research and Public Health. 2021; 18 (13):6856.
Chicago/Turabian StyleConnor Donegan; Yongwan Chun; Daniel Griffith. 2021. "Modeling Community Health with Areal Data: Bayesian Inference with Survey Standard Errors and Spatial Structure." International Journal of Environmental Research and Public Health 18, no. 13: 6856.
Existing interfaces between mathematics and art, and geography and art, began overlapping in recent years. This newer overarching intersection partly is attributable to the scientific visualization of the concept of an eigenvector from the subdiscipline of matrix algebra. Spectral geometry and signal processing expanded this overlap. Today, novel applications of the statistical Moran eigenvector spatial filtering (MESF) methodology to paintings accentuates and exploits spatial autocorrelation as a fundamental element of art, further expanding this overlap. This paper studies MESF visualizations by compositing identified relevant spatial autocorrelation components, examining a particular Van Gogh painting for the first time, and more intensely re-examining several paintings already evaluated with MESF techniques. Findings include: painting replications solely based upon their spatial autocorrelation components as captured and visualized by certain eigenvectors are visibly indistinguishable from their original counterparts; and, spatial autocorrelation supplies measurements allowing a differentiation of paintings, a potentially valuable discovery for art history. GRAPHICAL ABSTRACT
Daniel A. Griffith. Eigenvector visualization and art. Journal of Mathematics and the Arts 2021, 1 -18.
AMA StyleDaniel A. Griffith. Eigenvector visualization and art. Journal of Mathematics and the Arts. 2021; ():1-18.
Chicago/Turabian StyleDaniel A. Griffith. 2021. "Eigenvector visualization and art." Journal of Mathematics and the Arts , no. : 1-18.
A research team collected 3609 useful soil samples across the city of Syracuse, NY; this data collection fieldwork occurred during the two consecutive summers (mid-May to mid-August) of 2003 and 2004. Each soil sample had fifteen heavy metals (As, Cr, Cu, Co, Fe, Hg, Mo, Mn, Ni, Pb, Rb, Se, Sr, Zn, and Zr), measured during its assaying; errors for these measurements are analyzed in this paper, with an objective of contributing to the geography of error literature. Geochemistry measurements are in milligrams of heavy metal per kilogram of soil, or ppm, together with accompanying analytical measurement errors. The purpose of this paper is to summarize and portray the geographic distribution of these selected heavy metals measurement errors across the city of Syracuse. Doing so both illustrates the value of the SAAR software’s uncertainty mapping module and uncovers heavy metal characteristics in the geographic distribution of Syracuse’s soil. In addition to uncertainty visualization portraying and indicating reliability information about heavy metal levels and their geographic patterns, SAAR also provides optimized map classifications of heavy metal levels based upon their uncertainty (utilizing the Sun-Wong separability criterion) as well as an optimality criterion that simultaneously accounts for heavy metal levels and their affiliated uncertainty. One major outcome is a summary and portrayal of the geographic distribution of As, Cr, Cu, Co, Fe, Hg, Mo, Mn, Ni, Pb, Rb, Se, Sr, Zn, and Zr measurement error across the city of Syracuse.
Daniel Griffith; Yongwan Chun. Soil Sample Assay Uncertainty and the Geographic Distribution of Contaminants: Error Impacts on Syracuse Trace Metal Soil Loading Analysis Results. International Journal of Environmental Research and Public Health 2021, 18, 5164 .
AMA StyleDaniel Griffith, Yongwan Chun. Soil Sample Assay Uncertainty and the Geographic Distribution of Contaminants: Error Impacts on Syracuse Trace Metal Soil Loading Analysis Results. International Journal of Environmental Research and Public Health. 2021; 18 (10):5164.
Chicago/Turabian StyleDaniel Griffith; Yongwan Chun. 2021. "Soil Sample Assay Uncertainty and the Geographic Distribution of Contaminants: Error Impacts on Syracuse Trace Metal Soil Loading Analysis Results." International Journal of Environmental Research and Public Health 18, no. 10: 5164.
When data for observations are missing, scientists often remove those observations from an analysis, or replace them with imputations, with few other options available to these analysts. Confining an analysis to those observations with complete data can waste resources expended for, especially, those observations with near-complete data. Selectively retaining variables with complete data for observations with incomplete data can compromise mathematical properties of data analyses (e.g., covariance matrices constructed with pairwise deletion having negative eigenvalues). Unless missing data observations are a random subsample of a given sample, entirely removing these observations can result in biased statistical results. Imputations, such as those furnished by kriging, are best linear unbiased predictors (BLUPs), which can be conditional expectations. As such, they are smoothed values that may be viewed as representing attribute values with measurement error, and hence estimated attribute variance based upon them tends to be biased downward. Because, for example, regression coefficients use variance estimates in their calculations, this downward bias can propagate through a data analysis and its statistical inferences. This paper compares spatial regression analyses between complete datasets and the same datasets in which data values are suppressed and then these missing data are imputed, investigating the presence of such imputations in a response variable as well as in covariates. This study employs the following three imputation methods: kriging, spatial autoregression, and Moran eigenvector spatial filtering. Its emphasis is on predictive modeling as well as spatial data quality and uncertainty.
Daniel A. Griffith; Yan-Ting Liau. Imputed spatial data: Cautions arising from response and covariate imputation measurement error. Spatial Statistics 2021, 42, 100419 .
AMA StyleDaniel A. Griffith, Yan-Ting Liau. Imputed spatial data: Cautions arising from response and covariate imputation measurement error. Spatial Statistics. 2021; 42 ():100419.
Chicago/Turabian StyleDaniel A. Griffith; Yan-Ting Liau. 2021. "Imputed spatial data: Cautions arising from response and covariate imputation measurement error." Spatial Statistics 42, no. : 100419.
Spatial weights matrices used in quantitative geography furnish maps with their individual latent eigenvectors, whose geographic distributions portray distinct spatial autocorrelation (SA) components. These polygon patterns on maps have specific meaning, partially in terms of geographic scale, which this article describes. The goal of this description is to enable spatial analysts to better understand and interpret these maps individually, as well as mixtures of them, when accounting for SA in a spatial analysis. Linear combinations of Moran eigenvector maps supply a powerful and relatively simple tool that can explain SA in regression residuals, with an ability to render reasonably accurate reproductions of empirical geographic distributions with or without the aid of substantive covariates. The focus of this article is positive SA, the most commonly encountered nature of autocorrelation in georeferenced data. The principal innovative contribution of this article is establishing a better clarification of what the synthetic SA variates extracted from spatial weights matrices epitomize with regard to global, regional, and local clusters of similar values on a map. This article shows that the Getis-Ord Gi* statistic provides a useful tool for classifying Moran eigenvector maps into these three qualitative categories, illustrating findings with a range of specimen geographic landscapes.
Daniel A. Griffith. Interpreting Moran Eigenvector Maps with the Getis-Ord Gi* Statistic. The Professional Geographer 2021, 1 -17.
AMA StyleDaniel A. Griffith. Interpreting Moran Eigenvector Maps with the Getis-Ord Gi* Statistic. The Professional Geographer. 2021; ():1-17.
Chicago/Turabian StyleDaniel A. Griffith. 2021. "Interpreting Moran Eigenvector Maps with the Getis-Ord Gi* Statistic." The Professional Geographer , no. : 1-17.
Small areas refer to small geographic areas, a more literal meaning of the phrase, as well as small domains (e.g., small sub-populations), a more figurative meaning of the phrase. With post-stratification, even with big data, either case can encounter the problem of small local sample sizes, which tend to inflate local uncertainty and undermine otherwise sound statistical analyses. This condition is the opposite of that afflicting statistical significance in the context of big data. These two definitions can also occur jointly, such as during the standardization of data: small geographic units may contain small populations, which in turn have small counts in various age cohorts. Accordingly, big spatial data can become not-so-big spatial data after post-stratification by geography and, for example, by age cohorts. This situation can be ameliorated to some degree by the large volume of and high velocity of big spatial data. However, the variety of any big spatial data may well exacerbate this situation, compromising veracity in terms of bias, noise, and abnormalities in these data. The purpose of this paper is to establish deeper insights into big spatial data with regard to their uncertainty through one of the hallmarks of georeferenced data, namely spatial autocorrelation, coupled with small geographic areas. Impacts of interest concern the nature, degree, and mixture of spatial autocorrelation. The cancer data employed (from Florida for 2001–2010) represent a data category that is beginning to enter the realm of big spatial data; its volume, velocity, and variety are increasing through the widespread use of digital medical records.
Daniel A. Griffith; Yongwan Chun; Monghyeon Lee. Deeper Spatial Statistical Insights into Small Geographic Area Data Uncertainty. International Journal of Environmental Research and Public Health 2020, 18, 231 .
AMA StyleDaniel A. Griffith, Yongwan Chun, Monghyeon Lee. Deeper Spatial Statistical Insights into Small Geographic Area Data Uncertainty. International Journal of Environmental Research and Public Health. 2020; 18 (1):231.
Chicago/Turabian StyleDaniel A. Griffith; Yongwan Chun; Monghyeon Lee. 2020. "Deeper Spatial Statistical Insights into Small Geographic Area Data Uncertainty." International Journal of Environmental Research and Public Health 18, no. 1: 231.
Space‐time data are becoming more abundant as time goes by, with hands‐on interest in them becoming more prevalent. These data have a very sensitive ordering in space and time, one that the simplest of recording errors can scramble. These data are also complex, containing both spatial and temporal autocorrelation coupled with their interaction. One goal of many researchers is to disentangle and account for these autocorrelation components in a parsimonious way. This article presents three competing model specifications to achieve this end. In addition, it outlines seven best practices for vetting space‐time datasets. This article cites a publicly available corrupt (containing at least errors of omission) rabies dataset to illustrate how a large volume of potentially valuable data can be rendered meaningless. In addition, it exemplifies postulated contentions about the United States National Cancer Institute Surveillance, Epidemiology, and End Results Program’s 1969–2018 population‐by‐county dataset, a collection of population counts held in high esteem. One major empirical finding is that this particular dataset exhibits traits that may merit remedial revisions action. A key conceptual finding is a suggested set of best practices for space‐time data proofreading. These two findings contribute to an ultimate goal of a large collection of certified open access space‐time datasets supporting repeatable and replicable scientific analyses.
Daniel A. Griffith. Important considerations about space‐time data: Modeling, scrutiny, and ratification. Transactions in GIS 2020, 25, 291 -310.
AMA StyleDaniel A. Griffith. Important considerations about space‐time data: Modeling, scrutiny, and ratification. Transactions in GIS. 2020; 25 (1):291-310.
Chicago/Turabian StyleDaniel A. Griffith. 2020. "Important considerations about space‐time data: Modeling, scrutiny, and ratification." Transactions in GIS 25, no. 1: 291-310.
This paper proposes a new classification of correlated data types based upon the relative number of direct connections among observations, producing a family of correlated observations embracing seven categories, one whose empirical counterpart currently is unknown, and ranging from independent (i.e., no links) to approaching near-complete linkage (i.e., n(n – 1)/2 links). Analysis of specimen datasets from publicly available data sources furnishes empirical illustrations for these various categories. Their descriptions also include their historical context and calculation of their effective sample sizes (i.e., an equivalent number of independent observations). Concluding comments contain some state-of-the-art future research topics.
Daniel A. Griffith. A Family of Correlated Observations: From Independent to Strongly Interrelated Ones. Stats 2020, 3, 166 -184.
AMA StyleDaniel A. Griffith. A Family of Correlated Observations: From Independent to Strongly Interrelated Ones. Stats. 2020; 3 (3):166-184.
Chicago/Turabian StyleDaniel A. Griffith. 2020. "A Family of Correlated Observations: From Independent to Strongly Interrelated Ones." Stats 3, no. 3: 166-184.
Spatial cancer data analyses frequently utilize regression techniques to investigate associations between cancer incidences and potential covariates. Model specification, a process of formulating an appropriate model, is a well-recognized task in the literature. It involves a distributional assumption for a dependent variable, a proper set of predictor variables (i.e., covariates), and a functional form of the model, among other things. For example, one of the assumptions of a conventional statistical model is independence of model residuals, an assumption that can be easily violated when spatial autocorrelation is present in observations. A failure to account for spatial structure can result in unreliable estimation results. Furthermore, the difficulty of describing georeferenced data may increase with the presence of a positive and negative spatial autocorrelation mixture, because most current model specifications cannot successfully explain a mixture of spatial processes with a single spatial autocorrelation parameter. Particularly, properly accounting for a spatial autocorrelation mixture is challenging. This paper empirically investigates and uncovers a possible spatial autocorrelation mixture pattern in breast cancer incidences in Broward County, Florida, during 2000–2010, employing different model specifications. The analysis results show that Moran eigenvector spatial filtering provides a flexible method to examine such a mixture.
Lan Hu; Yongwan Chun; Daniel A. Griffith. Uncovering a positive and negative spatial autocorrelation mixture pattern: a spatial analysis of breast cancer incidences in Broward County, Florida, 2000–2010. Journal of Geographical Systems 2020, 22, 291 -308.
AMA StyleLan Hu, Yongwan Chun, Daniel A. Griffith. Uncovering a positive and negative spatial autocorrelation mixture pattern: a spatial analysis of breast cancer incidences in Broward County, Florida, 2000–2010. Journal of Geographical Systems. 2020; 22 (3):291-308.
Chicago/Turabian StyleLan Hu; Yongwan Chun; Daniel A. Griffith. 2020. "Uncovering a positive and negative spatial autocorrelation mixture pattern: a spatial analysis of breast cancer incidences in Broward County, Florida, 2000–2010." Journal of Geographical Systems 22, no. 3: 291-308.
House prices tend to be spatially correlated due to similar physical features shared by neighboring houses and commonalities attributable to their neighborhood environment. A multilevel model is one of the methodologies that has been frequently adopted to address spatial effects in modeling house prices. Empirical studies show its capability in accounting for neighborhood specific spatial autocorrelation (SA) and analyzing potential factors related to house prices at both individual and neighborhood levels. However, a standard multilevel model specification only considers within-neighborhood SA, which refers to similar house prices within a given neighborhood, but neglects between-neighborhood SA, which refers to similar house prices for adjacent neighborhoods that can commonly exist in residential areas. This oversight may lead to unreliable inference results for covariates, and subsequently less accurate house price predictions. This study proposes to extend a multilevel model using Moran eigenvector spatial filtering (MESF) methodology. This proposed model can take into account simultaneously between-neighborhood SA with a set of Moran eigenvectors as well as potential within-neighborhood SA with a random effects term. An empirical analysis of 2016 and 2017 house prices in Fairfax County, Virginia, illustrates the capability of a multilevel MESF model specification in accounting for between-neighborhood SA present in data. A comparison of its model performance and house price prediction outcomes with conventional methodologies also indicates that the multilevel MESF model outperforms standard multilevel and hedonic models. With its simple and flexible feature, a multilevel MESF model can furnish an appealing and useful approach for understanding the underlying spatial distribution of house prices.
Lan Hu; Yongwan Chun; Daniel A. Griffith. A Multilevel Eigenvector Spatial Filtering Model of House Prices: A Case Study of House Sales in Fairfax County, Virginia. ISPRS International Journal of Geo-Information 2019, 8, 508 .
AMA StyleLan Hu, Yongwan Chun, Daniel A. Griffith. A Multilevel Eigenvector Spatial Filtering Model of House Prices: A Case Study of House Sales in Fairfax County, Virginia. ISPRS International Journal of Geo-Information. 2019; 8 (11):508.
Chicago/Turabian StyleLan Hu; Yongwan Chun; Daniel A. Griffith. 2019. "A Multilevel Eigenvector Spatial Filtering Model of House Prices: A Case Study of House Sales in Fairfax County, Virginia." ISPRS International Journal of Geo-Information 8, no. 11: 508.
Negative spatial autocorrelation is one of the most neglected concepts in quantitative geography, regional science, and spatial statistics/econometrics in general. This paper focuses on and contributes to the literature in terms of the following three reasons why this neglect exists: Existing spatial autocorrelation quantification, the popular form of georeferenced variables studied, and the presence of both hidden negative spatial autocorrelation, and mixtures of positive and negative spatial autocorrelation in georeferenced variables. This paper also presents details and insights by furnishing concrete empirical examples of negative spatial autocorrelation. These examples include: Multi-locational chain store market areas, the shrinking city of Detroit, Dallas-Fort Worth journey-to-work flows, and county crime data. This paper concludes by enumerating a number of future research topics that would help increase the literature profile of negative spatial autocorrelation.
Daniel A. Griffith. Negative Spatial Autocorrelation: One of the Most Neglected Concepts in Spatial Statistics. Stats 2019, 2, 388 -415.
AMA StyleDaniel A. Griffith. Negative Spatial Autocorrelation: One of the Most Neglected Concepts in Spatial Statistics. Stats. 2019; 2 (3):388-415.
Chicago/Turabian StyleDaniel A. Griffith. 2019. "Negative Spatial Autocorrelation: One of the Most Neglected Concepts in Spatial Statistics." Stats 2, no. 3: 388-415.
Hyeongmo Koo; Monghyeon Lee; Yongwan Chun; Daniel A. Griffith. Space-time cluster detection with cross-space-time relative risk functions. Cartography and Geographic Information Science 2019, 47, 67 -78.
AMA StyleHyeongmo Koo, Monghyeon Lee, Yongwan Chun, Daniel A. Griffith. Space-time cluster detection with cross-space-time relative risk functions. Cartography and Geographic Information Science. 2019; 47 (1):67-78.
Chicago/Turabian StyleHyeongmo Koo; Monghyeon Lee; Yongwan Chun; Daniel A. Griffith. 2019. "Space-time cluster detection with cross-space-time relative risk functions." Cartography and Geographic Information Science 47, no. 1: 67-78.
This study develops a spatial additive mixed modeling (AMM) approach estimating spatial and non-spatial effects from large samples, such as millions of observations. Although fast AMM approaches are already well-established, they are restrictive in that they assume an known spatial dependence structure. To overcome this limitation, this study develops a fast AMM with the estimation of spatial structure in residuals and regression coefficients together with non-spatial effects. We rely on a Moran coefficient-based approach to estimate the spatial structure. The proposed approach pre-compresses large matrices whose size grows with respect to the sample size N before the model estimation; thus, the computational complexity for the estimation is independent of the sample size. Furthermore, the pre-compression is done through a block-wise procedure that makes the memory consumption independent of N. Eventually, the spatial AMM is memory-free and fast even for millions of observations. The developed approach is compared to alternatives through Monte Carlo simulation experiments. The result confirms the accuracy and computational efficiency of the developed approach. The developed approaches are implemented in an R package spmoran.
Daisuke Murakami; Daniel A. Griffith. A memory-free spatial additive mixed modeling for big spatial data. 2019, 1 .
AMA StyleDaisuke Murakami, Daniel A. Griffith. A memory-free spatial additive mixed modeling for big spatial data. . 2019; ():1.
Chicago/Turabian StyleDaisuke Murakami; Daniel A. Griffith. 2019. "A memory-free spatial additive mixed modeling for big spatial data." , no. : 1.
Moran eigenvector spatial filtering (MESF) furnishes an alternative method to account for spatial autocorrelation in linear regression specifications describing georeferenced data, although spatial auto-models also are widely used. The utility of this MESF methodology is even more impressive for the non-Gaussian models because its flexible structure enables it to be easily applied to generalized linear models, which include Poisson, binomial, and negative binomial regression. However, the implementation of MESF can be computationally challenging, especially when the number of geographic units, n, is large, or massive, such as with a remotely sensed image. This intensive computation aspect has been a drawback to the use of MESF, particularly for analyzing a remotely sensed image, which can easily contain millions of pixels. Motivated by Curry, this paper proposes an approximation approach to constructing eigenvector spatial filters (ESFs) for a large spatial tessellation. This approximation is based on a divide-and-conquer approach. That is, it constructs ESFs separately for each sub-region, and then combines the resulting ESFs across an entire remotely sensed image. This paper, employing selected specimen remotely sensed images, demonstrates that the proposed technique provides a computationally efficient and successful approach to implement MESF for large or massive spatial tessellations.
Daniel A. Griffith; Yongwan Chun. Implementing Moran eigenvector spatial filtering for massively large georeferenced datasets. International Journal of Geographical Information Science 2019, 33, 1703 -1717.
AMA StyleDaniel A. Griffith, Yongwan Chun. Implementing Moran eigenvector spatial filtering for massively large georeferenced datasets. International Journal of Geographical Information Science. 2019; 33 (9):1703-1717.
Chicago/Turabian StyleDaniel A. Griffith; Yongwan Chun. 2019. "Implementing Moran eigenvector spatial filtering for massively large georeferenced datasets." International Journal of Geographical Information Science 33, no. 9: 1703-1717.
Being a hot topic in recent years, many studies have been conducted with spatial data containing massive numbers of observations. Because initial developments for classical spatial autocorrelation statistics are based on rather small sample sizes, in the context of massive spatial datasets, this paper presents extensions to efficiency and statistical power comparisons between the Moran coefficient and the Geary ratio for different variable distribution assumptions and selected geographic neighborhood definitions. The question addressed asks whether or not earlier results for small n extend to large and massively large n, especially for non-normal variables; implications established are relevant to big spatial data. To achieve these comparisons, this paper summarizes proofs of limiting variances, also called asymptotic variances, to do the efficiency analysis, and derives the relationship function between the two statistics to compare their statistical power at the same scale. Visualization of this statistical power analysis employs an alternative technique that already appears in the literature, furnishing additional understanding and clarity about these spatial autocorrelation statistics. Results include: the Moran coefficient is more efficient than the Geary ratio for most surface partitionings, because this index has a relatively smaller asymptotic as well as exact variance, and the superior power of the Moran coefficient vis-à-vis the Geary ratio for positive spatial autocorrelation depends upon the type of geographic configuration, with this power approaching one as sample sizes become increasingly large. Because spatial analysts usually calculate these two statistics for interval/ration data, this paper also includes comments about the join count statistics used for nominal data.
Qing Luo; Daniel A. Griffith; Huayi Wu. Spatial autocorrelation for massive spatial data: verification of efficiency and statistical power asymptotics. Journal of Geographical Systems 2019, 21, 237 -269.
AMA StyleQing Luo, Daniel A. Griffith, Huayi Wu. Spatial autocorrelation for massive spatial data: verification of efficiency and statistical power asymptotics. Journal of Geographical Systems. 2019; 21 (2):237-269.
Chicago/Turabian StyleQing Luo; Daniel A. Griffith; Huayi Wu. 2019. "Spatial autocorrelation for massive spatial data: verification of efficiency and statistical power asymptotics." Journal of Geographical Systems 21, no. 2: 237-269.
While spatially varying coefficient (SVC) modeling is popular in applied science, its computational burden is substantial. This is especially true if a multiscale property of SVC is considered. Given this background, this study develops a Moran’s eigenvector-based spatially varying coefficients (M-SVC) modeling approach that estimates multiscale SVCs computationally efficiently. This estimation is accelerated through a (i) rank reduction, (ii) pre-compression, and (iii) sequential likelihood maximization. Steps (i) and (ii) eliminate the sample size N from the likelihood function; after these steps, the likelihood maximization cost is independent of N. Step (iii) further accelerates the likelihood maximization so that multiscale SVCs can be estimated even if the number of SVCs, K, is large. The M-SVC approach is compared with geographically weighted regression (GWR) through Monte Carlo simulation experiments. These simulation results show that our approach is far faster than GWR when N is large, despite numerically estimating 2K parameters while GWR numerically estimates only 1 parameter. Then, the proposed approach is applied to a land price analysis as an illustration. The developed SVC estimation approach is implemented in the R package “spmoran.”
Daisuke Murakami; Daniel A. Griffith. Spatially varying coefficient modeling for large datasets: Eliminating N from spatial regressions. Spatial Statistics 2019, 30, 39 -64.
AMA StyleDaisuke Murakami, Daniel A. Griffith. Spatially varying coefficient modeling for large datasets: Eliminating N from spatial regressions. Spatial Statistics. 2019; 30 ():39-64.
Chicago/Turabian StyleDaisuke Murakami; Daniel A. Griffith. 2019. "Spatially varying coefficient modeling for large datasets: Eliminating N from spatial regressions." Spatial Statistics 30, no. : 39-64.
Yongwan Chun; Mei-Po Kwan; Daniel A. Griffith. Uncertainty and context in GIScience and geography: challenges in the era of geospatial big data. International Journal of Geographical Information Science 2019, 33, 1131 -1134.
AMA StyleYongwan Chun, Mei-Po Kwan, Daniel A. Griffith. Uncertainty and context in GIScience and geography: challenges in the era of geospatial big data. International Journal of Geographical Information Science. 2019; 33 (6):1131-1134.
Chicago/Turabian StyleYongwan Chun; Mei-Po Kwan; Daniel A. Griffith. 2019. "Uncertainty and context in GIScience and geography: challenges in the era of geospatial big data." International Journal of Geographical Information Science 33, no. 6: 1131-1134.
Although spatially varying coefficient (SVC) models have attracted considerable attention in applied science, they have been criticized as being unstable. The objective of this study is to show that capturing the “spatial scale” of each data relationship is crucially important to make SVC modeling more stable and, in doing so, adds flexibility. Here, the analytical properties of six SVC models are summarized in terms of their characterization of scale. Models are examined through a series of Monte Carlo simulation experiments to assess the extent to which spatial scale influences model stability and the accuracy of their SVC estimates. The following models are studied: (1) geographically weighted regression (GWR) with a fixed distance or (2) an adaptive distance bandwidth (GWRa); (3) flexible bandwidth GWR (FB-GWR) with fixed distance or (4) adaptive distance bandwidths (FB-GWRa); (5) eigenvector spatial filtering (ESF); and (6) random effects ESF (RE-ESF). Results reveal that the SVC models designed to capture scale dependencies in local relationships (FB-GWR, FB-GWRa, and RE-ESF) most accurately estimate the simulated SVCs, where RE-ESF is the most computationally efficient. Conversely, GWR and ESF, where SVC estimates are naïvely assumed to operate at the same spatial scale for each relationship, perform poorly. Results also confirm that the adaptive bandwidth GWR models (GWRa and FB-GWRa) are superior to their fixed bandwidth counterparts (GWR and FB-GWR). Key Words: flexible bandwidth geographically weighted regression, Monte Carlo simulation, nonstationarity, random effects eigenvector spatial filtering, spatial scale.
Daisuke Murakami; Binbin Lu; Paul Harris; Chris Brunsdon; Martin Charlton; Tomoki Nakaya; Daniel A. Griffith. The Importance of Scale in Spatially Varying Coefficient Modeling. Annals of the American Association of Geographers 2018, 109, 50 -70.
AMA StyleDaisuke Murakami, Binbin Lu, Paul Harris, Chris Brunsdon, Martin Charlton, Tomoki Nakaya, Daniel A. Griffith. The Importance of Scale in Spatially Varying Coefficient Modeling. Annals of the American Association of Geographers. 2018; 109 (1):50-70.
Chicago/Turabian StyleDaisuke Murakami; Binbin Lu; Paul Harris; Chris Brunsdon; Martin Charlton; Tomoki Nakaya; Daniel A. Griffith. 2018. "The Importance of Scale in Spatially Varying Coefficient Modeling." Annals of the American Association of Geographers 109, no. 1: 50-70.