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Twenty years have passed since Bivand and Gebhardt (J Geogr Syst 2(3):307–317, 2000. https://doi.org/10.1007/PL00011460) indicated that there was a good match between the then nascent open-source R programming language and environment and the needs of researchers analysing spatial data. Recalling the development of classes for spatial data presented in book form in Bivand et al. (Applied spatial data analysis with R. Springer, New York, 2008, Applied spatial data analysis with R, 2nd edn. Springer, New York, 2013), it is important to present the progress now occurring in representation of spatial data, and possible consequences for spatial data handling and the statistical analysis of spatial data. Beyond this, it is imperative to discuss the relationships between R-spatial software and the larger open-source geospatial software community on whose work R packages crucially depend. [ABSTRACT FROM AUTHOR]

Zhou and Hanson; Zhou and Hanson; Zhou and Hanson (2015 , Nonparametric Bayesian Inference in Biostatistics, pages 215–46. Cham: Springer; 2018, Journal of the American Statistical Association, 113, 571–81; 2020, spBayesSurv: Bayesian Modeling and Analysis of Spatially Correlated Survival Data. R package version 1.1.4) and Zhou et al. (2020, Journal of Statistical Software, Articles, 92, 1–33) present methods for estimating spatial survival models using areal data. This article applies their methods to a dataset recording New Orleans business decisions to re-open after Hurricane Katrina; the data were included in LeSage et al. (2011b , Journal of the Royal Statistical Society: Series A (Statistics in Society), 174, 1007—27). In two articles (LeSage etal., 2011a , Significance, 8, 160—63; 2011b, Journal of the Royal Statistical Society: Series A (Statistics in Society), 174, 1007—27), spatial probit models are used to model spatial dependence in this dataset, with decisions to re-open aggregated to the first 90, 180 and 360 days. We re-cast the problem as one of examining the time-to-event records in the data, right-censored as observations ceased before 175 businesses had re-opened; we omit businesses already re-opened when observations began on Day 41. We are interested in checking whether the conclusions about the covariates using aspatial and spatial probit models are modified when applying survival and spatial survival models estimated using MCMC and INLA. In general, we find that the same covariates are associated with re-opening decisions in both modelling approaches. We do however find that data collected from three streets differ substantially, and that the streets are probably better handled separately or that the street effect should be included explicitly. [ABSTRACT FROM AUTHOR]

Bayesian methods and software for spatial data analysis are well-established now in the broader scientific community generally and in the spatial data analysis community specifically. Despite the wide application of spatial models, the analysis of multivariate spatial data using the integrated nested Laplace approximation through its R package (R-INLA) has not been widely described in the existing literature. Therefore, the main objective of this article is to demonstrate that R-INLA is a convenient toolbox to analyse different types of multivariate spatial datasets. This will be illustrated by analysing three datasets which are publicly available. Furthermore, the details and the R code of these analyses are provided to exemplify how to fit models to multivariate spatial datasets with R-INLA. [ABSTRACT FROM AUTHOR]

When estimating spatial regression models by maximum likelihood using spatial weights matrices to represent spatial processes, computing the Jacobian, ln(| I − λ W|), remains a central problem. In principle, and for smaller data sets, the use of the eigenvalues of the spatial weights matrix provides a very rapid resolution. Analytical eigenvalues are available for large regular grids. For larger problems not on regular grids, including those induced in spatial panel and dyadic (network) problems, solving the eigenproblem may not be feasible, and a number of alternatives have been proposed. This article surveys selected alternatives, and comments on their relative usefulness, covering sparse Cholesky and sparse LU factorizations, and approximations such as Monte Carlo, Chebyshev, and using lower-order moments with interpolation. The results are presented in terms of component-wise differences between sets of Jacobians for selected data sets. In conclusion, recommendations are made for a number of analytical settings. Al estimar modelos de regresión espacial con el método del máxima verosimilitud (máximum likelihood) y usando matrices de pesos espaciales para representar procesos espaciales, cálculo del término jacobiano ( jabobian)-ln(| I−λ W|)- sigue siendo un problema central. En principio, y para bases de datos más pequeñas, el uso de los valores propios ( eigenvalues) de la matriz de pesos espaciales proporciona una solución muy rápida. Los eigenvalues analíticos para retículas o grillas grandes y regulares son ya conocidos. Para problemas más grandes, que no se presentan en mallas regulares -incluyendo aquellos que se inducen en problemas de paneles espaciales y en problemas de (redes) diádicas-, es posible que resolver el eigenproblem no sea posible. Este artículo estudia una selección de alternativas y comenta acerca de su relativa utilidad. Se cubren las facorizaciones de tipo Cholesky disperso ( sparse Cholesky) y de tipo LU dispersas ( sparse LU), las aproximaciones Monte Carlo, y Chebyshev, así mismo se utiliza momentos de bajo-orden ( lower-order) con interpolación. Los resultados se presentan en términos de diferencias de componentes entre sets de términos jacobianos para bases de datos seleccionadas. En conclusión, se hacen recomendaciones para una serie de contextos analíticos. 当采用表征空间过程的空间权重矩阵对空间回归模型进行最大似然估计时，雅可比矩阵ln(|I−λW|)的计算仍是核心问题。对于小数据集，原则上可利用空间权重矩阵的特征值提供一种快速的解决方案，对于大型规则格网数据特征值分析同样有效。但对于不规则格网大型问题，包括从空间面板和二元（网络）问题中引伸的问题，利用特征值的解决方案可能不适用，对此学术界提出了多种可选替代方案。本文选取已有的几种替代方案并评论各自的相对有效性，其中包括稀疏Cholesky分解和稀疏LU分解法，Monte Carlo和 Chebyshev近似模拟法以及低阶矩插值法。结果以所选数据集雅可比矩阵间特定组份的差异方式显示。最后，推荐了一些分析设定。 [ABSTRACT FROM AUTHOR]

Knowing about the challenges and opportunities of spatial autocorrelation is one thing, but applying the measures to one's own data is another matter entirely. While manual computation of the measures for toy data sets is possible, applying them to small data sets required the use of computers and thus software. This article will shed some light on how the measures were and are implemented in software and on implementation issues that are still not fully resolved. [ABSTRACT FROM AUTHOR]

The integrated nested Laplace approximation (INLA) provides a fast and effective method for marginal inference in Bayesian hierarchical models. This methodology has been implemented in the R-INLA package which permits INLA to be used from within R statistical software. Although INLA is implemented as a general methodology, its use in practice is limited to the models implemented in the R-INLA package. Spatial autoregressive models are widely used in spatial econometrics but have until now been lacking from the R-INLA package. In this paper, we describe the implementation and application of a new class of latent models in INLA made available through R-INLA. This new latent class implements a standard spatial lag model. The implementation of this latent model in R-INLA also means that all the other features of INLA can be used for model fitting, model selection and inference in spatial econometrics, as will be shown in this paper. Finally, we will illustrate the use of this new latent model and its applications with two data sets based on Gaussian and binary outcomes. [ABSTRACT FROM AUTHOR]

Since spatial issues have become more important in economic theory, it is of interest to examine how space is represented. In empirical terms, this concerns at least the representation of distance and proximity. Both of these may be represented and operationalized in a number of ways, with possible consequences for inferences when modeling. This question is related to the representation of spatial entities, and itself plays into the treatment of spatial dependence as substantive and/or just a nuisance. Because other disciplines face similar questions—for example ecology or epidemiology, their conceptualizations and operationalizations of space will also be used for comparative purposes. [ABSTRACT FROM AUTHOR]

The work discussed in Bivand and Brunstad (2003 ) was an attempt to throw light on apparent variability in regional convergence in relation to agriculture as a sector subject to powerful political measures, in Western Europe, 1989–1999. The present study takes up a number of points made in conclusion in that paper. Since it is possible that the non-stationarity found there is related to further missing variables, including the inadequacy of the way in which agricultural subsidies are represented, we attempt to replace the agriculture variables with better estimates of producer subsidy equivalents. It is also sensible to check that agricultural support is not masking or masked by other variables, for example human capital. The article is also an account of the development of software contributed to the project ( Development Core Team, 2005 ) as packages, in particular the spdep package for spatial econometrics. New functions generously contributed by researchers will be presented and compared. We find that agricultural support does impact regional economic growth after human capital is taken into consideration, and that we can show that apparent non-stationarity is alleviated by adding these variables.We further find that the moderated remaining spatial autocorrelation can best be represented by a substantive spatial lag model. [ABSTRACT FROM AUTHOR]

This article reports on work in progress on the implementation of functions for spatial statistical analysis, in particular of lattice/area data in the language environment. The underlying spatial weights matrix classes, as well as methods for deriving them from data from commonly used geographical information systems are presented, handled using other contributed packages. Since the initial release of some functions in 2001, and the release of the spdep package in 2002, experience has been gained in the use of various functions. The topics covered are the ingestion of positional data, exploratory data analysis of positional, attribute, and neighborhood data, and hypothesis testing of autocorrelation for univariate data. It also provides information about community building in using for analyzing spatial data. [ABSTRACT FROM AUTHOR]

Placing spatial econometrics and more generally spatial statistics in the context of an extensible data analysis environment such as R exposes similarities and differences between traditions of analysis. This can be fruitful, and is explored here in relation to prediction and other methods usually applied to fitted models in R. Objects in R may be assigned a class attribute, including fitted model objects. Such fitted model objects may be provided with methods allowing them to be displayed, compared, and used for prediction, and it is of interest to see whether fitted spatial models can be treated in the same way. [ABSTRACT FROM AUTHOR]

Abstract. R is a language similar to S for statistical data analysis, based on modern programming concepts and released under the GNU General Public License. It permits the integration of program scripts with compiled dynamically loaded libraries of functions when computing speed is important. Following a broad outline of existing collections of functions for spatial statistics written for s, we show how they may be ported to R, and compare their characteristics. We further demonstrate how existing work may be extended to topics not yet covered, and how libraries of functions may be constructed. [ABSTRACT FROM AUTHOR]

The software for spatial econometrics available in the R system for statistical computing is reviewed. The methods are illustrated in a historical perspective, highlighting the main lines of development and employing historically relevant datasets in the examples. Estimators and tests for spatial cross-sectional and panel models based either on maximum likelihood or on generalized moments methods are presented. The paper is concluded reviewing some current active lines of research in spatial econometric software methods. [ABSTRACT FROM AUTHOR]

The impact of localisation and urbanisation economies on regional manufacturing development in Poland 1976-96 is assessed in terms of employment and the regional convergence or divergence of the economy. Current research on the role of dynamic production externalities in regional manufacturing development is examined, starting with a review of recent literature on the nature of such externalities in manufacturing location, and how positive externalities may influence the spatial clustering of manufacturing industries. The paper shows that radical changes have occurred in patterns of Polish regional manufacturing employment, both with regard to sectors and regions. Transition is refocusing the regional economy on strong regional centres, and on sectors regarded with little favour in the planned economy. [ABSTRACT FROM AUTHOR]

Species distributional or trait data based on range map (extent-of-occurrence) or atlas survey data often display spatial autocorrelation, i.e. locations close to each other exhibit more similar values than those further apart. If this pattern remains present in the residuals of a statistical model based on such data, one of the key assumptions of standard statistical analyses, that residuals are independent and identically distributed (i.i.d), is violated. The violation of the assumption of i.i.d. residuals may bias parameter estimates and can increase type I error rates (falsely rejecting the null hypothesis of no effect). While this is increasingly recognised by researchers analysing species distribution data, there is, to our knowledge, no comprehensive overview of the many available spatial statistical methods to take spatial autocorrelation into account in tests of statistical significance. Here, we describe six different statistical approaches to infer correlates of species’ distributions, for both presence/absence (binary response) and species abundance data (poisson or normally distributed response), while accounting for spatial autocorrelation in model residuals: autocovariate regression; spatial eigenvector mapping; generalised least squares; (conditional and simultaneous) autoregressive models and generalised estimating equations. A comprehensive comparison of the relative merits of these methods is beyond the scope of this paper. To demonstrate each method's implementation, however, we undertook preliminary tests based on simulated data. These preliminary tests verified that most of the spatial modeling techniques we examined showed good type I error control and precise parameter estimates, at least when confronted with simplistic simulated data containing spatial autocorrelation in the errors. However, we found that for presence/absence data the results and conclusions were very variable between the different methods. This is likely due to the low information content of binary maps. Also, in contrast with previous studies, we found that autocovariate methods consistently underestimated the effects of environmental controls of species distributions. Given their widespread use, in particular for the modelling of species presence/absence data (e.g. climate envelope models), we argue that this warrants further study and caution in their use. To aid other ecologists in making use of the methods described, code to implement them in freely available software is provided in an electronic appendix. [ABSTRACT FROM AUTHOR]

Global and local analyses of spatial autocorrelation are commonplace in spatial archaeology. However, they are exclusively focused on continuous numerical parameters, even though logical (presence/absence) and categorical parameters are equally frequent in archaeological research. Global tests of spatial dependence for categorical data are routinely used in other fields, and local versions of these tests (known as LICD) have recently been developed. This paper provides a detailed description of such methods, and presents the first adaptation and application of LICD to archaeological data. Different LICD versions have been tested on two case-studies: (a) an archaeological grid, with object presence or absence recorded for each cell; (b) Historic Landscape Characterisation, with the origin of character types (mediaeval, post-mediaeval or modern) recorded for each region. These examples seek to showcase and promote the use of LICD in landscape and intra-site archaeology. • Spatial autocorrelation analysis is commonplace in archaeology, but exclusively focused on continuous numerical parameters. • Global tests of spatial autocorrelation for categorical data are routinely used in other fields. • Local indicators of spatial association for categorical data (LICD) have recently been developed. • This paper provides the first adaptation of LICD to archaeological data. • LICD can be used to analyse archaeological grids as well as regions of variable size. [ABSTRACT FROM AUTHOR]