Gaussian Process Regression and Bayesian Model Averaging: An Alternative Approach to Modeling Spatial Phenomena

Gaussian Process Regression (GPR) is a nonparametric technique that is capable of yielding reliable out‐of‐sample predictions in the presence of highly nonlinear unknown relationships between dependent and explanatory variables. But in terms of identifying relevant explanatory variables, this method is far less explicit about questions of statistical significance. In contrast, more traditional spatial econometric models, such as spatial autoregressive models or spatial error models, place rather strong prior restrictions on the functional form of relationships, but allow direct inference with respect to explanatory variables. In this article, we attempt to combine the best of both techniques by augmenting GPR with a Bayesian Model Averaging (BMA) component that allows for the identification of statistically relevant explanatory variables while retaining the predictive performance of GPR. In particular, GPR‐BMA yields a posterior probability interpretation of model‐inclusion frequencies that provides a natural measure of the statistical relevance of each variable. Moreover, while such frequencies offer no direct information about the signs of local marginal effects, it is shown that partial derivatives based on the mean GPR predictions do provide such information. We illustrate the additional insights made possible by this approach by applying GPR‐BMA to a benchmark BMA data set involving potential determinants of cross‐country economic growth. It is shown that localized marginal effects based on partial derivatives of mean GPR predictions yield additional insights into comparative growth effects across countries.     

Computational Modeling of the Seismic Performance of Beam-Column Subassemblies

Analytical studies are carried out to investigate the effectiveness of finite element modeling procedures in accurately capturing the nonlinear cyclic response of beam-column subassemblies. The analyses are performed using program VecTor2, employing only default or typical material constitutive models and behavior mechanisms in order to assess analysis capabilities without the need for special modeling techniques or program modifications. The specimens considered cover a wide range of conditions, and include interior and exterior seismically and non seismically designed beam-column subassemblies. It is shown that finite element analyses can achieve good accuracy in determining the strength, deformation response, energy dissipation, and failure mode of reinforced concrete beam-column subassemblies under seismic loading conditions.     

Spatial Moving Behavior of Two-Earner Households

Economic theory suggests that job choice, residential choice and commuting behavior are simultaneously determined. The case of two-earner households deserves special attention because the two wage earners share a dwelling but have different workplaces. We base our analysis of spatial moving behavior on search theory. We demonstrate that job mobility depends positively on the distance between the workplaces of the two wage earners. Residential mobility seems to be negatively influenced by the distance between the workplaces of the two wage earners. The search model also indicates that two-earner households will, on average, move less often than single wage earners.     

Levels of Spatial Knowledge and Urban Travel Modeling

Models of spatial behavior implicitly assume a direct connection between the individual's utility function and his actual behavior. In reality, this link is mediated by the extent and quality of his spatial knowledge. Without sufficient knowledge, the chosen behavior will be selected from a small number of known alternatives. Using a route choice study in Beer Sheva, this paper investigates the extent and the level of spatial knowledge exhibited by the public in episodic, nonroutine travel. It demonstrates that their knowledge stabilizes at the intermediate “route level,” whereas only professional drivers attain the highest “survey level.” The cognitive opportunity sets of drivers at the route level are idiosyncratic. Accordingly, route selection by the general public was found largely unpredictable. Implications for urban travel modeling are discussed.     

Duration Modeling of Spatial Point Patterns

This paper attempts to further the research by Odland and Ellis (1992) in applying event history methodology to the analysis of spatial point patterns (that is, event patterns). Its empirical focus is the event pattern derived from the adoption of an agricultural innovation, the Harvestore, in southern Ontario, Canada, from 1963 to 1986. Event history analysis involves the use of discrete-state, continuous-time stochastic models to investigate a temporal longitudinal record on discrete variables. Event history models are usually concerned with durations of time between events and the effects of intertemporal time dependencies on future event occurrences. As such, they are often referred to as duration models. Many of the methods used in event history analysis allow the use of other nonnegative interval measurements in place of standard temporal intervals to investigate a series of events. In particular, spatial intervals (or durations) of distances between events may also be accommodated by event history models. Our analysis extends the previous research of Odland and Ellis (1992) by using a wider range of parametric models to explore duration dependence, investigating the role of spatial censoring, and using a more extensive set of explanatory variables. In addition, simulation experiments and graphical tests are used to evaluate the empirical event pattern against one generated from Complete Spatial Randomness. Results indicate that the event pattern formed by the Harvestore adopter farms is clustered (that is, is described by positive duration dependency), the sales agent is a significant factor in the distribution of adopters, and that contrasting results are obtained from the analysis using censored data versus uncensored data.     

Cognitive Maps and Spatial Behavior Of Consumers

Two multidimensional scaling algorithms are used to externally measure cognitive maps of supermarket locations for a sample of sixty-one supermarket shoppers. Issues raised in the construction of the cognitive maps are discussed. The relationship between the derived cognitive maps and consumer behavior is compared to the relationship between physical maps and consumer behavior. Behavior is shown to be more closely related to cognitive maps. Differences in cognitive maps are defined and canonically correlated with consumers' socioeconomic and locational attributes. While aggregate cognitive maps are closely associated with physical maps, there is substantial variation between individual maps. This variation is related to shopping behavior and selected socioeconomic and locational characteristics of consumers.     

Set-determined Process and the Growth of Spatial Structure

We present an analysis of the effects of different information flow patterns on the growth of spatial structure in a broad class of systems. Examples are drawn from plant and message diffusion processes, the growth of herding in animal populations and, in particular, the evolution of cities in human populations. We model the actions of an “individual” as a response to gradients in a transformation of the “real” space, this transformation being the individual's information map of the space. Interesting deductions occur as a result of allowing the individual's information map to vary from extremely local to extremely global. In the city growth model for example, if migration decisions are based upon extremely local information, then the system is characterized by instability and the lack of any well-defined spatial structure. As the localness of this information map decreases, the system is characterized by the development of well defined spatial structure with a characteristic distance separating the “cities.” In a particular case, we show that the wavelength of the dominant spatial structure is directly related to the size of an individual's information field. These effects are a consequence of interactions between individuals that arise from the nonlocalness of the information fields. We interpret the early growth stages in these models in terms of linear filters.     

Single and Multiscale Models of Process Spatial Heterogeneity

Recent work in local spatial modeling has affirmed and broadened interest in multivariate local spatial analysis. Two broad approaches have emerged: Geographically Weighted Regression (GWR) which follows a frequentist perspective and Bayesian Spatially Varying Coefficients models. Although several comparisons between the two approaches exist, recent developments, particularly in GWR, mean that these are incomplete and missing some important axes of comparison. Consequently, there is a need for a more thorough comparison of the two families of local estimators, including recent developments in multiscale variants and their relative performance under controlled conditions. We find that while both types of local models generally perform similarly on a series of criteria, some interesting and important differences exist.     

A Methodology for Neural Spatial Interaction Modeling

This paper attempts to develop a mathematically rigid and unified framework for neural spatial interaction modeling. Families of classical neural network models, but also less classical ones such as product unit neural network ones are considered for the cases of unconstrained and singly constrained spatial interaction flows. Current practice appears to suffer from least squares and normality assumptions that ignore the true integer nature of the flows and approximate a discrete‐valued process by an almost certainly misrepresentative continuous distribution. To overcome this deficiency we suggest a more suitable estimation approach, maximum likelihood estimation under more realistic distributional assumptions of Poisson processes, and utilize a global search procedure, called Alopex, to solve the maximum likelihood estimation problem. To identify the transition from underfitting to overfitting we split the data into training, internal validation, and test sets. The bootstrapping pairs approach with replacement is adopted to combine the purity of data splitting with the power of a resampling procedure to overcome the generally neglected issue of fixed data splitting and the problem of scarce data. In addition, the approach has power to provide a better statistical picture of the prediction variability. Finally, a benchmark comparison against the classical gravity models illustrates the superiority of both, the unconstrained and the origin constrained neural network model versions in terms of generalization performance measured by Kullback and Leibler's information criterion.     

Some Spatial Representation Problems in Disease Modeling

The paper examines the applicability of spatial representation ideas to the determination of equilibrium solutions for multiregion disease models. In particular, alternatives to the standard specification of regionally variable infectivity rates are devised and their impact on the space-time behavior of a carrier model for Hodgkin's disease is assessed using data for Greater Manchester.     

Continuous‐Time Modeling with Spatial Dependence

(Spatial) panel data are routinely modeled in discrete time (DT). However, compelling arguments exist for continuous‐time (CT) modeling of (spatial) panel data. Particularly, most social processes evolve in CT, so that statistical analysis in DT is an oversimplification, gives an incomplete representation of reality, and may lead to misinterpretation of estimation results. The most compelling reason for a CT approach is that, in contrast to DT modeling, it allows adequate modeling of dynamic adjustment processes. This article introduces spatial dependence in a CT modeling framework. We propose a nonlinear structural equation model (SEM) with latent variables for estimation of the exact discrete model (EDM), which links CT model parameters to DT observations. The use of a SEM with latent variables enables a specification that accounts for measurement errors in the variables, leading to a reduction of attenuation bias (i.e., disattenuation). The SEM‐CT model with spatial dependence developed here is the first dynamic SEM with spatial dependence. A simple regional labor market model for Germany, comprising changes in unemployment and population as endogenous state variables, and changes in regional average wages and in the structure of the manufacturing sector as exogenous input variables, illustrates this spatial econometric SEM‐CT framework. El modelamiento de datos panel espaciales se realiza habitualmente utilizando una conceptualización del tiempo discreto (TD). Sin embargo, existen argumentos de peso para conceptualizar el tiempo de manera continua (TC). En concreto, la mayoría de procesos sociales se desarrolla en TC, por lo que el análisis estadístico en DT trae como consecuencia una simplificación excesiva de los procesos, da una representación incompleta de la realidad, y puede conducir a una interpretación errónea de los resultados de la estimación. La razón más convincente para el uso de un enfoque CT es que a diferencia de modelos DT, una conceptualización CT permite el modelado adecuado de los procesos de ajuste dinámico (dynamic adjustment). Este artículo incorpora la dependencia espacial en un marco de modelamiento con CT. Los autores proponen un modelo de ecuaciones estructurales no lineal (nonlinear structural equation model ‐SEM) con variables latentes para la estimación del modelo discreto exacto (exact discrete model‐EDM), que vincula los parámetros del modelo CT a las observaciones de DT. El uso de un SEM con variables latentes permite una especificación que da cuenta de los errores de medición en las variables, dando lugar a una reducción del sesgo de atenuación (es decir, “desatenuacion”). El modelo SEM‐CT con dependencia espacial desarrollado en el presente estudio es el primer SEM dinámico con dependencia espacial. Para ilustrar el marco conceptual SEM‐CT los autores presentan un modelo simple del mercado laboral regional de Alemania. El modelo está compuesto por los cambios en el desempleo y la población como variables endógenas de estado, y los cambios en los salarios regionales promedio y en la estructura del sector manufacturero como variables de entrada exógenas. （空间）面板数据通常基于离散时间（DT）进行建模。然而更令人信服的观点是基于连续时间（CT）进行（空间）面板数据建模。特别是多数社会过程均在连续时间中演化,基于离散时间的统计分析可能过度简化,使得对现实状况的表达不完备,并可能导致对估计结果的错误解释。相比于离散时间（DT）建模,连续时间（CT）建模最具说服力的原因在于在建模过程中允许足够多的动态调整。本文介绍了CT模型框架中的空间依赖性。把CT模型参数链接到DT观察值中,我们提出了用于估计精确离散模型（EDM）的包含潜变量的非线性结构方程模型（SEM）。包含潜在变量的SEM提供了变量测量误差的计算方案,使得衰减偏差（如反衰减性）减小。本文了提出的空间相关SEM‐CT模型是第一个动态空间相关的SEM模型,并以德国一个简单的区域劳动力市场模型为例,以失业和人口构成变化为内生状态变量,以区域平均工资和制造业结构部门变化为外生输入变量,阐述了该空间计量SEM‐ CT模型的框架。     

Decomposition as Practice and Process: Creating Boundary Objects in Computational Humanities

Abstract

The emergent reflexive process, by which researchers in a computational humanities project work towards a viable organizational modality for interdisciplinary collaboration, is analyzed. Using the metaphor of decomposition, successful collaboration between computer scientists and humanities scholars can be seen to require a reflexive scrutiny — a decomposition — of the disciplinary research processes that are involved, thus allowing crucial differences with respect to typical ways of posing research questions, the role of data, and the rhythm of the research process to be highlighted. It is argued that the currently popular expectation towards data as a self-identical organizational unit tends to downplay the role of decomposition as practice and process. A European cyberinfrastructure initiative that tries to respect the specificities of scholarly practice in the humanities is critically assessed, reflecting in particular on the inherent tension between ‘mutual shaping’ of digital tools and their users on the one hand, and the policy interest in efficient, functionalist design principles on the other.     

Nonlinear Multivariate Spatial Modeling Using NLPCA and Pair‐Copulas

A novel geostatistical modeling approach is developed to model nonlinear multivariate spatial dependence using nonlinear principal component analysis (NLPCA) and pair‐copulas. In spatial studies, multivariate measurements are frequently collected at each location. The dependence between such measurements can be complex. In this article, a multivariate geostatistical model is developed that can capture both nonlinear spatial dependence across locations and nonlinear dependence between measurements at a particular location. Nonlinear multivariate dependence between spatial variables is removed using NLPCA. Subsequently, a pair‐copula based model is fitted to each transformed variable to model the univariate nonlinear spatial dependencies. NLPCA and pair‐copulas, within the proposed model, are compared with stepwise conditional transformation (SCT) and conventional kriging. The results show that, for the two case studies presented, the proposed model that utilizes NLPCA and pair‐copulas reproduces nonlinear multivariate structures and univariate distributions better than existing methods based on SCT and kriging.     

Modeling the Uncertainty of Slope and Aspect Estimates Derived from Spatial Databases

Estimates of slope and aspect are commonly made from digital elevation models (DEMs), and are subject to the uncertainty present in such models. We show that errors in slope and aspect depend on the spatial structure of DEM errors. We propose a general-purpose model of DEM errors in which a spatially auto-regressive random field is added as a disturbance term to elevations. In addition, we propose a general procedure for propagating such errors through GIS operations. In the absence of explicit information on the spatial structure of DEM errors, we demonstrate the potential utility of a worst-case analysis. A series of simulations are used to make general observations about the nature and severity of slope and aspect errors.