A Statistical Toolbox For Mining And Modeling Spatial Data

Most data mining projects in spatial economics start with an evaluation of a set of attribute variables on a sample of spatial entities, looking for the existence and strength of spatial autocorrelation, based on the Moran’s and the Geary’s coefficients, the adequacy of which is rarely challenged, despite the fact that when reporting on their properties, many users seem likely to make mistakes and to foster confusion. My paper begins by a critical appraisal of the classical definition and rational of these indices. I argue that while intuitively founded, they are plagued by an inconsistency in their conception. Then, I propose a principled small change leading to corrected spatial autocorrelation coefficients, which strongly simplifies their relationship, and opens the way to an augmented toolbox of statistical methods of dimension reduction and data visualization, also useful for modeling purposes. A second section presents a formal framework, adapted from recent work in statistical learning, which gives theoretical support to our definition of corrected spatial autocorrelation coefficients. More specifically, the multivariate data mining methods presented here, are easily implementable on the existing (free) software, yield methods useful to exploit the proposed corrections in spatial data analysis practice, and, from a mathematical point of view, whose asymptotic behavior, already studied in a series of papers by Belkin & Niyogi, suggests that they own qualities of robustness and a limited sensitivity to the Modifiable Areal Unit Problem (MAUP), valuable in exploratory spatial data analysis

A relational approach to knowledge spillovers in biotech. Network structures as drivers of inter-organizational citation patterns

In this paper, we analyze the geography of knowledge spillovers in biotech by investigating the way in which knowledge ties are organized. Following a relational account on knowledge spillovers, we depict knowledge networks as complex evolving structures that build on pre-existing knowledge and previously formed ties. In economic geography, there is still little understanding of how structural network forces (like preferential attachment and closure) shape the structure and formation of knowledge spillover networks in space. Our study investigates the knowledge spillover networks of biotech firms by means of inter-organizational citation patterns based on USPTO biotech patents in the years 2008-2010. Using a Stochastic Actor-Oriented Model (SAOM), we explain the driving forces behind the decision of actors to cite patents produced by other actors. Doing so, we address directly the endogenous forces of knowledge dynamics.knowledge spillovers, network structure, patent citations, biotech, proximity

Spatial effects in multivariate ARCH

This paper proposes a new approach for the specification of multivariate GARCH models for data sets with a potentially large cross-section dimension. The approach exploits the spatial dependence structure associated with asset characteristics, like industrial sectors and capitalization size. We use the acronym SEARCH for this model, short for Spatial Effects in ARCH. This parametrization extends current feasible specifications for large scale GARCH models, while keeping the numbers of parameters linear with respect to the number of assets. An application to daily returns on 20 stocks from the NYSE for the period January 1994 to June 2001 shows the benefits of the present specification.

Modeling Spatial Autocorrelation in Spatial Interaction Data: A Comparison of Spatial Econometric and Spatial Filtering Specifications

The need to account for spatial autocorrelation is well known in spatial analysis. Many spatial statistics and spatial econometric texts detail the way spatial autocorrelation can be identified and modelled in the case of object and field data. The literature on spatial autocorrelation is much less developed in the case of spatial interaction data. The focus of interest in this paper is on the problem of spatial autocorrelation in a spatial interaction context. The paper aims to illustrate that eigenfunction-based spatial filtering offers a powerful methodology that can efficiently account for spatial autocorrelation effects within a Poisson spatial interaction model context that serves the purpose to identify and measure spatial separation effects to interregional knowledge spillovers as captured by patent citations among high-technology-firms in Europe.

Spatial and Temporal Diffusion of House Prices in the UK

This paper provides a method for the analysis of the spatial and temporal diffusion of shocks in a dynamic system. We use changes in real house prices within the UK economy at the level of regions to illustrate its use. Adjustment to shocks involves both a region specific and a spatial effect. Shocks to a dominant region – London – are propagated contemporaneously and spatially to other regions. They in turn impact on other regions with a delay. We allow for lagged effects to echo back to the dominant region. London in turn is influenced by international developments through its link to New York and other financial centers. It is shown that New York house prices have a direct effect on London house prices. We analyse the effect of shocks using generalised spatio-temporal impulse responses. These highlight the diffusion of shocks both over time (as with the conventional impulse responses) and over space.spatial dependence, cross sectional dependence, house prices

Spatial and Temporal Diffusion of House Prices in the UK

This paper provides a method for the analysis of the spatial and temporal diffusion of shocks in a dynamic system. We use changes in real house prices within the UK economy at the level of regions to illustrate its use. Adjustment to shocks involves both a region specific and a spatial effect. Shocks to a dominant region - London - are propagated contemporaneously and spatially to other regions. They in turn impact on other regions with a delay. We allow for lagged effects to echo back to the dominant region. London in turn is influenced by international developments through its link to New York and other financial centers. It is shown that New York house prices have a direct effect on London house prices. We analyse the effect of shocks using generalised spatio-temporal impulse responses. These highlight the diffusion of shocks both over time (as with the conventional impulse responses) and over space.House Prices, Cross Sectional Dependence, Spatial Dependence

A Mutually-Dependent Hadamard Kernel for Modelling Latent Variable Couplings

We introduce a novel kernel that models input-dependent couplings across multiple latent processes. The pairwise joint kernel measures covariance along inputs and across different latent signals in a mutually-dependent fashion. A latent correlation Gaussian process (LCGP) model combines these non-stationary latent components into multiple outputs by an input-dependent mixing matrix. Probit classification and support for multiple observation sets are derived by Variational Bayesian inference. Results on several datasets indicate that the LCGP model can recover the correlations between latent signals while simultaneously achieving state-of-the-art performance. We highlight the latent covariances with an EEG classification dataset where latent brain processes and their couplings simultaneously emerge from the model.Comment: 17 pages, 6 figures; accepted to ACML 201

Spatial and Temporal Diffusion of House Prices in the UK

This paper provides a method for the analysis of the spatial and temporal diffusion of shocks in a dynamic system. We use changes in real house prices within the UK economy at the level of regions to illustrate its use. Adjustment to shocks involves both a region specific and a spatial effect. Shocks to a dominant region - London - are propagated contemporaneously and spatially to other regions. They in turn impact on other regions with a delay. We allow for lagged effects to echo back to the dominant region. London in turn is influenced by international developments through its link to New York and other financial centers. It is shown that New York house prices have a direct effect on London house prices. We analyse the effect of shocks using generalised spatio-temporal impulse responses. These highlight the diffusion of shocks both over time (as with the conventional impulse responses) and over space.house prices, cross sectional dependence, spatial dependence

Hierarchical spatial models for predicting tree species assemblages across large domains

Spatially explicit data layers of tree species assemblages, referred to as forest types or forest type groups, are a key component in large-scale assessments of forest sustainability, biodiversity, timber biomass, carbon sinks and forest health monitoring. This paper explores the utility of coupling georeferenced national forest inventory (NFI) data with readily available and spatially complete environmental predictor variables through spatially-varying multinomial logistic regression models to predict forest type groups across large forested landscapes. These models exploit underlying spatial associations within the NFI plot array and the spatially-varying impact of predictor variables to improve the accuracy of forest type group predictions. The richness of these models incurs onerous computational burdens and we discuss dimension reducing spatial processes that retain the richness in modeling. We illustrate using NFI data from Michigan, USA, where we provide a comprehensive analysis of this large study area and demonstrate improved prediction with associated measures of uncertainty.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS250 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org