Modelling spatial processes: The identification and analysis of spatial relationships in regression residuals by means of Moran\u27s I (Germany)

This thesis deals with the implementation, identification and analysis of relationships between geo-referenced objects. Significant spatial relationships manifest themselves in a spatial process which is modelled on a combination of spatial structure and spatial autocorrelation levels. Simple spatial structures reflect plain spill-over effects between adjacent spatial objects, whereas theoretical guided spatial structure mirror functional exchange relationships within the system of spatial objects. In empirical work, the underlying spatial process is unknown. The linking mechanism between a hypothetical spatial structure and a stochastic input must be identified from the observed data. This is accomplished here by means of the test statistic Moran\u27s I for regression residuals from a Gaussian spatial process. A closed statistical theory on the conditional distribution of Moran\u27s I under the influence of an hypothetical underlying spatial process is developed. In contrast to simulation experiments or the asymptotic maximum likelihood approach, the presented results are exact for samples of any size and they are not necessarily normally distributed. A direct link of an observed value Io of Moran\u27s I to the autocorrelation level po of an underlying spatial process is derived by means of the conditional expectation of Moran’s I. Furthermore, the distribution of local Moran\u27s I; conditional to forces of a global spatial process is developed. It permits identification of local heterogeneity in a global spatial process. Finally, a procedure based on the conditional significance is presented to distinguish between two competing hypothetical spatial processes. A preliminary model to describe the empirical spatial distribution of bladder cancer incidence rats in 219 counties of the former German Democratic Republic is used to demonstrate the feasibility and flexibility of the proposed exact approach. A theoretical basis to address the migration problem in spatial epidemiology, which blurs the observed local disease rats, is presented and tested by the proposed methodology against a simple spatial clustering process

Spatial Filtering and Eigenvector Stability: Space-Time Models for German Unemployment Data

Regions, independent of their geographic level of aggregation, are known to be interrelated partly due to their relative locations. Similar economic performance among regions can be attributed to proximity. Consequently, a proper understanding, and accounting, of spatial liaisons is needed in order to effectively forecast regional economic variables. Several spatial econometric techniques are available in the literature, which deal with the spatial autocorrelation in geographically-referenced data. The experiments carried out in this paper are concerned with the analysis of the spatial autocorrelation observed for unemployment rates in 439 NUTS-3 German districts. We employ a semi-parametric approach – spatial filtering – in order to uncover spatial patterns that are consistently significant over time. We first provide a brief overview of the spatial filtering method and illustrate the data set. Subsequently, we describe the empirical application carried out: that is, the spatial filtering analysis of regional unemployment rates in Germany. Furthermore, we exploit the resulting spatial filter as an explanatory variable in a panel modelling framework. Additional explanatory variables, such as average daily wages, are used in concurrence with the spatial filter. Our experiments show that the computed spatial filters account for most of the residual spatial autocorrelation in the data.spatial filtering, eigenvectors, Germany, unemployment

The Use of Spatial Filtering Techniques: The Spatial and Space-time Structure of German Unemployment Data

Socio-economic interrelationships among regions can be measured in terms of economic flows, migration, or physical geographically-based measures, such as distance or length of shared areal unit boundaries. In general, proximity and openness tend to favour a similar economic performance among adjacent regions. Therefore, proper forecasting of socio-economic variables, such as employment, requires an understanding of spatial (or spatio-temporal) autocorrelation effects associated with a particular geographic configuration of a system of regions. Several spatial econometric techniques have been developed in recent years to identify spatial interaction effects within a parametric framework. Alternatively, newly devised spatial filtering techniques aim to achieve this end as well through the use of a semi-parametric approach. Experiments presented in this paper deal with the analysis of and accounting for spatial autocorrelation by means of spatial filtering t! echniques for data pertaining to regional unemployment in Germany. The available data set comprises information about the share of unemployed workers in 439 German districts (the NUTS-III regional aggregation level). Results based upon an eigenvector spatial filter model formulation (that is, the use of orthogonal map pattern components), constructed for the 439 German districts, are presented, with an emphasis on their consistency over several years. Insights obtained by applying spatial filtering to the database are also discussed

Multicollinearity and correlation among local regression coefficients in geographically weighted regression

Geographically weighted regression, Multicollinearity, Local regression diagnostics, Spatial eigenvectors, Experimental spatial design,

Semiparametric filtering of spatial autocorrelation: the eigenvector approach

In the context of spatial regression analysis, several methods can be used to control for the statistical effects of spatial dependencies among observations. Maximum likelihood or Bayesian approaches account for spatial dependencies in a parametric framework, whereas recent spatial filtering approaches focus on nonparametrically removing spatial autocorrelation. In this paper we propose a semiparametric spatial filtering approach that allows researchers to deal explicitly with (a)�spatially lagged autoregressive models and (b)�simultaneous autoregressive spatial models. As in one nonparametric spatial filtering approach, a specific subset of eigenvectors from a transformed spatial link matrix is used to capture dependencies among the disturbances of a spatial regression model. However, the optimal subset in the proposed filtering model is identified more intuitively by an objective function that minimizes spatial autocorrelation rather than maximizes a model fit. The proposed objective function has the advantage that it leads to a robust and smaller subset of selected eigenvectors. An application of the proposed eigenvector spatial filtering approach, which uses a cancer mortality dataset for the 508 US State Economic Areas, demonstrates its feasibility, flexibility, and simplicity.

Spatial filtering and eigenvector stability: Space-time model for German unemployment data

Regions, independent of their geographic level of aggregation, are known to be interrelated partly due to their relative locations. Similar economic performance among regions can be attributed to proximity. Consequently, a proper understanding, and accounting, of spatial liaisons is needed in order to effectively forecast regional economic variables. Several spatial econometric techniques are available in the literature, which deal with the spatial autocorrelation in geographically-referenced data. The experiments carried out in this paper are concerned with the analysis of the spatial autocorrelation observed for unemployment rates in 439 NUTS-3 German districts. We employ a semi-parametric approach – spatial filtering – in order to uncover spatial patterns that are consistently significant over time. We first provide a brief overview of the spatial filtering method and illustrate the data set. Subsequently, we describe the empirical application carried out: that is, the spatial filtering analysis of regional unemployment rates in Germany. Furthermore, we exploit the resulting spatial filter as an explanatory variable in a panel modelling framework. Additional explanatory variables, such as average daily wages, are used in concurrence with the spatial filter. Our experiments show that the computed spatial filters account for most of the residual spatial autocorrelation in the data

Spatial Filtering and Eigenvector Stability: Space-Time Models for German Unemployment Data

Regions, independent of their geographic level of aggregation, are known to be interrelated partly due to their relative locations. Similar economic performance among regions can be attributed to proximity. Consequently, a proper understanding, and accounting, of spatial liaisons is needed in order to effectively forecast regional economic variables. Several spatial econometric techniques are available in the literature, which deal with the spatial autocorrelation in geographically-referenced data. The experiments carried out in this paper are concerned with the analysis of the spatial autocorrelation observed for unemployment rates in 439 NUTS-3 German districts. We employ a semi-parametric approach – spatial filtering – in order to uncover spatial patterns that are consistently significant over time. We first provide a brief overview of the spatial filtering method and illustrate the data set. Subsequently, we describe the empirical application carried out: that is, the spatial filtering analysis of regional unemployment rates in Germany. Furthermore, we exploit the resulting spatial filter as an explanatory variable in a panel modelling framework. Additional explanatory variables, such as average daily wages, are used in concurrence with the spatial filter. Our experiments show that the computed spatial filters account for most of the residual spatial autocorrelation in the data.spatial filtering, eigenvectors, Germany, unemployment

Spatial Filtering and Eigenvector Stability: Space-Time Models for German Unemployment Data

Regions, independent of their geographic level of aggregation, are known to be interrelated partly due to their relative locations. Similar economic performance among regions can be attributed to proximity. Consequently, a proper understanding, and accounting, of spatial liaisons is needed in order to effectively forecast regional economic variables. Several spatial econometric techniques are available in the literature, which deal with the spatial autocorrelation (SAC) in geographically referenced data. The experiments carried out in this article are concerned with the analysis of the SAC observed for unemployment rates in 439 NUTS-3 German districts. The authors employ a semiparametric approach—spatial filtering—in order to uncover spatial patterns that are consistently significant over time. The authors first provide a brief overview of the spatial filtering method and illustrate the data set. Subsequently, they describe the empirical application carried out: that is, the spatial filtering analysis of regional unemployment rates in Germany. Furthermore, the authors exploit the resulting spatial filter as an explanatory variable in a panel modeling framework. Additional explanatory variables, such as average daily wages, are used in concurrence with the spatial filter. Their experiments show that the computed spatial filters account for most of the residual SAC in the data.spatial filtering; eigenvectors; Germany; unemployment; GLMM

Space-Time Models for German Unemployment Data

Spatial filtering and eigenvector stability: space-time model for German unemployment dat