The Assessment of Spatial Autocorrelation through Constrained Multiple Regression

Most published measures of spatial autocorrelation (SA) can be recast as a (normalized) cross-product statistic that indexes the degree of relationship between corresponding entries from two matrices—one specifying the spatial connections among a set of n locations, and the other reflecting a very explicit definition of similarity between the set of values on some variable x realized over the n locations. We first give a very brief sketch of the basic cross-product approach to the evaluation of SA, and then generalize this strategy to include less restrictive specifications for the notion of similarity between the values on x. Using constrained multiple regression, the characterization of variate similarity basic to any assessment of SA can itself be framed according to the information present in the measure of spatial separation. These extensions obviate the inherent arbitrariness in how SA is usually evaluated, which now results from the requirement of a very restrictive definition of variate similarity before a cross-product index can be obtained.     

Statistical Inferences in Bidimensional Regression Models

This paper proposes formal procedures of significance tests for bidimensional regression models (Tobler 1994): (1) significance tests of estimated parameters, (2) significance tests of bidimensional correlation coefficient, and (3) significance tests for comparison of bidimensional regression models. These tests are demonstrated by reexamination of the cognitive map study in Kanazawa City (Wakabayashi 1994). The empirical results statistically support the systematic distortion in the cognitive map, enlargement and rotation, indicated by the Euclidean model in the previous study, and discern the affine model as a more proper model that can identify more components of systematic cognitive distortion.     

Analysis of Interregional Labor Migration in Spain Using Gross Flows

In this paper we study the economic determinants of Spanish interregional labor force flows from an aggregate perspective. The study is based on a matching model of the labor market applied to migration, and uses gross rather than net flows as other studies do. Among the main results, we find that unemployment increases out-migration because unemployed people search more actively, but when the unemployment rate is above a certain level this effect is reduced. We also find that the rate of change of relative wages is a significant determinant of migration in Spain.     

Improving Distance Estimates between Areal Units in Migration Models

There are many methods of modeling migrant flows within a set of areal units, but it is common in most to incorporate some measure of distance as an explanatory variable. These distances are effectively meant to represent the typical distance between pairs of areas that would be traveled by potential migrants. They are usually calculated between population-weighted centroids derived for each zone. It is argued here that this method of calculating distance is biased and that the zonal system used will influence the final model parameters that are intended to describe the underlying migration process. The distances between nearby zones will be particularly poorly specified using this approach, but other problems arise which relate to the shape of the zones and the position of the zones in relation to each other. This paper describes an alternative method of calculating these distances which reduces this bias. It is shown that the resulting models fit the data far more satisfactorily and that the residuals from models incorporating this approach are significantly different from those identified from models that use the standard method of specifying distance.     

Neural Network Modeling of Constrained Spatial Interaction Flows: Design, Estimation, and Performance Issues

In this paper a novel modular product unit neural network architecture is presented to model singly constrained spatial interaction flows. The efficacy of the model approach is demonstrated for the origin constrained case of spatial interaction using Austrian interregional telecommunication traffic data. The model requires a global search procedure for parameter estimation, such as the Alopex procedure. A benchmark comparison against the standard origin constrained gravity model and the two–stage neural network approach, suggested by Openshaw (1998), illustrates the superiority of the proposed model in terms of the generalization performance measured by ARV and SRMSE.     

Generalized Additive Models,Graphical Diagnostics,and Logistic Regression

Generalized additive models (GAMs), although little known in geographical analysis, have considerable utility. In particular, they allow the conventional linear relationships of multiple regression to be generalized to permit a much broader class of nonlinear, but still additive, relationships between response and predictor variables. This paper illustrates how GAMs can be extended to the important case of logistic regression with binary response. Details of the distinctive form of logistic regression GAMs are provided, and appropriate means of estimation are outlined. The paper provides the first use, in the context of a logistic regression GAM, of the expansion method of assessing parameter variation. These techniques are illustrated by a reanalysis of information on hydrocarbon exploration wells drilled in south-central Kansas.     

Properties of Tests for Spatial Dependence in Linear Regression Models

Based on a large number of Monte Carlo simulation experiments on a regular lattice, we compare the properties of Moran's I and Lagrange multiplier tests for spatial dependence, that is, for both spatial error autocorrelation and for a spatially lagged dependent variable. We consider both bias and power of the tests for six sample sizes, ranging from twenty-five to 225 observations, for different structures of the spatial weights matrix, for several underlying error distributions, for misspecified weights matrices, and for the situation where boundary effects are present. The results provide an indication of the sample sizes for which the asymptotic properties of the tests can be considered to hold. They also illustrate the power of the Lagrange multiplier tests to distinguish between substantive spatial dependence (spatial lag) and spatial dependence as a nuisance (error autocorrelation).     

A General Misspecification Test for Spatial Regression Models: Dependence, Heterogeneity, and Nonlinearity

There is an increasing awareness of the potentials of nonlinear modeling in regional science. This can be explained partly by the recognition of the limitations of conventional equilibrium models in complex situations, and also by the easy availability and accessibility of sophisticated computational techniques. Among the class of nonlinear models, dynamic variants based on, for example, chaos theory stand out as an interesting approach. However, the operational significance of such approaches is still rather limited and a rigorous statistical-econometric treatment of nonlinear dynamic modeling experiments is lacking. Against this background this paper is concerned with a methodological and empirical analysis of a general misspecification test for spatial regression models that is expected to have power against nonlinearity, spatial dependence, and heteroskedasticity. The paper seeks to break new research ground by linking the classical diagnostic tools developed in spatial econometrics to a misspecification test derived directly from chaos theory—the BDS test, developed by Brock, Dechert, and Scheinkman (1987). A spatial variant of the BDS test is introduced and applied in the context of two examples of spatial process models, one of which is concerned with the spatial distribution of regional investments in The Netherlands, the other with spatial crime patterns in Columbus, Ohio.     

Empirical Evaluation of Alternative Model Specifications to Predict Commuting Flows

This study is devoted to empirical and modeling aspects on how characteristics of spatial structure influence commuting flows. Within a doubly-constrained framework, results from a competing-destinations formulation are evaluated and compared to results from the traditional gravity model. The evaluation depends critically upon the specification of within-zone journeys-to-work. Specific labor-market characteristics are found to be significant to explain how workers are absorbed in diagonal elements of the trip-distribution matrix. We also find that the parametric specification of the accessibility measure is important, and that the competing-destinations formulation is superior to the traditional gravity model.     

An Information-theoretic Analysis: An Application to Soviet-COMECON Trade Flows

This paper develops a classificatory methodology designed to assign geographic entities to groupings based upon the multivariate flow profiles displayed by the entities and a dispersion statistic designed to detect dynamic shifts in these flow profiles over time. Information statistic, provide the mathematical basis of the analysis and the changing trade profiles of the member nations of COMECON provide an illustrative case study.     

明代蒙古部落大批入据青海考论

本文考证明代蒙古部落大批入据青海这一纷乱、复杂的历史过程,深入分析多方面矛盾交织的内、外因,对厘定明代中后期这一影响巨大的西北边疆少数民族迁徙事件的历史真相有重要史学价值,同时对当代处理民族关系问题和民族宗教问题也有一定借鉴意义。     

明代蒙古部落大批人据青海考论

本文考证明代蒙古部落大批入据青海这一纷乱、复杂的历史过程,深入分析多方面矛盾交织的内、外因,对厘定明代中后期这一影响巨大的西北边疆少数民族迁徙事件的历史真相有重要史学价值,同时对当代处理民族关系问题和民族宗教问题也有一定借鉴意义。