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2011 | Buch

Introduction: Spatial Statistics Kapitel lesen Erstes Kapitel lesen

Non-standard Spatial Statistics and Spatial Econometrics

verfasst von: Daniel A. Griffith, Jean H. Paul Paelinck

Verlag: Springer Berlin Heidelberg

Buchreihe : Advances in Geographic Information Science

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Despite spatial statistics and spatial econometrics both being recent sprouts of the general tree "spatial analysis with measurement"—some may remember the debate after WWII about "theory without measurement" versus "measurement without theory"—several general themes have emerged in the pertaining literature. But exploring selected other fields of possible interest is tantalizing, and this is what the authors intend to report here, hoping that they will suscitate interest in the methodologies exposed and possible further applications of these methodologies. The authors hope that reactions about their publication will ensue, and they would be grateful to reader(s) motivated by some of the research efforts exposed hereafter letting them know about these experiences.

Inhaltsverzeichnis

Frontmatter

Non-standard spatial statistics

Chapter 1. Introduction: Spatial Statistics
Abstract
A wide array of topics in spatial statistics introduce methodological controversy: aggregate versus disaggregated data inference (e.g., the ecological fallacy), modelling the spatial covariance versus the spatial inverse covariance matrix, including fixed and/or random effects terms in a model specification, spatial autocorrelation specified as part of the mean response versus part of the variance parameter, and methods for simulating spatially autocorrelated random variables.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 2. Individual Versus Ecological Analyses
Abstract
Analyses of disease maps frequently require the use of an ecological approach, partially because aggregates of cases allow such measures as rates to be computed. In addition, group averages of individual measures often are more readily available, tend to reduce impacts of measurement error, and help to preserve the confidentiality of individuals in each aggregation group. Given this context, the resulting problematic issue concerns drawing sound inferences about individuals from such grouped data. The general drawback to this type of inference is known as the ecological fallacy: most often a difference exists between an ecological regression and the regression based upon individuals underlying it (i.e., aggregate-level relationships do not necessarily hold at the individual level).
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 3. Statistical Models for Spatial Data: Some Linkages and Communalities
Abstract
Introductory mathematical statistics textbooks discuss topics such as the sample variance by invoking the assumption of independent and identically distributed (iid). In other words, in terms of second moments, of the n 2 possible covariations for a set of n observations, the independence assumption posits that n(n – 1) of these covariations have an expected value of 0, leaving only the n individual observation variance terms for analysis. This independence assumption is for convenience, historically making mathematical statistical theory tractable. But it is an arcane specification that fails to provide an acceptable approximation to reality in many contexts.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 4. Frequency Distributions for Simulated Spatially Autocorrelated Random Variables
Abstract
Often quantitative data analysis begins with an inspection of attribute variable histograms. Ratio scale demographic variables, such as population density (which has a natural, meaningful absolute 0 value), are expected to conform, at least approximately, to a normal probability distribution. Frequently this conformity requires that these variables be subjected to a symmetricizing, variance stabilizing transformation, such as the Box-Cox class of power functions or the Manley exponential function. Counts (i.e., aggregated nominal measurement scale) data used to construct ratios, such as the crude fertility rate (i.e., number of births per number of women in the child bearing age cohort), are expected to conform to a Poisson probability distribution. And, counts data that constitute some subset of a total, such as the percentage of people at least 100 years of age or the percentage of a population that is the women in the child bearing age cohort, are expected to conform to a binomial probability distribution.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 5. Understanding Correlations Among Spatial Processes
Abstract
The Pearson product-moment, Spearman’s rank, point biserial and phi correlation coefficients are calculated to quantify the nature and degree of linear correspondence between observation pairs of attributes. Bivand (1980) and Griffith (1980) were among the very first spatial analysts to address the impacts of spatial autocorrelation (SA) on conventional Pearson correlation coefficients. In the decades since their studies, an increasing understanding has been attained about correlation coefficients computed with georeferenced data. This understanding includes how: SA alters conventional degrees of freedom and sample size, the nature and degree of SA affects correlation coefficients, and SA can simultaneously inflate and deflate correlation coefficients. The primary objective of this chapter is to review each of these topics, adding some extensions when possible.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 6. Spatially Structured Random Effects: A Comparison of Three Popular Specifications
Abstract
Random effects models are increasing in popularity (see, for example, Demidenko, 2004), partially because they have become estimable. One common specification is for the intercept term to be cast as a random effects, resulting in it representing variability about the conventional single-value, constant mean. The role of a random effects in this context may be twofold: (1) supporting inferences beyond the specific fixed values of covariates employed in an analysis; and, (2) accounting for correlation in a non-random sample of data being analyzed. Including a random effects term moves a frequentist analysis a bit closer to a Bayesian analysis, given that, for instance, the intercept term becomes a random variable rather than being a constant, and has a prior probability distribution (usually normal) attached to it. Nevertheless, a bone fide Bayesian analysis would have a random variable for each of the n intercept term components comprising such a random effects, maintaining some degree of differentiation here between the frequentist and Bayesian approaches.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 7. Spatial Filter Versus Conventional Spatial Model Specifications: Some Comparisons
Abstract
Spatial statistical analysis of geographically distributed counts data has been widely undertaken for many years, with initial analyses involving log-Gaussian approximations because only the normal probability model was first adapted in an implementable form (Ripley, 1990, pp. 9–10) to handle spatial autocorrelation (SA) effects (i.e., similar values tend to cluster on a map, indicating positive self-correlation among observations). In more recent years, linear regression techniques have given way to generalized linear model techniques that account for non-normality (e.g., logistic and Poisson regression), as well as geographic dependence. In very recent years, both linear and generalized linear models have been supplemented with hierarchical Bayesian models, in part to deal with geographic regions having small counts. The objective of this chapter is to furnish a comparison of this variety of principal techniques—both frequentist and Bayesian—available for map analysis with the newly formulated spatial filtering approach.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 8. The Role of Spatial Autocorrelation in Prioritizing Sites Within a Geographic Landscape
Abstract
Superfund program legislation—primarily the U.S. Comprehensive Environmental Response, Compensation and Liability Act—and its public health motivations catapulted environmental contamination issues into the forefront of society’s concerns. One outcome was a report by the U.S. National Research Council (NRC, 1994) examining principal methods considered or actually employed by federal and state government agencies to prioritize the remediation of hazardous waste sites. The emphasis was on between-site variation among locations, initially overlooking within-site variation for locations. The purpose of this paper is to extend more recent work on prioritizing the remediation of subregions within a given hazardous waste site, emphasizing within-site variation for locations. These extensions are illustrated with a case study of the Murray superfund site.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 9. General Conclusions: Spatial Statistics
Abstract
The original version of our Annals in Regional Science paper enumerates a number of topics that serve as focal points for the frontiers of spatial statistics and spatial econometrics.
Daniel A. Griffith, Jean H.P. Paelinck

Non-standard spatial econometrics

Chapter 10. Introduction: Spatial Econometrics
Abstract
In spatial econometrics, various topics have their own importance: specification, estimation and testing are the main building blocks of a spatial econometric model.
An economist should attach special importance to the specification stage; experience has taught that the functioning of spatial economies follows a complex pattern, and that is the pattern that should be adequately modeled.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 11. A Mixed Linear-Logarithmic Specification for Lotka-Volterra Models with Endogenously Generated SDLS-Variables
Abstract
In Arbia and Paelinck (2003a, b), a Lotka-Volterra model (LVM) is applied to the convergence-divergence problem of European regions in terms of incomes per capita. As the latter have to be non-negative, a double logarithmic version may be substituted for the original specification, a modification that removes at least part of the non-linearity of LVMs; this chapter introduces this non-linearity again. Discussion begins with a general section on LVMs, to go on with a mixed linear-logarithmic specification, of which the positivity of the (possible) equilibrium solution is proved, and for which a (sufficient) stability condition is derived.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 12. Selecting Spatial Regimes by Threshold Analysis
Abstract
The existence of differential spatial regimes has been revealed on different occasions (see for instance Arbia and Paelinck, 2003a, b; also see Chap. 14). Hence the necessity exists for developing workable specifications to compute possible frontiers or thresholds between those regimes.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 13. Finite Automata
Abstract
In Paelinck (2002), attention was drawn to a special algebra—called a min-algebra—that might rule quite a few spatial econometrics specifications; hereafter, applications of this idea are be presented in the form of finite automata.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 14. Learning from Residuals
Abstract
Residuals often are considered as a troublesome noise in spatial—or, for that matter—non-spatial econometric models. Current practice in spatial econometrics is to set up a spatial error model, more often than not with an exogenous W spatial weight matrix, in order to improve the efficiency of the estimators.
Looking closely into the residuals is less common practice. And still, residuals can represent extremely precious building blocks for further work, as other disciplines have shown. Around 1850 the British chemists, Mansfield and Perkin, had the—for that era of chemistry—strange idea to analyze the composition of tar, until then exclusively used to improve coverage of roads (John London McAdam had his name attached to that technique, tarmacadam); the result of the British chemists’ investigation was the roaring development of a whole branch of (industrial) chemistry: carbochemistry.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 15. Verhulst and Poisson Distributions
Abstract
The logistic curve (or Verhulst sigmoid curve) sometimes is used in spatial econometrics (see, e.g., Domencich and McFadden, 1975; Paelinck and Klaassen, 1979, pp. 68–72, 156–168). Two examples will be given hereafter, one for estimation in the binary case, the other for a dynamic specification. A related Poisson distribution problem is then treated; the latter distribution is less frequently used, because count data have to be available for econometric treatment.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 16. Qualireg, A Qualitative Regression Method
Abstract
Circumstances can produce themselves under which no cardinal data are available (see Ancot and Paelinck, 1990). To allow drawing inferences about at least the direction of influence of certain potentially explanatory variables, only available as ordinal data (“rankings”), methods should be developed to treat that problem. The method described here—QUALIREG—resulted from work on a qualitative multi-criteria method—QUALIFLEX, originated by Paelinck (1976)—which is detailed first, after which the logic of QUALIREG will be introduced.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 17. Filtering Complexity for Observational Errors and Spatial Bias
Abstract
In Chap. 12, complexity analysis of spatial data is advocated as a preliminary to spatial econometric regime selection, estimation and testing. That approach assumes that the endogenous variable—only a one-equation model was considered—was measure error free. The present chapter is devoted to controlling for that element of the problem.
Daniel A. Griffith, Jean H.P. Paelinck
Chapter 18. General Spatial Econometric Conclusions
Abstract
What should be clear from the exercises presented is that in most of them, classical “regression” has been combined with mathematical programming to obtain the desired estimators.
Daniel A. Griffith, Jean H.P. Paelinck
Backmatter
Metadaten
Titel
Non-standard Spatial Statistics and Spatial Econometrics
verfasst von
Daniel A. Griffith
Jean H. Paul Paelinck
Copyright-Jahr
2011
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-16043-1
Print ISBN
978-3-642-16042-4
DOI
https://doi.org/10.1007/978-3-642-16043-1