Geostatistical Smoothing of Areal Data: Mapping Employment Density with Factorial Kriging

This article summarizes area-to-point (ATP) factorial kriging that allows the smoothing of aggregate, areal data into a continuous spatial surface. Unlike some other smoothing methods, ATP factorial kriging does not suppose that all of the data within an area are located at a centroid or other arbitrary point. Also, unlike some other smoothing methods, factorial kriging allows the user to utilize an autocovariance function to control the smoothness of the output. This is beneficial because the covariance function is a physically meaningful statement of spatial relationship, which is not the case when other spatial kernel functions are used for smoothing. Given a known covariance function, factorial kriging gives the smooth surface that is best in terms of minimizing the expected mean squared prediction error. I present an application of the factorial kriging methodology for visualizing the structure of employment density in the Denver metropolitan area.     

Parameterization and Visualization of the Errors in Areal Interpolation

Areal interpolation involves the transfer of data from one zonation of a region to another, where the two zonations of space are geographically incompatible. By its very nature this process is fraught with errors. However, only recently have there been specific attempts to quantify these errors. Fisher and Langford (1995) employed Monte Carlo simulation methods, based on modifiable areal units, to compare the errors resulting from selected areal interpolation techniques. This paper builds on their work by parameterizing and visualizing the errors resulting from the areal weighting and dasymetric methods of areal interpolation. It provides the basis for further research by developing the methodology to produce predictive models of the errors in areal interpolation. Random aggregation techniques are employed to generate multiple sets of source zones and interpolation takes place from these units onto a fixed set of randomly generated target zones. Analysis takes place at the polygon, or target zone level, which enables detailed analysis of the error distributions, basic visualization of the spatial nature of the errors and predictive modeling of the errors based on parameters of the target zones. Correlation and regression analysis revealed that errors from the areal weighting technique were related to the geometric parameters of the target zones. The dasymetric errors, however, demonstrated more association with the population or attribute characteristics of the zones. The perimeter, total population, and population density of the target zones were shown to be the strongest predictive parameters.     

Geostatistical Prediction and Simulation of Point Values from Areal Data

The spatial prediction and simulation of point values from areal data are addressed within the general geostatistical framework of change of support (the term support referring to the domain informed by each measurement or unknown value). It is shown that the geostatistical framework (i) can explicitly and consistently account for the support differences between the available areal data and the sought-after point predictions, (ii) yields coherent (mass-preserving or pycnophylactic) predictions, and (iii) provides a measure of reliability (standard error) associated with each prediction. In the case of stochastic simulation, alternative point-support simulated realizations of a spatial attribute reproduce (i) a point-support histogram (Gaussian in this work), (ii) a point-support semivariogram model (possibly including anisotropic nested structures), and (iii) when upscaled, the available areal data. Such point-support-simulated realizations can be used in a Monte Carlo framework to assess the uncertainty in spatially distributed model outputs operating at a fine spatial resolution because of uncertain input parameters inferred from coarser spatial resolution data. Alternatively, such simulated realizations can be used in a model-based hypothesis-testing context to approximate the sampling distribution of, say, the correlation coefficient between two spatial data sets, when one is available at a point support and the other at an areal support. A case study using synthetic data illustrates the application of the proposed methodology in a remote sensing context, whereby areal data are available on a regular pixel support. It is demonstrated that point-support (sub-pixel scale) predictions and simulated realizations can be readily obtained, and that such predictions and realizations are consistent with the available information at the coarser (pixel-level) spatial resolution.     

Some Extensions of Mills's Method for Urban Population Density Gradient Estimation

This paper extends Milk's method for estimating urban population density gradients to general noncircular and asymmetrical urban forms, using Gauss-Legendre quadrature embedded in a Newton-Raphson root finding algorithm. We also examine the sensitivity of the Mills method to measurement errors in the assumptions. Several issues arising from the comparison of analytical, Mills type estimation procedures with statistical procedures are explored, particularly in light of recent work that questions the negative exponential formulation of urban density gradients. We note in particular the influence of secondary population centers as a source of estimation bias.     

A Mathematical Model of the Density Distribution of Moscow's Population

A student research project at Moscow University tests Colin Clark's formula for the distribution of the density of a single-center city by applying it to population data of Moscow for 1963, 1964, and 1965. The students obtain repression lines and equations for the population density of Moscow and draw the density field by means of isolines. The results suggest population movement from the central district to outlying areas where intensive housing construction is under way.     

A Structural Approach to the Form of the Population Density Function

The central objective of this paper is to explore a comprehensive structural modeling approach that extracts analytical density functions answering questions raised by recent empirical studies.     

The Politics of Reconstructing National Identity: A Corporatist Approach

In both liberal democracies like Australia and Canada and autocracies like Singapore, the state has stepped in to try to manage ethnic claims that had hitherto been marginalised or suppressed. Once the concept of corporatism is rescued from its recent economic-focused excursion, it provides a framework within which to examine new state strategies for managing ethnicity, and the resultant politics of national identity. The states have sought to license or create ethnic institutions as channels for ethnic interest articulation, for ethnic elite cooptation, and for the funding and political control of ethnic assertions. The corporatist strategies for ethnic management imply also attempts by the states to unify the disaggregated polyethnic societies by seeking new myths of organic national unity. The attempts to manage ethnic politics within these new institutional and ideological parameters generate tensions which exacerbate rather than ameliorate the decline in state authority.     

Target-Density Weighting Interpolation and Uncertainty Evaluation for Temporal Analysis of Census Data

Conducting temporal analysis of census data often requires applying areal interpolation to integrate data that have been spatially aggregated using incompatible zoning systems. This article introduces a method of areal interpolation, target-density weighting (TDW), that is useful for long-term temporal analysis because it requires only readily available historical data and basic geographic information system operations. Then, through regression analysis of a large sample of U.S. census tract data, a model is produced that relates the error in TDW estimates of tract population to four basic properties of tracts. An analysis of model residuals combined with theorized absolute limits on interpolation error yields formulas with which we can compute upper and lower prediction bounds on the population in a tract of one census at the time of a different census. These prediction intervals enable the interpretation of different interpolated estimates with appropriately varying degrees of uncertainty.     

Sequential, Bayesian Geostatistics: A Principled Method for Large Data Sets

The principled statistical application of Gaussian random field models used in geostatistics has historically been limited to data sets of a small size. This limitation is imposed by the requirement to store and invert the covariance matrix of all the samples to obtain a predictive distribution at unsampled locations, or to use likelihood-based covariance estimation. Various ad hoc approaches to solve this problem have been adopted, such as selecting a neighborhood region and/or a small number of observations to use in the kriging process, but these have no sound theoretical basis and it is unclear what information is being lost. In this article, we present a Bayesian method for estimating the posterior mean and covariance structures of a Gaussian random field using a sequential estimation algorithm. By imposing sparsity in a well-defined framework, the algorithm retains a subset of " basis vectors " that best represent the " true " posterior Gaussian random field model in the relative entropy sense. This allows a principled treatment of Gaussian random field models on very large data sets. The method is particularly appropriate when the Gaussian random field model is regarded as a latent variable model, which may be nonlinearly related to the observations. We show the application of the sequential, sparse Bayesian estimation in Gaussian random field models and discuss its merits and drawbacks.     

Population Density,Economic Growth and Societies in Transition: Boserup Reconsidered in a Kenyan Case-study

In examining the relationship between population growth and income growth, this article first looks at the Malthusian, transition and revisionist positions. The first is not borne out by historical experience, and the latter two do not explain why greater affluence generally leads to lower rates of population growth. It is argued here that the crucial population characteristic is density. Rising densities from a low base facilitate more productive agriculture and greater specialization and exchange within a society, as Boserup (1965) pointed out. This leads to increased wealth but also to higher costs for education and land. This provides a link to Caldwell's (1976) explanation of changing attitudes to family size: at low densities in simple societies benefits from children exceed costs, while at higher densities in complex societies costs exceed benefits. The changes in societies and economies are illustrated by a Kenyan case study. Kenya has experienced particularly rapid population growth this century, and high economic growth; it is now experiencing the transition to lower birth rates.     

Reconstructing Nineteenth-Century Midwest Foodways: Ceramic and Zooarchaeological Information from the Moore-Youse House and Huddleston Farmstead

Settled by families from the South and the Northeast, during the 1800s Indiana was a cultural crossroads. Ceramic and faunal data recovered from excavations conducted at the Moore-Youse house and Huddleston farmstead in east central Indiana provide a relevant archaeological example of midwestern foodways during the nineteenth century. Vertebrate faunal material from the two sites reveals early use of wild resources followed by greater reliance on beef and pork after the 1850s. Stratigraphic analysis results of zooarchaeological information are also presented to illustrate diachronic trends in faunal use at the two residences.     

A Half Century of Health Data for the U.S. Population: The Integrated Health Interview Series

The U.S. National Health Interview Survey (NHIS) is the world's longest survey time series of health data and a rich source of information on health conditions, behaviors, and care from the 1960s to the present. NHIS public-use files are difficult to use for long-term analysis, due to complex file structure, changes in questionnaire content, and evolving variable names and coding schemes. Researchers at the Minnesota Population Center have created the Integrated Health Interview Series (IHIS) to overcome these problems. IHIS provides access to thousands of consistently coded and well-documented NHIS variables on the Internet and makes it easy to analyze health trends and differentials. IHIS multiplies the value of NHIS data by allowing researchers to make consistent comparisons over half a century and thus to study U.S. health status as a dynamic process. This article describes the main features of IHIS and suggests fruitful avenues for historical research using these invaluable health data.