Model Comparison and Model Validation Issues in Empirical Work on Urban Density Functions

Anselin, Luc; Can, Ayşe

doi:10.1111/j.1538-4632.1986.tb00092.x

Cited by 37 publications

(13 citation statements)

References 62 publications

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“…Clark () was one of the first researchers to introduce density functions to urban populations, although without presenting a structured model as Alonso () did. This functional form has been modified by many other studies trying to find a better match to actual spatial distributions of densities (Anderson ; Anselin and Can ; McMillen ; Griffith and Wong ).…”

mentioning

confidence: 99%

Urban Centrality: A Simple Index

Pereira

Nadalin

Monastério

et al. 2012

Geographical Analysis

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This study introduces a new measure of urban centrality. The proposed urban centrality index (UCI) constitutes an extension to the spatial separation index. Urban structure should be more accurately analyzed when considering a centrality scale (varying from extreme monocentricity to extreme polycentricity) than when considering a binary variable (monocentric or polycentric). The proposed index controls for differences in size and shape of the geographic areas for which data are available, and can be calculated using different variables such as employment and population densities, or trip generation rates. The properties of the index are illustrated with simulated artificial data sets and are compared with other similar measures proposed in the existing literature. The index is then applied to the urban structure of four metropolitan areas: Pittsburgh and Los Angeles in the United States; São Paulo, Brazil; and Paris, France. The index is compared with other traditional spatial agglomeration measures, such as global and local Moran's I, and density gradient estimations. El presente estudio introduce una nueva medida de centralidad. El índice de centralidad urbana propuesto (UCI, por sus siglas en inglés) es una extensión al índice de separación espacial (spatial separation index)(Midelfart‐Knarvik et al. 2000). El análisis de la estructura urbana resulta más preciso al usar el índice cuando se toma en cuenta una escala de continua de centralidad (que puede variar de un monocentrismo extremo a un policentrismo extremo) que cuando se considera una variable binaria (monocéntrica o policéntrica). El índex propuesto controla las diferencias de tamaño y forma de las áreas geográficas de las que se tienen datos, y puede ser calculada utilizando diferentes variables, como empleo y densidad poblacional, o tasas de generación de viajes. Las propiedades del índice se ilustran con conjuntos de datos artificiales simulados, y se comparan con otras mediciones similares en la literatura ya existente. Posteriormente, el índice es aplicado a la estructura urbana de cuatro áreas metropolitanas: Pittsburgh y Los Ángeles, en EEUU; San Pablo, en Brasil; y París, Francia. Finalmente, se compara el índice con otras mediciones tradicionales de aglomeración espacial, como el índice de Moran local y global, y estimaciones de gradiente de densidad. 本文介绍了一种度量城市中心性的新方法，提出的城市中心性指数（UCI）是对空间分离指数的扩展。当涉及到中心性规模（从极单中心到极多中心），不仅仅是二元变量（单中心或多中心），城市结构则需更加精确的测度。本文构建的指数可以通过数据可获取的不同大小和形状的地理单元控制，并通过不同变量（如就业与人口密度或者旅次产生率）测算得到。该指数的属性可以通过人工数据集的模拟示例说明，或者通过对比已有文献对相似指数的阐述加以说明。然后，通过将该指数应用于全球四个大都市区（美国匹兹堡和洛杉矶、巴西圣保罗和法国巴黎）的城市结构中进行检验。最后，将该指数与其他测度传统空间集聚指数如全局和局部Moran指数及密度梯度估计进行对比.

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mentioning

confidence: 99%

Urban Centrality: A Simple Index

Pereira

Nadalin

Monastério

et al. 2012

Geographical Analysis

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“…Many studies also investigate different ways to estimate or formulate the population density function using traditional statistical and econometric methods (Muth 1969, Mills 1970, Griffith 1981a, 1981b, Alperovich 1983, Anselin and Can 1986, Batty and Kim 1992. However, most of these modeling efforts, except those by Anselin and Can (1986), Griffith (1981a), and Griffith and Can (1995), do not take into account that population density is spatially autocorrelated. A recent analysis uses spatial regression to model the population density of the 20 largest US metropolitan areas according to the 2000 Census (Griffith and Wong 2007).…”

Section: Population Density Structurementioning

confidence: 97%

Exploring and simulating the regularities in intra-urban population density structure

Wong

Griffith

2009

Annals of GIS

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Sizes in a system of cities follow the so-called rank-size distribution or the more general Zipf's law. Previous research demonstrates that the rank-size relationship can be explained and simulated by a rather simple spatial choice model, describing individual residential behavior across cities. In studying population density within each of the 20 largest metropolitan areas in the United States, we discovered another type of regularity: population density at the tract level and the logarithm of the rank by tract density within a city exhibit a linear relationship. We call this rank-density regularity. In this article, we explore whether the simple spatial choice model originally developed to simulate city size distribution at the inter-urban scale can be used at the intra-urban scale to explain the rank-density pattern and the formation of urban density structure. We found that after adjusting the simple model for the city-edge constraint, the model can simulate the rankdensity relationship reasonably well. In order to depict the spatial structure of population density more realistically, the model must include sub-centers, which increase the complexity of the model. Overall, the spatial choice model can reproduce the rank-density structure quite well. We believe the model captures the dominant forces in the formation of the population density distribution at the intra-urban scale.

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“…The classical study undertaken by Clark (1951) has generated an extensive body of literature dealing with empirical implementations for a wide range of metropolitan areas and cities, in different countries and at different times. The generalisation of the functional form and the comparison of results are the work of McDonald and Bowman (1976), Anselin and Can (1986) and Zielinski (1979). The functional form of urban population density is not unique and this implies that a selection process must be adopted in each case.…”

Section: The Basic Modelmentioning

confidence: 99%

Income, distance and amenities. An empirical analysis

2013

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This paper analyses the income distribution of households in Barcelona metropolitan area. For this purpose we use the monocentric model. As the basic model does not have direct implications for this distribution, we survey the extensions of the model that have been used in empirical literature. One of the most promising ways is to introduce externalities in the decision process; they can result directly from exogenous amenities (given traits of urban area) or be created by other agents' decisions. We first test the simple model relating income to distance. Then we introduce and test the model with exogenous amenities; recreational areas, transportation systems, health, educational and cultural infrastructure. In the third stage we test the model with spatial effects. We present evidence that any model with spatial effects improves significantly the empirical results.

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Model Comparison and Model Validation Issues in Empirical Work on Urban Density Functions

Cited by 37 publications

References 62 publications

Urban Centrality: A Simple Index

Urban Centrality: A Simple Index

Exploring and simulating the regularities in intra-urban population density structure

Income, distance and amenities. An empirical analysis

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