Quantile Regression for Spatial Data

verfasst von: Daniel P. McMillen

Verlag: Springer Berlin Heidelberg

Buchreihe : SpringerBriefs in Regional Science

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

Einloggen, um Zugang zu erhalten

Über dieses Buch

Quantile regression analysis differs from more conventional regression models in its emphasis on distributions. Whereas standard regression procedures show how the expected value of the dependent variable responds to a change in an explanatory variable, quantile regressions imply predicted changes for the entire distribution of the dependent variable. Despite its advantages, quantile regression is still not commonly used in the analysis of spatial data. The objective of this book is to make quantile regression procedures more accessible for researchers working with spatial data sets. The emphasis is on interpretation of quantile regression results. A series of examples using both simulated and actual data sets shows how readily seemingly complex quantile regression results can be interpreted with sets of well-constructed graphs. Both parametric and nonparametric versions of spatial models are considered in detail.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Quantile Regression: An Overview

Abstract

Linear regression is the standard tool for empirical studies in most of the social sciences. When the relationship between a dependent variable, y, and a set of explanatory variables, X, can be written as \( y = X\beta + u \), a simple ordinary least squares (OLS) regression of y on X can potentially provide unbiased estimates of the parameters, β, and a predicted value, \( \widehat{y} = X\widehat{\beta } \) is the best guess of the value of y given values for X. A glance at any journal in the social sciences quickly reveals the dominance of regression analysis as the tool for empirical analysis.

Daniel P. McMillen

Chapter 2. Linear and Nonparametric Quantile Regression

Abstract

Quantile regression estimates can be presented in tables alongside linear regression estimates. A possible advantage of this approach to presenting quantile regression results is that it is easy to compare the values of the coefficients and standard errors with OLS estimates and across quantiles. As we have seen, quantile estimates actually contain far more information than can be presented in simple tables. The estimates imply a full distribution of values for the dependent variable. It also is easy to show how changes in the explanatory variables affect the distribution of the dependent variable.

Daniel P. McMillen

Chapter 3. A Quantile Regression Analysis of Assessment Regressivity

Abstract

In this chapter, I compare OLS and quantile regression approaches to analyzing assessment regressivity. Property assessments have a pivotal but woefully neglected role in determining the distribution of property tax payments across homeowners. The example used in this chapter is based on sales of homes in DuPage County, Illinois, which is a suburban part of the Chicago metropolitan area. Like all other counties in Illinois (other than the largest, Cook County), properties in DuPage County are supposed to be assessed at 1/3 of market value. All properties in a tax district are then subject to the same tax rate. Apart from homestead exemptions and other relatively minor deductions, this flat-rate tax system should result in tax payments that are proportional to market value. However, a common finding in studies of assessment practices is that assessment ratios—the ratio of the assessed values to actual sales prices—decline with market value. Declining assessment ratios will result in a regressive property tax structure even in the case of a statutorily proportional system (where “regressive” is defined as a system in which the ratio of tax payments to sales prices declines with sale price).

Daniel P. McMillen

Chapter 4. Quantile Version of the Spatial AR Model

Abstract

The analysis up to this point has not been explicitly spatial. Although the explanatory variables might include measures of access to various amenities such as a city’s central business district, parks, or lakes, nothing yet is unique to the analysis of spatial data. Several attempts have been made to adapt the standard spatial autoregressive (AR) model for quantile regression. The studies by Kostov (2009), Liao and Wang (2012), and Zeitz et al. (2008) represent the first attempts to estimate quantile versions of the spatial AR model.

Daniel P. McMillen

Chapter 5. Conditionally Parametric Quantile Regression

Abstract

Chapter 2 demonstrated that nonparametric approaches can easily be adapted to quantile regression models. In the case of a single explanatory variable, x, all that is necessary to make the model nonparametric is to add a kernel weight function \( k\left( {\left( {x - x_{t} } \right)/h} \right) \) when estimating a quantile regression for a target point \( x_{t} \). After estimating the function for a series of target points, the estimates can then be interpolated to all values of x. The nonparametric approach is a flexible way to add nonlinearity to the estimated quantile regressions.

Daniel P. McMillen

Chapter 6. Guide to Further Reading

Abstract

I have tried to keep the chapters more readable by avoiding footnotes and limiting citations to a few critical papers. A guide to additional reading may prove useful, however.

Daniel P. McMillen

Backmatter

Titel: Quantile Regression for Spatial Data
verfasst von: Daniel P. McMillen
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-642-31815-3
Print ISBN: 978-3-642-31814-6
DOI: https://doi.org/10.1007/978-3-642-31815-3