Academic journal article Cityscape

Using Dual Kernel Density Estimation to Examine Changes in Voucher Density over Time

Academic journal article Cityscape

Using Dual Kernel Density Estimation to Examine Changes in Voucher Density over Time

Article excerpt

Abstract

The measurement of participants in the Housing Choice Voucher Program across time is an important analytical step toward understanding their settlement patterns, particularly whether they concentrate or deconcentrate. Many analyses of voucher-holder settlement patterns employ some areal unit in which counts are divided by unit area to calculate a density. This approach has methodological problems and produces less-than-accurate results because it does not directly measure the locations of voucher holders. In this article, I show how to apply a technique, known as Dual Kernel Density Estimation, to measure directly the concentration of voucher-holder locations to produce more accurate results about where voucher holders have concentrated and deconcentrated over time.

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Introduction

Many housing and urban development problems are inextricably tied to place. Because of this link to place, certain questions often arise. Will foreclosures concentrate and spread to neighboring areas through falling house prices? Will tax increases in one county send residents to nearby counties to shop or relocate? Will crime displace to adjacent neighborhoods in the event of a concerted effort to break up a concentration of incidents? Answers to such questions require the measurement of spatial relationships between places that classical statistical techniques are not capable of measuring. In this premier article of SpAM, I demonstrate how to use a spatial smoothing technique to identify changing patterns of voucher-holder concentration between two points in time.

Housing researchers are often concerned about the concentration of voucher holders. A typical approach to measuring voucher-holder density change is by comparing areal densities (events per acre or per square mile) at two different times using already defined political or administrative units (for example, nations, states, counties, or census tracts). Chances are high that measuring change with these units will produce less-than-accurate results, because it does not directly measure the locations of voucher holders. In this article, I show how to apply a more accurate technique, Levine's Dual Kernel Density Estimation (DKDE), using the locations of housing choice voucher holders in the Charlotte-Mecklenburg, NC metropolitan region for purposes of illustration. For a more detailed exposition, see chapter 8 in Levine (2010).

The Housing Choice Voucher Program (HCVP) enables low-income families to relocate to neighborhoods of their choice. In 2010 alone, approximately 2.1 million families received assistance through the HCVP.1 One common concern about the relocation freedom that HCVP offers is that participants will concentrate in certain neighborhoods. Research has shown that voucher holders often relocate to neighborhoods comparable with those in which they lived before receiving assistance (Freeman and Botien, 2002; Huartung and Henig, 1997; McClure, 2010; Pendall, 2000; Varady, Walker, and Wang, 2001; Wang, Varady, and Wang, 2008).

Moving Beyond Measuring Density Calculations With Areal Units

Many voucher-holder location analyses use census tracts to measure density. In a typical calculation of densities from areal units, a count of observations within the unit is divided by the unit area. This approach has two main problems. First, the aggregation of observations to the areal units forces an incorrect assumption that voucher-holder locations are evenly spread across the unit; the larger the census tract, the more unrealistic the assumption becomes. Second, the variation in census tract shapes will arbitrarily influence the unit within which an observation falls; this method may split up groups of voucher-holder locations.2

With DKDE, single kernel density surfaces are created by interpolating estimates from a geographically distributed set of observations. Estimates are calculated by overlaying a grid system across a geography in which the distance from each cell to every observation within a specified distance is measured and weighted. …

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