«Urban Problems and sPatial methods VolUme 17, nUmber 1 • 2015 U.S. Department of Housing and Urban Development | Office of Policy Development and ...»
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126 Urban Problems and Spatial Methods An Integrated Framework To Support Global and Local Pattern Assessment for Residential Movements Yin Liu Sichuan Normal University Alan T. Murray Drexel University Abstract Residential mobility is a defining characteristic of society in the United States. A 2003 U.S. Census Bureau migration report highlights that more than 22 million people were characterized as domestic migrants between 1995 and 2000. Understanding resulting patterns is important because it provides insights on rationale for movement and for housing, services, and supporting infrastructure implications. The method for facilitating pattern identification and exploration of movements unfortunately is lacking. It is often the case that migration and movement are considered in aggregate terms—between cities and counties in a state or region. Individual behavior reflective of a movement trajectory is therefore masked in various ways. Survey evidence also indicates that residential movements of short distance—for example, those occurring within a city or county—reflect the greatest proportion of total migrations. To address limitations, this research proposes a framework integrating spatial analytical methods to support pattern analysis for individual movements, relying on detailed information of origin and destination change. The framework can explore the patterns at both the global and local levels. The framework is designed using various visual analytic interfaces coupled with statistical evaluation and significance testing, representing both exploratory and confirmatory assessment. The integrated framework is applied to study residential movement involving 2,636 housing changes in Franklin County, Ohio, and effectively estimates some special global and local patterns from those events.
Cityscape 127 Cityscape: A Journal of Policy Development and Research • Volume 17, Number 1 • 2015 U.S. Department of Housing and Urban Development • Office of Policy Development and Research Liu and Murray Introduction Residential mobility is a defining characteristic of U.S. society today. Studies of residential changes can enable better understanding of how humans and the environment engage in mutual interactions in different places and at different scales. For the researchers, including geographers and urban planners whose major interest is to comprehend and design better urban environment, it is especially meaningful to examine the effect of a collection of residential movements, if such spatial data are available, as a way of studying the immediate changes in the composition of many urban neighborhoods. The information associated with change of residence can also provide insights into the mechanism under which urban structure constrains residential choices. Therefore, residential movement is an important issue.
Research on residential movement has been carried out for more than a century (Quigley and Weinberg, 1977; Ravenstein, 1885) and is still of broad interest to researchers today (Dieleman, 2001; Rae, 2009). A major part of those research attempts was rooted in cartographic technique and gradually has developed to spatial data visual analytics, in which computational tools have been extensively involved (Andrienko et al., 2008; Rae, 2009; Ravenstein, 1885; Tobler, 1987).
The disadvantage of spatial data visual analytics is its incapability for confirmatory hypothesis testing in spatial pattern identification.
On the other hand, the confirmatory analyses actually have been applied into movement pattern since the 1960s. Depending on mathematical and statistical methods, those works essentially transformed the spatially complex form of movements into manageable geometry and so focused more attention on the movements’ spatial pattern (Adams, 1969; Brunsdon and Corcoran, 2006;
Fotheringham and Pitts, 1995; Morrill, 1963). The disadvantage of those works is that they were excessively focused on the “global map” or general “law.” Meanwhile, such method is heavily based on aggregated data.
Compared with the study based on aggregated data at the macro level, it is actually more important for geographers and urban planners to understand the pattern of residential movement at the micro scale with individual records, because the pattern can directly and accurately illuminate the change of social composition in a county or city. The difficulty with such perspective shifting is the significant raising of data size. With hundreds and thousands of individual movement records, significant patterns can be masked (Andrienko et al., 2008). Taken with redesigned visual analytics, however, statistical methods might prove efficient and effective for exploring and evaluating patterns in mass movement data. Exploratory spatial data analysis (ESDA)-based studies recently have recognized this necessity, and researchers have suggested possibilities for combining visual analytics and statistical methods (Thomas and Cook, 2005). As yet, a systematic framework has not been developed that reflects this necessity, synthesizing both confirmatory and exploratory approaches.
Method Generally speaking, spatial patterns refer to the specific spatial configuration or arrangement of features of interest over space (Chou, 1995). Insights into the characteristics of spatial patterns result in knowledge of the dynamics of spatial processes (Getis and Boots, 1978).
Movement data are records of spatial trajectory for tracking behavior over space or, more abstractly, as a directional line with fixed length. In geometry, such form of a trajectory is essentially a vector of distance and direction. Based on this perspective, the spatial pattern in residential movements can refer to a spatial arrangement of the dual components: moving distance and moving direction.
Distance is a basic means for measuring the space separating objects; it is also used to quantify the possible intensity of a relationship and interaction between geographical events. The distribution of moving directions is a reflection of urban evolution. Research in spatial arrangement of moving directions within a city can be used to examine whether a specific planning strategy has been effective in generating movements toward certain areas (Quigley and Weinberg, 1977). A research difficulty is figuring how to analyze the features of distance and direction simultaneously.
The proposed framework is to resolve this difficulty by both exploratory and confirmatory approaches.
Exhibit 1 illustrates a proposed framework with general structure for data analysis. First, the movement data records are processed and converted into a standard format. Using the manipulated Exhibit 1 Conceptual Framework of the Proposed Toolkit
data, visualization-based analysis is then performed, incorporating exploratory data analysis using multiple interfaces. Based on visual analytics, quantitative examination is included to test visually detected patterns at both the global and local scales.
Standardization of Movement Data
A unique method of data standardization is suggested here as the first step for pattern analysis:
moving all the vectors’ origin or destination to an identical center while maintaining distance and direction. The effect is shown in exhibit 2.
The standardized movements intuitively provide a more direct and clear illustration of the distribution of distances and directions. Distances are abreast with each other from the same start, and directions are arranged in a uniform circle to form something like a rose. In this standardized interface, potential patterns in the arrangement of distances and directions cannot be easily masked.
Thus, patterns in the distances and directions can be simultaneously illustrated.
Exploratory Analysis Interface Given the standardized movement data, one can imagine that they are distributed along a series of circular sections. The width for each circular section represents a unit range of length away from the established center. Further, each circular section can be separated into several equal fan sectors based on a directional range. Based on this idea, as shown in exhibit 3, a partition scheme is possible.
Based on the partition scheme over standardized vectors, a color gradation is applied to each section to enable visual understanding. The darkness of color in each section is in accordance with the counts of endpoints in this section. The more endpoints in a particular section, the darker the fill color.
Exhibit 3 A Partition Scheme for Standardized Vectors a b Notes: (a) The partition scheme is generated by identical distance and direction intervals; concentric circles surrounding an established center partition the vectors by equal length interval (the radius of the largest circle equals the largest vector length), and homocentric rays from the center partition the vectors by equal angle interval. (b) The partition scheme is set over standardized vectors.
Statistical Analysis of Movement Patterns Because the partitioned scheme parallels the quadrat analysis interface, a type of statistical testing, the goodness-of-fit metrics, can be applied to examine whether the actual distribution of distance and direction follows a theoretical pattern. Such a method is also meaningful for exploring the pattern for a specific subset of movements and for testing whether this subset possesses a pattern that is similar to or different from the global pattern. Using this kind of comparison, it is possible to explore whether community dissimilation or mixture is occurring in a city or region.
where Li equals the counts of the endpoints for local data in section i, Gi equals the counts of the endpoints for entire data in the same section i, a and b are the regression parameters, and εi is the regression error for the section i. The similarity between global and local patterns can be tested by the coefficient of determination, R-square, of the linear regression model. Here, R-square indicates the proportion of the local pattern “explained” by the global pattern. The lower the R-square value, the less consistency exists between local and global patterns.
Distance Decay and Directional Bias That locations separated by shorter distances are more related has been globally examined and has become a fundamental theory for spatial science, the theory of “Distance Decay” (Fotheringham and
O’Kelly, 1989; Taylor, 1975). Given this global theory, within a study area, more residential movements will reasonably be expected with short distance than with longer movements. The question is how to quantitatively measure the frequency of movements with specific moving distances.
Taylor (1975) has given two model categories and five specific expressions for describing the quantitative relationship between the moving distance and the movement intensity.
1. Single-log models f(d) = dm.
where I is the intensity of movements, d is the distance, and a and b are regression parameters to be estimated. Among these five specific forms, the issue to resolve is which one, if any, would best describe the distance decay tendency in observed behavior. Different estimates and values in parameters may help reveal information associated with moving behaviors. The estimation relies on a statistical test, such as R-square or P-value. The test can be formalized as—
where λx is a test index (that is, R-square or P-value) used for evaluating the regression equation gx (I,d).
In the standardized interface, intensity of movements is equivalent to intensity of endpoints; thus, movement intensity is derived based on endpoints within different distance ranges. Exhibit 4 illustrates this consideration.