The Multi Nearest Neighbor Distance Method for Analyzing the Compound Effect of Infrastructural Elements on the Distribution of Activity Points

Abstract

W e propose a statistical method to analyze the compound effect of infroastmctural elements (such as stations, arterial streets, and lakes) on the distribution of activity points (such as retail stores) over a region. First, we f m u l a t e a function that explicitly shows the compound effect of infrastmctural e h t s . Second, we show an eficient computational method for estimating this compound function from data. Third, we develop multivariate statistical methods for testing several hypotheses about these compound effects. Last, we examine the compound effect of a r t d l streets and subway stations on the distribution of "high-chs"apartmt buildings in Sumida-Kohto, Tokyo.

2.15 or Not 2.15? An Historical‐Analytical Inquiry into the Nearest‐Neighbor Statistic

“…Where authors notably depart from NNA, the situation is quite different. A few, uncoincidentally from engineering backgrounds, have deployed substantially reframed species of nearest-neighbor measures to probe an expansive "geometry" of features-"point-like, line-like, surface-like"; maybe networked and amenable to representation and analysis as "graphs" or "sub-graphs" (Pace and Zou 2000)-before addressing the implications for calculating test statistics, estimating distances to different orders of nearest-neighbor "facilities" under differing conditions, and then practically planning for facility opening or closure (e.g., Okabe and Yoshikawa 1989;Okabe and Yamada 2001;Miyagawa 2009Miyagawa , 2014.…”

“…Two examples are: Jones (1971, p. 367), who explored the behavior of R n across different orders of neighbors for different sorts of random and regular lattice, one finding being that the statistic appears to “converge asymptotically to the value of 2.1491 quoted by Clark and Evans … for the hexagonal case”; and Thomas (1977, p. 415), who proposed a different nearest‐neighbor statistic, based not on Poisson but rather the geometric distribution and its principle of “equal likelihood,” although he still took 2.1491 as the maximum when comparing the Clark and Evans statistic with his alternative for analyzing regular distributions based on the “equilateral triangle.” Where authors notably depart from NNA, the situation is quite different. A few, uncoincidentally from engineering backgrounds, have deployed substantially reframed species of nearest‐neighbor measures to probe an expansive “geometry” of features—“point‐like, line‐like, surface‐like”; maybe networked and amenable to representation and analysis as “graphs” or “sub‐graphs” (Pace and Zou 2000)—before addressing the implications for calculating test statistics, estimating distances to different orders of nearest‐neighbor “facilities” under differing conditions, and then practically planning for facility opening or closure (e.g., Okabe and Yoshikawa 1989; Okabe and Yamada 2001; Miyagawa 2009, 2014).…”

Distribution of the Sum of Distances to the First and Second Nearest Facilities

“…The nearest neighbor distance method introduced by Clark and Evans (1954) is based on the distance between neighboring points. The nearest neighbor distance also has been applied to analyze the effect of infrastructural elements on the distribution of activity points (Okabe and Fujii 1984;Okabe and Miki 1984;Okabe et al 1988;Okabe and Yoshikawa 1989). The nearest neighbor distance also has been applied to analyze the effect of infrastructural elements on the distribution of activity points (Okabe and Fujii 1984;Okabe and Miki 1984;Okabe et al 1988;Okabe and Yoshikawa 1989).…”

“…The nearest neighbor distance method on a network was developed by Okabe, Yomono, and Kitamura (1995). The nearest neighbor distance also has been applied to analyze the effect of infrastructural elements on the distribution of activity points (Okabe and Fujii 1984;Okabe and Miki 1984;Okabe et al 1988;Okabe and Yoshikawa 1989). Although the nearest distance is the most important, the distance to the kth nearest point is necessary to deal with complicated patterns.…”

Statistical Analysis of the Distribution of Points on a Network

“…In the subseuent two subsections, using two types of general binomial point processes, we 8scuss how to analyze the effect of a single kind of infrastructural elements (section 5.1) and the compound effect of multiple kinds of infrastructural elements (section 5.2). [Note that a similar study assuming a continuous plane is done by Okabe and Yoshikawa (1989). ]…”