Dependent variable: the location of retail and food establishments

Our main question variables are the observed locations of retail and food establishments. The decision to couple retail and food establishments together originates from functional similarities in these types of establishments. In Webber’s classification of economic activities as production, exchange, and consumption, both retail and food establishments belong to the exchange category, where the supplies of producers and the demands of consumers meet (Weber and Friedrich 1929). Unlike production activities, whose location choices maximize access to production inputs, or consumption activities, whose location choices maximize access to goods and services, exchange activities maximize access to customers. Location choices of retail and food establishments thus share an important commonality: both rely heavily on spatial access to patrons (See Figure 4). We therefore begin our analysis by treating retail and food establishments as a single group and later also look at the location preferences of each retail and food establishment type separately.

Figure 4 Davis Square in Somerville in 2009. The ground floor of a corner building is occupied by a number of retail and food establishments: a diner, a tobacco and convenience store, a café, a dollar store, and a pastry shop.

The InfoUSA 2009 data include a total of 8,163 individual establishments of all NAICS categories in Cambridge and Somerville. Of these, we selected establishments that are categorized as retail trade (NAICS 44-45) and food services (NAICS 722) as our dependent variables, which yielded a total of 1, 941

73

NAICS Description n

establishments in the two neighboring towns: 1,258 retail establishments, and 683 eating establishments. In accordance with retail location theory, the number of establishments reflects their frequency of visits (DiPasquale and Wheaton 1996). Food Services and Drinking Places, which are visited frequently, have the most establishments (683), followed by Food and Beverage Stores (231), Electronics and Appliance Stores (230), Miscellaneous Store Retailers (189), and so on. The three-digit NAICS categories observed in Cambridge and Somerville are listed in Table 1. Figure 5 illustrates how these establishments are geographically distributed across the two cities.

441 Motor Vehicle and Parts Dealers 86

442 Furniture and Home Furnishings Stores 11

443 Electronics and Appliance Stores 230

444 Building Material and Garden Equipment Dealers 66

445 Food and Beverage Stores 231

446 Health and Personal Care Stores 35

447 Gasoline Stations 45

448 Clothing and Clothing Accessories Stores 166

451 Sporting Goods, Hobby, Book, and Music Stores 142

452 General Merchandise Stores 41

453 Miscellaneous Store Retailers 189

454 Nonstore Retailers 16

722 Food Services and Drinking Places 683

Total: 1941

Table 1 Categories and counts of retail or food establishments found in Cambridge and Somerville, MA.

We assigned each retail and food establishment to a corresponding building in both towns, as shown in Figure 6. Eighty-one per cent of the InfoUSA establishment points were matched to a building directly by address coding in GIS, the rest were spatially joined to the nearest building. Each building thus obtained a dichotomous variable (0 or 1) showing whether or not the building contains retail or food establishments and a continuous variable (0 – n) indicating the count of establishments in each of the three- digit NAICS categories. Since some buildings contain multiple retail establishments, the number of observations diminishes from 1,941 individual establishments to 961 buildings containing retail or food establishments. The dichotomous variable, representing the presence or lack of retail or food establishments in each building, defines our dependent variable in the following analysis.

Figure 5 Locations of retail and food establishments in Cambridge and Somerville, MA. (n=1, 941).

Cambridge & Somerville city limits Food service establishments Retail establishments 0 0.2 0.4 0.8 1.2 1.6 Miles

b

N T Subway station Teele Sq Kendall Sq Inman Sq Lechmere Union Sq Ball Sq Davis Sq Fresh Pond Porter Sq Harvard Sq Central Sq T T T T T T 74

Figure 6 Map of 961 buildings containing retail or food establishments in Cambridge and Somerville, MA.

Cambridge & Somerville city limits Retail / Food Services

0 0.2 0.4 0.8 1.2 1.6 Miles

b

N

Figure 5 and Figure 6 suggest that retail and food service establishments in Cambridge and Somerville are spatially clustered in limited geographic locations, but often locate in the same places. Harvard Sq, Central Sq, Porter Sq, Davis Sq and other well-known business clusters accommodate a notably higher concentration of establishments than an average locality in the two towns. During a ten-minute walk around Harvard Sq, the busiest retail cluster in Cambridge, a visitor can find 131 retailers and 90 food service establishments. A similar pattern, with a smaller total count, is observed at other popular retail clusters of the area. Whether these spatial concentrations of retail and food establishments are statistically significant can be tested using spatial cluster analysis.

A commonly used index for describing the spatial clustering of geographic phenomena is the Moran’s I index. The Moran’s I, named after Patrick A. P. Moran, compares the observed distribution of retail and food establishments to a hypothetical random distribution of the same number of points (Anselin 1988). In order to describe adjacency relationships between observed events, a spatial weights matrix is first specified to describe binary neighbor relationships between buildings in a given radius. Using a 100-meter (328-foot) radius produces an adjacency matrix where a building is shown to be neighbors with all other buildings that are located within a 100-meter distance from it. Though this radius has traditionally been measured using straight-line Euclidean distances, we measured our weights matrix on the street network of Cambridge and Somerville. Our weights matrix thus lists binary (0 or 1) neighbor relationships between buildings that are up to a 100-meters apart from one another along actual street network paths. Using the dichotomous dependent variable of each building, indicating the presence or lack of retail and food establishments, allows the Moran’s I to estimate the degree of clustering between businesses. If a greater number of neighboring retailers are observed within the 100-meter radius than in a random distribution, then establishments are considered clustered. If fewer retail neighbors are observed than expected in a hypothetical random distribution, then the establishments are considered dispersed. In order to achieve statistical confidence, the random point distribution is repeated numerous times in Monte Carlo simulations, 999 times in our case to achieve a 99.9% pseudo-significance level.

Our data show that Moran’s I for retail and food establishments in Cambridge and Somerville is 0.1551 (p< 0.001), suggesting that the observed geographic concentration of businesses is statistically highly significant. However, since this global Moran’s I is the mean of all local Moran’s I statistics, then its reliability can be challenged if the distribution of local values is highly asymmetric, or dominated by a few outliers. Therefore in Figure 7 we illustrate how the significance levels of Moran’s I are locally distributed among individual buildings. The map suggests that the 95 - 99.9% significance range distinguishes most of the anecdotally known retail clusters of both towns. Harvard Square, Central Square, Inman Square, and Union Square stand out with particularly significant clustering coefficients, but even very small business clusters that include only a couple of stores, also appear statistically different from a random distribution at the 95% significance level. Our data thus suggest that the pattern of intra-urban retail and food service establishments exhibit significant spatial clustering. Diverging from theoretical expectations of Central Place Theory, centers do not form a clearly hierarchical pattern of hexagonal market areas. Though indeed scattered throughout the two towns, centers appear concentrated around important intersections and thoroughfares of the street network.

Figure 7 Significance map of local spatial autocorrelation of retail and food service establishments in Cambridge and Somerville (n=961).

In order to gain further insight from the observed pattern, we also analyzed the degree of clustering using Nearest Neighbor Distance (NND) analysis (Okabe, Okunuki et al. 2001). The Nearest Neighbor Distance method measures the distance between each event and its nearest neighboring event. Similar to Moran’s I, NND compares the observed neighbor relationships with the hypothetical random neighbor relationships, but additionally also outlines the differences in distance units. The index is expressed as the ratio of the observed distance between retailers divided by the randomly expected distance:

_ _ e o D D NND=

where is the observed average distance between neighbors and is the expected average distance between neighbors. The observed average distance is determined as follows:

_ o D D__e n d D n i i o

∑

= = 1 _

where di equals the distance between event i and its nearest neighbor event, and n is the total number of

events. The expected distance is based on a hypothetical Poisson distribution with the same number of events covering the same total length of streets L:

L n D_e 0.5

_

=

Though NND, too, has traditionally been measured on a Euclidian plane (Diggle 1983; Boots and Getis 1988), the detailed intra-urban scale of our analysis required that the distances be computed on the actual street network. A GIS toolset for calculating event distributions on a network has recently been developed at the Center for Spatial Science in Tokyo University (Okabe, Okunuki et al. 2001). Professor Okabe, has generously shared their GIS-based SANET toolbox for the purposes of the present research. Figure 8 illustrates the results of NND analysis for retail and food establishments on the street network of Cambridge and Somerville.

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 20 ₁₄0 ₂₆0 ₃₈0 0_{50 62}0 ₇₄0 ₈₆0 ₉₈0 1100 1220 1340 1460 1580 1700 1820 1940 2060 2180 2300 2420 2540 2660 2780 2900 3020 3140 3260 3400 3520 3640 3760 3880 4000 Cum u la ti ve  pe rc e nt ag e  of  re ta ile rs Distance between retailers (in feet) Random Mean Upper 5% Random  boundary Lower 5% Random boundary Observed Data

Figure 8 Observed and random nearest neighbor distances of Cambridge and Somerville retail and food establishments.

The graph shows that for approximately 95 % of retail establishments, the distance to nearest neighbors in the observed data is much shorter than it would be if the distribution were random. The solid black trajectory describes the observed nearest neighbor distances. The lighter gray trajectories describe the mean and ±95% significance boundaries of a hypothetical random distribution. At the bottom of the scale (lower left corner of the graph), we observe around 45% of retailers with nearest neighbors available at less than 25 feet from their location, suggesting that numerous retailers locate in the same or immediately adjacent buildings. Roughly half of the establishments have access to a neighboring establishment within 80ft from their location along the street network. In a random distribution, the average distance to the nearest neighbor among these 50% of retailers would be 320ft, which is four times as long. The exploratory analysis using network-based NND thus further confirms that retail and food establishments in our study area are significantly concentrated and suggests that our analysis of location choices should account for clustering as a possibly important location choice factor for retail and food establishments.

In document Study of urban geometry and retail activity in Cambridge and Somerville, MA (Page 82-89)