Goal • The purpose of this project is to examine the concentration of fast-food

restaurants around schools in Phoenix, Arizona

• Characterize school neighborhood food environments

Data List of 1029 Fast-food restaurants and coordinates in Longitude and Latitude

come from Yelp Dataset Challenge and cross-checked with yellowpage.com.

List of 310 schools

(elementary, middle,

and high schools) and

addresses come from

city-data.com. All

addresses geocoded

using Google Map.

Methods Distance to nearest Fast-food restaurants from schools • Earth surface distances measured in kilometers • 23/310 schools have at least one Fast-food restaurant within 0.5 km radius • 120 schools have at least one Fast-food restaurant within 1 km radius • 223 schools have at least one Fast-food restaurant within 1.5 km radius

Assess Spatial Clustering of Fast-Food Restaurants Around Schools in Phoenix, AZ Yao Wang, Loyola University Chicago - Fall 2015

Bivariate K-function for Marked Data If the points of a process are marked, the K-function takes a general form in

where is the number of extra events of label j within a positive distance

r of a randomly chosen event of label i, and λ is the intensity of events.

• If points are approximately homogeneous, each event is equally likely to

occur in the study area. K-function should be approximately equal to .

• Events that are attractive produce clustering and are more likely to occur

with each other in the available study area.

Dixon Pairwise Segregation Index Off-diagonal elements of the nearest-neighbor contingency table

where N(i) is the number of events of label i, N(ij) is the frequency of event i

as neighbor of event j, and N is the total number of events.

• S(ij) is larger than 0 when N(ij), the frequency of neighbors of event j around

points of events i, is larger than expected under random labelling; and less

than 0 when N(ij) is smaller than expected under random labelling.

Results Estimated K-functions of Fast-Food (1,1), Fast-Food to Schools (1,2), and

Schools (2,2) are plotted in black color. K-function for Poisson process CSR

and 95% CI are plotted in red and grey scale.

We see higher number of Fast-food exists at a distance r to schools compared

to CSR (Poisson) in plot (1,2), indicating strong clustering of Fast-food

relevant to Schools.

However, the level of clustering is weaker compared to K-function of schools

at (2,2). This might be the result of existing high concentration (clustering) of

both Fast-food and Schools in Phoenix, AZ area.

Dixon function in R software calculates pairwise segregation index S using

a combined dataset of 310 schools and nearest neighbors with labels

(fastfood or school).

Interestingly, S(fast food, school) < 0: the frequency of fast-food

restaurants existing around schools is smaller than expected under

random labeling. This is because the observed count of fast-food with

schools as NN, and vise versa, are both significantly lower than the

expected counts under random labeling, using Z-score and p-value under

randomness distribution of labels (fastfood or school).

S (fast food, fast food) > 0, and S (school, school) >0: Strong concentration

of individual label itself. This is same situation as we observed in

univariate and bivariate K-functions.

Conclusion • Small number of school have at least one fast-food restaurants within

0.5 km radius, which is 6~7 minutes walking distance

• Majority of the distances between a school and its closest fast-food

restaurants are between 0.5 ~ 2 km, i.e. 7~40 minutes walking distance

• Strong spatial clustering of Fast-food restaurants within Phoenix,AZ

area

• Strong spatial clustering of Schools within Phoenix,AZ area

• Evidence do not support statistically significant clustering of Fast-food

restaurants around schools within Phoenix,AZ area

Study shows mild risk of school neighborhood food environment impacted by high clustering of fast-food restaurants around schools in Phoenix, AZ.

Future Research • Limited to only city area

• Divide area by zip code

• K function control for edge effect

• Include convenient stores,

grocery and food stores as healthy

and unhealthy food sources for

students in schools

References 1. Austin, S. Bryn, Steven J. Melly, Brisa N. Sanchez, Aarti Patel, Stephen Buka, and Steven L. Gortmaker. "Clustering of fast-food restaurants around schools: a novel application of spatial statistics to the study of food environments." American Journal of Public Health 95, no. 9 (2005): 1575. 2. Analyzing Multiple Independent Spatial Point Processes, Neal Grantham, Advised By Dr. Andrew Schaffner May 2012 California Polytechnic State University, San Luis Obispo http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1020&context=statsp 3. Dixon, P.M. 2002. Nearest-neighbor contingency table analysis of spatial segregation for several species. Ecoscience, 9 (2): 142-151. 4. New Tests of Spatial Segregation Based on Nearest Neighbor Contingency Tables, Elvan Ceyhan , arXiv:0808.1409v3 [stat.ME] 28 Jul 2009

Univariate (1,1) (2,2) & Cross (1,2) K-functions