Explore other distance terms

[gregmacfarlane]

Reviewer 2

I’m concerned by the use of tract centroid and Euclidean distance. I see that you’ve mentioned this in the limitations, but the difference between tract centroid vs parcel distance to a park can be around a 1000 meters (Logan et al. 2019) and this is using network (not Euclidean) distance. As a result, I have little confidence in the findings regarding the relationship between park access and health. However, I defer to the editor as to whether the paper’s novelty is solely the utility-based access measure, or if it’s the findings related to parks and health.

please provide details of the park distance data. Is it tract centroids to all parks? Using Euclidean, walking network, driving network etc.? what is the park distance data and how did you calculate it? (I see you discuss this in the limitations, but this should be in the data section)

[gregmacfarlane]

I have Connor working on a block group-to-park boundary network distance calculator.

[gregmacfarlane]

The calculator is complete as of 2be41f858dda142a5aa091a47a7a098fb131a829.

[gregmacfarlane]

First, we calculate the nearest node in the OpenStreetMap network to the population-weighted tract centroid. Then, we calculate the Euclidean distance between each park and each park point. We then find the nearest node to that Euclidean points, and calculate the shortest network distance between the two nodes.

There appears to have been an issue in calculating the shortest paths to Staten Island. The plot below shows the distance between tract centroids and parks calculated by Euclidean and Network distance, facetted by park borough ("B"rooklyn, "M"anhattan, "Q"ueens, "R" for Staten Island, and Bron"X") across the top. Cemeteries get their own category "C". The tract borough is listed by FIPS code going down. Staten Island is 085.

It is clear that something is wrong with the OpenStreetMap network in Staten Island. Almost every exchange between park and tract appears to have a shorter network distance than a Euclidean distance, which violates several laws of geometry.

[gregmacfarlane]

So, in cases where the network distance was shorter than the Euclidean distance, we used the Euclidean distance instead. This only appears to affect tracts in Staten Island. The resulting accessibility map for network distances is below:

And the map for Euclidean distances for comparison:

Even here, you can see that the most noticeable difference is for tracts in Staten Island.

[gregmacfarlane]

Does this make a difference? The model results suggest that the network-based calculation results in a somewhat more conservative estimate of the effect of park accessibility on physical activity, but the two estimates are extremely similar and the models as a whole are effectively identical. The Euclidean distance models have a higher likelihood, and the network distance is kind of a Frankenstein metric because of what we saw earlier. So let's stick with Euclidean distance.

======================================================================================
                     Access Euclidean  Access Network  Multi Euclidean  Multi Network 
--------------------------------------------------------------------------------------
(Intercept)            -24.8266 **       -24.6491 **     -24.8920 **      -24.7534 ** 
                        (8.6317)          (8.6228)        (8.6457)         (8.6366)   
log(density)             0.1766 *          0.1716 *        0.1757 *         0.1715 *  
                        (0.0710)          (0.0709)        (0.0710)         (0.0710)   
log(income)              5.9976 ***        5.9801 ***      5.9964 ***       5.9795 ***
                        (0.2163)          (0.2160)        (0.2164)         (0.2161)   
fulltime                 0.1275 ***        0.1280 ***      0.1275 ***       0.1280 ***
                        (0.0094)          (0.0094)        (0.0094)         (0.0094)   
college                  0.0076            0.0072          0.0073           0.0070    
                        (0.0119)          (0.0119)        (0.0119)         (0.0119)   
single                  -0.0362 ***       -0.0362 ***     -0.0360 ***      -0.0361 ***
                        (0.0084)          (0.0084)        (0.0084)         (0.0084)   
youth                   -0.1311 ***       -0.1312 ***     -0.1310 ***      -0.1311 ***
                        (0.0135)          (0.0135)        (0.0135)         (0.0135)   
young_adults             0.0293 **         0.0288 **       0.0294 **        0.0289 ** 
                        (0.0103)          (0.0103)        (0.0103)         (0.0103)   
seniors                  0.0403 **         0.0413 **       0.0408 **        0.0417 ** 
                        (0.0140)          (0.0139)        (0.0140)         (0.0139)   
black                   -0.0499 ***       -0.0499 ***     -0.0498 ***      -0.0498 ***
                        (0.0045)          (0.0045)        (0.0045)         (0.0045)   
asian                   -0.0767 ***       -0.0767 ***     -0.0768 ***      -0.0768 ***
                        (0.0054)          (0.0054)        (0.0054)         (0.0054)   
hispanic                -0.1025 ***       -0.1025 ***     -0.1025 ***      -0.1025 ***
                        (0.0047)          (0.0046)        (0.0047)         (0.0047)   
other                    0.0035            0.0025          0.0037           0.0027    
                        (0.0452)          (0.0452)        (0.0452)         (0.0452)   
log(lag.density)         1.0987 ***        1.1053 ***      1.1030 ***       1.1072 ***
                        (0.1954)          (0.1952)        (0.1956)         (0.1954)   
log(lag.income)          1.9646 ***        1.9557 ***      1.9570 ***       1.9532 ***
                        (0.5243)          (0.5238)        (0.5249)         (0.5245)   
lag.fulltime            -0.0396           -0.0378         -0.0388          -0.0373    
                        (0.0241)          (0.0241)        (0.0241)         (0.0241)   
lag.college             -0.0711 *         -0.0718 *       -0.0721 *        -0.0726 *  
                        (0.0304)          (0.0303)        (0.0304)         (0.0304)   
lag.single              -0.0085           -0.0088         -0.0077          -0.0080    
                        (0.0215)          (0.0215)        (0.0215)         (0.0215)   
lag.youth               -0.0111           -0.0109         -0.0101          -0.0099    
                        (0.0352)          (0.0352)        (0.0353)         (0.0353)   
lag.young_adults         0.0842 **         0.0832 **       0.0848 **        0.0840 ** 
                        (0.0259)          (0.0258)        (0.0259)         (0.0259)   
lag.seniors              0.0589            0.0600          0.0603           0.0611    
                        (0.0353)          (0.0353)        (0.0353)         (0.0353)   
lag.black                0.0011            0.0012          0.0008           0.0010    
                        (0.0082)          (0.0082)        (0.0082)         (0.0082)   
lag.asian               -0.0398 ***       -0.0401 ***     -0.0401 ***      -0.0403 ***
                        (0.0095)          (0.0095)        (0.0095)         (0.0095)   
lag.hispanic            -0.0009            0.0000         -0.0008           0.0000    
                        (0.0088)          (0.0087)        (0.0088)         (0.0088)   
lag.other                0.0715            0.0713          0.0710           0.0706    
                        (0.1312)          (0.1312)        (0.1313)         (0.1312)   
euc_access               0.1610 *                                                     
                        (0.0700)                                                      
lambda                   0.6906 ***        0.6898 ***      0.6917 ***       0.6909 ***
                        (0.0200)          (0.0200)        (0.0199)         (0.0199)   
net_access                                 0.1453 *                                   
                                          (0.0621)                                    
euc_multi                                                  0.1472 *                   
                                                          (0.0722)                    
net_multi                                                                   0.1352 *  
                                                                           (0.0649)   
--------------------------------------------------------------------------------------
Num. obs.             2099              2099            2099             2099         
Parameters              28                28              28               28         
Log Likelihood       -4435.5066        -4435.4363      -4436.0465       -4435.9701    
AIC (Linear model)    9717.9489         9699.7602       9725.1486        9707.9035    
AIC (Spatial model)   8927.0133         8926.8725       8928.0930        8927.9403    
LR test: statistic     792.9356          774.8877        799.0556         781.9633    
LR test: p-value         0.0000            0.0000          0.0000           0.0000    
======================================================================================
*** p < 0.001, ** p < 0.01, * p < 0.05

[gregmacfarlane]

For more context, the "Multi" models use more terms in the utility equation besides park size and distance.

[gregmacfarlane]

TLDR; the difference between network and Euclidean distance in tract-level accessibility is negligible. We will stick with Euclidean distance for simplicity.