Transit Service Gap Technical Documentation Introduction This document is an accompaniment to the AllTransit TM transit gap methods document. It is a detailed explanation of the process used to develop the transit service gaps. Notes about this Document In this Document where maps are used to display a concept there are four maps. The areas mapped are the Chicago Area, the Denver Area, the Louisville KY Area and the New York City Area (note that the Area is not the CBSA or MPO region, it is just a convenient zoom). All the maps are at the same scale, and are meant to represent cities of various sized and transit coverage. The calculation of all variables is done so for all Census Block Groups in fifty states and DC. AllTransit uses R as for statistical software, QGIS as for GIS tool, and PostgreSQL and PostGIS as the database and spatial analysis engine. Coefficient values are given to the least significant value, relative to their estimated error. Transit Quality/Service The AllTransit TM Performance Score is a ranking of the AllTransit Performance Index (API 1 ) in order to rank all the Census Block Groups in the country. The API is the result of a multivariate linear regression of several transit service quality measures with respect to the mode share of transit for the journey to work. The dependent variable for this regression is the percent of commuters within the block group using transit for their journey to work (pctj2w) from the ACS (100*B08301_010/B08303_001). The independent variables are the ones used for our H+T transit model and are listed in Table 1 below, included in the table is the linearization function used in the regression (since many of these variables have a non-linear relationship to the pctj2w). 1 This index is described in the AllTransit methods document https://alltransit.cnt.org/methods/alltransit- Methods.pdf on pages 6-8 and is referred to as the intermediate index. 1
Table 1: Independent variables used in percent transit journey to work regression Variable Transit Variables Transit Connectivity Index (TCI) Level of Service (LOS) Transit Area Shed Jobs (TAS Jobs) Neighborhood Control Variables Household Gravity Employment Gravity Employment Mix Block Density Fraction Rental Housing Units Gross HH Density Fraction Single Family Detached Household Control Variables Median HH Income Description Sum of a combination of frequency of service, distance to all transit stop/stations and level of neighborhood coverage for transit stops/stations within 1 mile of block group 2. Sum of trips per week made by every transit route with stops within the block group and a ¼ mile buffer. The total number of jobs within in a ¼ mile of all transit stops that can be accessed from the block group with a 30 min. transit ride with one transfer. Sum of number of households for all block groups divided by the distance (in miles) squared. Sum pf the number of jobs for all block groups divided by the distance (in miles) squared. Optimized weighted sum of employment type (2 digit NAICS) for all block groups divided by the distance (in miles) squared. Census blocks per acre that make up the block group. Number of occupied rental housing units divided by all occupied housing units within the block group. Number of households in the block group divided by the land area (in acres) Number of single family detached housing units divided by all housing units within the block group. Median household income for the block group. Function Coefficient Value x.529.005 sqrt(x).033.001 Error x.0000023.0000001 x.000214.000001 x -.0000492.0000004 x -.213.002 x 2.1.2 x 2.06.09 sqrt(x).65.02 sqrt(x) -3.55.10 x.0000301.0000006 Commuters per HH Number of workers not working at home 1/(1+x) 5.9.2 2 See https://alltransit.cnt.org/methods/alltransit-methods.pdf pages 4-6 2
HH Size Variable Description divided by the total number of households within the block group. Average number of people in households divided by the number of households within the block group. Function Coefficient Value x.73.03 The API is calculated by taking the log 3 of the sum of the three transit variables TCI, TAS Jobs and LOS (linearized) multiplied by their coefficient, and then normalized such that the highest value is set at 100 and the lowest value (which is obviously zero) set to zero. To be explicit - for a given block group (i) the non-normalized value is: And this is then normalized: T i = log (1 + {.529 TCI +.033 LOS +.0000023 TAS Jobs}) API i = T i 100 Max(T) Max(T) is the maximum value for all block groups in US (W 40 th St. and 7 th Ave. in Manhattan). Because so many places in the US have no transit the distribution of this variable over all block groups has a spike at zero as show in Figure 1 below. The mean value for all block groups is 22.1 and the median is 19.2 for all 217,182 block groups. Figure 2 below shows the same distribution for the 146,135 block groups that have a non-zero value for API, their mean is 32.9 with a median of 31.3. Error Figure 1: Histogram of API for all US block groups (bin = 5) Figure 2: Histogram of API for non-zero block groups (bin = 1) 3 The log of (1+x) is used since the value of the sum is often zero and is skewed toward zero. 3
The API, which uses the weighted sum three transit variables TCI, TAS Jobs and LOS, in such a way that is driven by pctj2w, address the three questions: 1. How much is the transit in a neighborhood used (pctj2w), 2. Can neighborhood members find a bus stop or train station (TCI) and how long do they have to wait for a ride (TCI and LOS) and 3. Can I get to jobs and other economic activity using this transit system (TAS Jobs)? The following three graphs show the relationships between the three variables used in the API and how strongly they relate to the pctj2w, and the fourth shows the API itself note that transit commute choice is driven by other variables, such as walkability, income, tenure etc. Figure 3: Percent Transit Commute vs. Trips/Week Figure 4: Percent Transit Commute vs. TCI Figure 5: Percent Transit Commute vs. Jobs in 30-miunte Transit Access Shed Figure 6: Percent Transit Commute vs. API The API is a measure of transit quality, and is used to measure of service for this analysis. The spatial distribution of this variable can be seen in Figure 7, Figure 8, Figure 9 and Figure 10. 4
Figure 7: Chicago IL Region - Showing Calculated API 5
Figure 8: Denver CO Region - Showing Calculated API 6
Figure 9: Louisville Region - Showing Calculated API 7
Figure 10: New York City Region - Showing Calculated API 8
Transit Market The API, as a measure of transit quality of service, is used to benchmark transit service across the US. In order to evaluate if a location has transit service that meets the average service, a regression is performed to estimate how much transit is currently supplied to neighborhoods given its demographics and urban form. The dependent variable is the API and the independent variables that are drivers for transit demand, are listed in Table 2. Using previously unpublished work of a former CNT staff (Greg Newmark 4 currently Assistant Professor at Kansas State University) and in consultation with a set of experts we have arrived at this list of variables. This list, while meant to examine transit service demand, also represents the choices that transit agencies have made in where and how much service is to provide. Table 2: Variables used in Transit Market Estimate Demographic Adults/Sq. Mile Youth/Sq. Mile Seniors/Sq. Mile Variable Description/Hypotheses Source Poverty Pop/Sq. Mile Access and Urban Form Compact Neighborhood Score Population density drives transit demand 5, the more people in a given neighborhood the more transit demanded. This is broken into three cohorts by age. Transit agencies have been challenged to provide equitable transit to low income communities 6. This variable is included to test how this has influenced the transit provided. Like the API this variable is derived from the neighborhood control variables in the auto ownership model developed for the H+T Affordability Index 7. It uses neighborhood physical characteristics that drive auto ownership, which has been found to drive transit demand 8. Rather than examining auto ownership explicitly, this variable focuses on the built infrastructure of a given location. 2015 ACS 5 Year Sample 2015 ACS 5 Year Sample HT Affordability Index 4 See Greg Newmark s Transport Chicago presentation: http://www.transportchicago.org/uploads/5/7/2/0/5720074/2a1_tdi.pdf. Table 2 list of variables does not align exactly with those in this presentation, but have been modified slightly for use on a national scale. 5 http://www.its.berkeley.edu/sites/default/files/publications/ucb/2011/vwp/ucb-its-vwp-2011-6.pdf, http://theoverheadwire.blogspot.com/2010/07/pushkarev-zupan-on-employment-ridership.html, http://uctc.berkeley.edu/access/40/access40_transitanddensity.shtml, http://pedshed.net/?p=131 or http://www.u.arizona.edu/~gpivo/lu%20and%20tbehavior.pdf 6 https://tomsanchez.files.wordpress.com/2011/02/sanchez2008.pdf or https://www.ncbi.nlm.nih.gov/pmc/articles/pmc5476368/ 7 https://htaindex.cnt.org/about/htmethods_2016.pdf see pages 30-32 8 https://www.brookings.edu/wp-content/uploads/2016/06/0818_transportation_tomer.pdf 9
Variable Description/Hypotheses Source Non-Retail Employment Gravity Retail Employment Gravity Employment access has been shown to be an important element of transit demand 9. Using a gravity measure one that does not limit itself to the neighborhood but weighs employment in nearby locations related to the distance avoids the boundary problem 10. Retail and mixed use enhance the demand for transit 11. This variable tests if retail employment (as a surrogate for retail itself) captures this effect. Using the gravity measure for this variable allows for nearby retail to be valued 10. 2014 LED 2014 LED The sample used in this fit is only the Census Block Groups that have any transit service within ½ mile from their boarders. The regression is not meant to model performance but rather to reveal correlation of these inputs with the provided transit service to use as weights in a sum so that we can estimate the average transit service for a given set of demand inputs, and thus expose the local transit market benchmarked against the average service. The final modeled average will give the average current service for these demand inputs. This assumes that by finding the relationship (in the 130,763 block groups in the US with transit service) between these demand inputs and the average service we will have an estimate of the average transit market in the US, and then can compare this to the local service. In future iterations of this project one could consider only using Census Block Groups where pctj2w is greater than the median for the US to get a measure of where the supplied transit is used more often, and thus a better measure of real demand. However, for this project all locations with access to transit are used, thus the prediction from this model is an estimate of the average transit service provided for the given place s people and urban form. Figure 11 12 below shows that there is a clear (and non-linear 13 ) relationship between these variables and API. The form for the regression used in one known as Flexible Fit where every two way interaction is included in the fit (see Appendix A: Transit Market Regression for a more complete description), this type of regression give a slightly better R 2 than an Ordinary Least Square (OLS) fit, however more importantly the interaction allow the model to be more robust in the tails of distributions; the last two plots in Figure 11 show an example of this. Figure 12 below shows how well the average is estimated. The maps in Figure 13, Figure 14, Figure 15 and Figure 16 show how the transit market is spatially distributed. 9 http://www.ppic.org/content/pubs/report/r_211jkr.pdf 10 http://planningandactivity.unc.edu/mixed%20land%20uses%20white%20paper.pdf see section 3.1.2 11 https://nctr.usf.edu/jpt/pdf/jpt%206-4%20johnson.pdf 12 These plots display a few things the grey dots are the value for every block group, the blue diamond is the mean y-value for 50 bins in x, the green circles are the median, and the line is the linear fit to the grey dots with fit stats in the lower right. 13 The Safe Natural Log, (defined in this memo as ln(1+x)), transformation is used to linearize the variables 10
Figure 11: API vs Transformed Transit Market Inputs and the Comparison of Residuals vs Adults/Sq. Mile for Flex Fit and the OLS fit (as an example). 11
Figure 12: API vs. Final Transit Market 12
Figure 13: Transit Market for Chicago IL Region 13
Figure 14: Transit Market for Denver CO Region 14
Figure 15: Transit Market for Louisville Region 15
Figure 16: Transit Market for New York City Region 16
Finding the Gaps These synthesized variables reflect the average of the current local conditions, and the difference between the transit service and the transit market indicate if the service is meeting the average market. Figure 17 below is a repeat of Figure 12 above but with the points colored to display the size of the mismatch between transit service and the transit market. Figure 17: API vs. Transit Market with Color Coding for Transit Service - Market (The Darker Purple the bigger the Gap, Orange no Gap). Figure 18, Figure 19, Figure 20 and Figure 21 show maps with Census Block Groups shaded using the 10 categories shown in Figure 17. 17
Figure 18: Transit Service - Transit Market difference in Chicago IL Region 18
Figure 19: Transit Service - Transit Market difference in Denver CO Region 19
Figure 20: Transit Service- Transit Market difference Louisville Region 20
Figure 21: Transit Supply - Transit Market difference New York City Region 21
Figure 22 below is again a repeat of Figure 12 above but this time with the color coding to depict the transit gaps, showing where there is no gap (Service Meets Market), where the market is small (< 20) and different levels of transit market where there is a transit service gap. Figure 22: API vs. Final Transit Market with Transit Market Ranges The interpretation to be presented on the AllTransit website is based on Figure 22 and will be presented in maps using a similar coloring scheme, but limited to only three groups medium, high and strong. Figure 23, Figure 24, Figure 25 and Figure 26 show the transit service gap maps. 22
Figure 23: Transit Gap Map for Chicago Region 23
Figure 24: Transit Gap Map for Denver Region 24
Figure 25: Transit Gap Map for Louisville Region 25
Figure 26: Transit Gap Map for New York Region Summary The AllTransit Performance Index (API) provides a measure of transit service by neighborhoods (Census Block Groups). Using a weighted sum of local demographics and urban form variables the transit market is calculated, derived from the average service provided to any given neighborhood based on these variables. By looking at the difference between the service and the market, transit service gaps are identified. 26
Appendix A: Transit Market Regression The regression to estimate the average API by demand inputs uses the API as the dependent variable and the variables listed in Table 3 below, the independent variables are listed with the average, minimum and maximum value from the sample used in the regression (all Census Block Groups with a transit station/stop within ½ mile from its boundary n=130,763). Table 3: Independent Variables Variable Function Average Value Minimum Value Maximum Value Adults/Sq. Mile sqrt(x) 7017 0 452143 Compact Neighborhood Score x 44.3 5.7 100 Non-Retail Gravity ln(1+x) 44571 42 1487506 Poverty Pop/Sq. Mile sqrt(x) 2026 0 277397 Retail Gravity ln(1+x) 4625 6 115768 Seniors/Sq. Mile sqrt(x) 539 0 96467 Youth/Sq. Mile sqrt(x) 2074 0 185288 We used the variables themselves and the all interaction terms, but only kept the ones that were statistically significant (i.e. Pr(> t )<5%) this produced an R 2 of 76.1%. Table 4: Values for Coefficients with Errors Variable Interacting Variable Value Error Intercept 28 1 Adults/Sq. Mile.219.004 Adults/Sq. Mile Compact Neighborhood Score -.00279.00006 Compact Neighborhood Score.275.005 Compact Neighborhood Score Seniors/Sq. Mile -.0008.0001 Compact Neighborhood Score Youth/Sq. Mile.0046.0001 Non-Retail Gravity -1.1.1 Non-Retail Gravity Retail Gravity 1.46.02 Non-Retail Gravity Youth/Sq. Mile -.0250.0008 Poverty Pop/Sq. Mile.060.002 Poverty Pop/Sq. Mile Youth/Sq. Mile -.00030.00002 Retail Gravity -15.0.2 Seniors/Sq. Mile.074.008 27
Table 5 below lists the full set of statistically significant independent variables with the appropriate interaction terms, ranked in order of their effect on R 2. Table 5: Independent Variables with Interaction Variables Ranked 14 in order of Effect on R 2 Rank Variable Individual R 2 Incremental R 2 Change 1 Non-Retail Gravity Retail Gravity 66.1% 66.1% NA 2 Compact Neighborhood Score 54.6% 73% 6.9% 3 Retail Gravity 57.2% 74.6% 1.6% 4 Adults/Sq. Mile 52.4% 75.1% 0.5% 5 Adults/Sq. Mile Compact Neighborhood Score 49.7% 75.7% 0.6% 6 Poverty Pop/Sq. Mile 35.8% 75.8% 0.1% 7 Seniors/Sq. Mile 24.7% 75.9% 0% 8 Compact Neighborhood Score Seniors/Sq. Mile 30.7% 75.9% 0% 9 Non-Retail Gravity Youth/Sq. Mile 40.7% 75.9% 0% 10 Compact Neighborhood Score Youth/Sq. Mile 39.4% 76% 0.1% 11 Poverty Pop/Sq. Mile Youth/Sq. Mile 20.5% 76.1% 0.1% 12 Non-Retail Gravity 66.1% 76.1% 0% Figure 27: Plot of Incremental R 2 Improvement 14 Colors correspond to the amount of increase in R 2 : Gold > 5%, Green >1%, Tan>0.5%, Salmon>0.05% and Red<0.05%. 28
Fixing the S Curve Figure 28 below shows the scatter plot of the API vs. Raw Transit Market, note that on the high end of the scale the transit market is slightly over estimated, and at the low end it is over estimated as well and at the very low end it is underestimated. Figure 28: API vs The Raw Transit Market from the Regression before Adjusting for the S Curve While on average the fit is very good the mismatch affects our goal to estimate if the transit service matches the supply, especially where service is very high. Consider the two maps in Figure 29 below, the first shows that, with this bias in place, Manhattan would mostly be underserved; however, once this is adjusted for as in the second map, it shows a more reasonable transit service market match. In order to compensate for this S curve, that results from the non-linear and multimodal nature 15 of this fit, we use a simple solution by fitting three intersecting lines to the distribution and then adjust the final model to compensate for these variations, see Figure 12 on page 12. 15 http://www.itl.nist.gov/div898/handbook/pri/section2/pri24.htm 29
Figure 29: Comparison of the Service - Market for Manhattan, before and after Adjusting for the "S Curve" Figure 30: API vs. Final Transit Market with Fit Lines 16 used to Adjust for the S Curve 16 The equation for the three lines are: yblue = 0.49 + 0.16x, ygreen = -11.6 + 1.22x and yred = 31.79 + 0.58x 30
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