Spatio-Temporal Analysis of TNC Effect on Transit Trips in Chicago
Vadim Sokolov (GMU), Joshua Auld (ANL) and Natalia Zuniga (ANL)
Introduction
We develop regression models for analyzing impact of the ride sharing services on transit demand. Our analysis is motivated by the problem of the loss of transit ridership over the past several years. Those losses overlap with the introduction of Transportation Network Companies (TNCs). There is a seeming correlation between the two, which has led to speculation that TNCs have caused transit ridership loss. However, many other factors outside of TNC ridership could be driving transit ridership loss, including changing populations, shifting land use patterns, transit service changes, macro-economic factors, and so on. Our model allows for disaggregate analysis of long-term transit ridership data from Chicago between 2010 and 2020, before and after the introduction of TNC services, along with TNC trip patterns to determine relationships between TNC ridership and transit ridership for similar areas.
Our work builds on the previous analysis of Jacob W. Ward et al. (2021) who analysed the effect of TNC on transit ridership and vehicle ownership across US during the 2011-2017 period. Similar to our results, they found out that there is no effect of TNC on transit use on averages, however there are local effects in the areas with large transit ridershops and high income. Jacob W. Ward et al. (2019) and Jacob W. Ward et al. (2018) authors analysed 2005-2015 data and dound out that vehicle registration declined by 3% on average as a result of TNC eneting the transportaiton market.
We analyze TNC and transit data collected in Chicago at monthly time resolution and community areas as spacial units of analysis. The analysis of non-overlapping spatial areal units has been analyzed in statistics, agriculture, and epidemiology (Wall (2004), Brewer and Nolan (2007), Besag and Higdon (1999), Lesage (1997)).
Data
Transportation Network Companies (TNC)
The TNC data provided by the city of Chicago contains hourly number of trips between each origin/destination community areas. We have first summarized this table to daily trips, the resulting data has 794179 and ranged from 2018-11-01 to 2020-02-29. Each record has origin, destination, date and averages over attributes of the trip.
| tripdate | pickupca | dropoffca | ntrips | cost | ttime |
|---|---|---|---|---|---|
| 2018-11-01 | 1 | 5 | 6 | 13.08333 | 1.333333 |
| 2018-11-01 | 1 | 7 | 12 | 16.16667 | 79.750000 |
| 2018-11-01 | 1 | 8 | 179 | 18.24453 | 60.082353 |
| 2018-11-01 | 1 | 10 | 2 | 20.00000 | 1.000000 |
| 2018-11-01 | 1 | 11 | 2 | 13.75000 | 1.500000 |
| 2018-11-01 | 1 | 12 | 1 | 20.00000 | 1.000000 |
Then we have aggregated TNC trips by month and drop-off location, so the resulting table has daily average departures for each CA and each month of the observed period
| ca | my | tnc |
|---|---|---|
| 1 | 2018-11-01 | 567.6364 |
| 1 | 2018-12-01 | 609.3333 |
| 1 | 2019-01-01 | 453.8696 |
| 1 | 2019-02-01 | 636.5238 |
| 1 | 2019-03-01 | 701.9524 |
| 1 | 2019-04-01 | 648.4762 |
The average number of daily trips across the region 1.6082857^{5} and the following barplot shows daily averages for each month of the observed period
The map below shows daily averages (on the log scale) across the entire observed period for each of the community areas
L-System
The average number of daily trips across the region 4.6336576^{5} and the daily plot is given below
barplot(height = tmp$ct,names.arg = tmp$my)
The map below shows daily averages (on the log scale) across the entire observed period for each of the community areas
Bus
The average number of daily trips across the region 7.0193534^{5} and the daily plot is given below
barplot(height = tmp$ct,names.arg = tmp$my)
The map below shows daily averages (on the log scale) across the entire observed period for each of the community areas
Community Area Analysis
We use a model proposed by Bernardinelli et al. (1995), which represents the spatio-temporal pattern in the mean response with spatially varying linear time trends. We assume the data is Gaussian. The model estimates autocorrelated linear time trends for each community area (areal unit). Thus it is appropriate if the goal of the analysis is to estimate which areas are exhibiting increasing or decreasing (linear) trends in the response over time. The full model specification is given below.
We assume we have a set of \(K\) non-overlaping areal units \(S_1,\ldots,S_K\) and data is recorded for each areal unit for \(N\) consecutive time steps \(t = 1,\ldots,N\), then the general hierarchical model is \[ \begin{aligned} Y_{kt} \sim & f(y_{kt} \mid \mu_{kt},\nu^2)\\ g(\mu_{kt}) = & x^T_{kt}\beta+O_{kt} + \psi_{kt}\\ \beta \sim & N(\mu_{\beta},\Sigma_{\beta}) \end{aligned} \] Given that we assume Normal (continious) data, we use \(f =\) Noraml density and link function \(g\) to be identity function.
The spatio-temporal correlations are modeled using \[ \psi_{kt} = \phi_k + (\alpha + \delta_k)\left(\dfrac{t - \bar t}{N}\right) \] Thus, the temporal pattern is modeled by a local trend \(\delta_k\) and the spatial correlations are modeled via \(\phi_k\), both are random effects, which are conditionally normal \[ \begin{aligned} \phi_k \mid \phi_{-k}, W \sim & N\left(\dfrac{1}{c}\sum_{j=1}^Kw_{kj}\phi_j, \dfrac{\tau^2_{int}}{c}\right),~~~c = \sum_{j=1}^Kw_{kj}-1 +1/\rho_{int}\\ \delta_k \mid \delta_{-k},W \sim & N\left(\dfrac{1}{q}\sum_{j=1}^Kw_{kj}\delta_j, \dfrac{\tau^2_{slo}}{q}\right),~~~q = \sum_{j=1}^Kw_{kj}-1 +1/\rho^2_{slo}\\ \tau^2_{int},\tau^2_{slo} \sim & IG(a,b)\\ \rho_{int},\rho_{slo} \sim & Uniform(0,1)\\ \alpha \sim N(\mu_{\alpha},\sigma^2_{\alpha}) \end{aligned} \] Each community area has its own linear trend with intercept \(\phi_k\) and slope \(\alpha + \delta_k\). Here \(\rho_{int},\rho_{slo}\) are spatial dependence parameters, with values of one corresponding to strong spatial smoothness that is equivalent to the intrinsic CAR prior proposed by Besag et al. (1991), while values of zero correspond to independence (for example if \(\rho_{slo}\) then \(\delta_k \sim N(0, \tau^2_{slo})\).
Analysis Results
Model with \(y\) being TNC counts (Poisson) and predictors are bus and rail average daily counts on log-scale
| Median | 2.5% | 97.5% | |
|---|---|---|---|
| (Intercept) | 0.8069 | 0.1768 | 1.4466 |
| log(bus) | 0.2332 | 0.1837 | 0.2796 |
| log(rail) | 0.3932 | 0.3489 | 0.4402 |
| alpha | -0.0847 | -0.1069 | -0.0605 |
| tau2.int | 3.3423 | 2.2283 | 5.3536 |
| tau2.slo | 0.0406 | 0.0237 | 0.0712 |
| rho.int | 0.7319 | 0.3979 | 0.9496 |
| rho.slo | 0.4749 | 0.1174 | 0.8667 |
- Bus and rail move in the same direction at TNC
- When bus goes up 1% TNC goes up 0.23%
- When rail goes up 1% TNC goes up 0.4%
- Overall the time trend is slightly negative \(\alpha = -0.08\)
tau2.intwhich is spatial random effect variance (\(\tau^2_{int}\)) is large (large fraction of variance is not explained by varaince in bus or rail)tau2.slowhich is temporal trend variance (\(\tau^2_{slo}\)) is low which corresponds to our initial observation that there is not much change in data over time (for the observed time period)rho.intwhich is the strength of the spatial correlation is high (\(\rho_{int} = 0.73\))- There is no local effect on the trend, most of the local effect coefficients \(\delta\) are around 0. Here is the estimated local trend for the first seven community areas
| var1 | var2 | var3 | var4 | var5 | var6 | var7 | |
|---|---|---|---|---|---|---|---|
| 5% | -0.0177575 | 0.0351669 | -0.042837 | -0.0259428 | 0.0135247 | -0.0230802 | 0.0162286 |
| 95% | 0.1139849 | 0.1142256 | 0.064057 | 0.0664844 | 0.0714912 | 0.0321995 | 0.0648056 |
Finally we can look at the medians on the map
- The model does a good job capturing the random and non-random effects
Finally, we can look at the random spatial effects \(\phi_k\) (correlations) not captured by the main effects
We can see that spatial effect is stronger in the central and northern parts of the city which
Origin-Destination Flows
Another hypothesis conidered in this analysis is that temporal analysis of flows between community areas will lead to descovering effects of specific areas. Modeled the flows using a gravity model, which is a class of log-linear regression that has been previously was shown to be effective in traffic flows modeling Chen, Banks, and West (2019).
Our gravity model is based on the class of poisson log-linear model of area-to-area flows. Given community areas \(1,\ldots,n\), we model \(y_{ij}\) the number of TNC trips from area \(i\) to area \(j\) as conditionally independet Poisson variables with mean \(t_{ij}\) \[y_{ij}\sim Poisson(t_{ij}).\]
The means \(t_{ij}\) depend on the characteristic of the origin and destination zones and on the characteristics of the flow. In the log-Poisson model we model the logarithm of the mean \[\theta_{ij} = \log t_{ij}.\]
In our particular version of the gravity model, we assume \[\theta_{ij} = m+\log a_i + \log b_{j} + \log f_{ij}\]
The characteristics of the areas as origins and destinatoin are incorporated into parameters \(a_i\) and \(b_j\) respectively, and the interaction term \(f_{ij}\) represents additional factors arising from network characteristics. Specifically, we consider \[f_{ij} = g^Tx_{ij} + \log h_{ij}.\] Here \(x_{ij}\) are known predictors, that characterize the flow on the network. Specifically , we use cost of TNC travel and cost of transit trvel between areas \(i\) and \(j\) and \(h_{ij}\) represents positive random interaction effect. We can see additioanl \(h_{ij}\) term as a way to allow additional variation in the Poisson model, when \(h_{ij}\) are assumed to be log-normal or gamma distributed with mean of 1. In the absence of regressors, the resulting distribution over \(y_{ij}\) is Negative Binomial, which is quite often used to model transportation flows.
The figure below shows a heat plot of the TNC flows
We used the observed TNC flows (averages are shown in the figure above) as our observed data set and used the POLARIS-estimated area-to-area generalized travel cost as our input \(x_{ij}\). Theis heat map for the generalized travel cost is shown below 
Below we analyze the random effect of a destination on the number of the TNC trips (on log-scale), while controlling for generalized cost and TNC. The bar plot of the number of trips for each destination shows that the variation is large 
Thus, we expect the random effect to be of non-trivial size for each of the destinations.
Summary of Findings
- Bus and rail move in the same direction at TNC
- Spatial random effect (large fraction of variance is not explained by varaince in bus or rail) in the model of outflows from each CA
- There is not much change in data over time (for the observed time period). We did not find neither globa (region overall) nor local (area-specific) trend coefficients to be significant
- The strength of the spatial correlation is high. Which probably explained by some latent variables. For example the high and low income ares are clustered and thus the usag if the TNC
- Analysis of the origin-destination flows just confirmed the finding of the analysis performed using out-flow data. Adding the control for generalized cost (as estimated by the POLARIS) router did not reduce the size of the random effects of each of the areas.