Spatiotemporal Analysis of the Relationships Between Pricing Strategies and Willingness to Share for Ridesourcing Modes

Abstract

Willingness to share trips and surge pricing schemes remain unexplored areas in ridesourcing research. This study first conducts an explorative spatiotemporal analysis on both features’ interdependencies, that is, willingness to share and surge pricing. The willingness-to-share behavior is analyzed with respect to its econometric and psychological aspects. Mile-price and hour-of-day are used as proxies for the elasticity and psychological perception of security to share rides with strangers, respectively. Surge pricing is discussed within the classic economic theory on supply and demand dynamics, as well as other factors such as traffic conditions and trip length. The willingness-to-share pattern mined in this analysis is further analyzed in a behavioral market segmentation context to identify the type of underlying existing spatiotemporal trends. The proposed methodological protocol builds on mining spatial heterogeneity and temporal trends to provide a comprehensive understanding of the willingness-to-share behavior. The study uses the large ridesourcing dataset collected in the City of Chicago to showcase the implementation and provides a critical and contextual discussion on the behavioral segmentation pattern and the underlying urban socioeconomic fabric. Two types of oscillating and sporadic trends were captured in statistically significant hot and cold willingness-to-share spots that relate to more and less socially disadvantaged community areas, respectively. Two regression models were developed to identify the determinants of the observed trends. The non-white population percentage, percentage of low-income households, and a younger population exhibit significant positive relationships with more willingness-to-share ridesourcing trips.

Keywords

equity analysis non-parametric attitudes/attitudinal data behavior analysis pattern (behavior choices etc.)ride hailing—ridesharing

In 2014, the big two transportation network companies (TNCs) introduced their shared-ride business lines. Uber introduced UberPool ( 1 ), rebranded then to UberX Share ( 2 ), and Lyft introduced Lyft Line ( 3 ), rebranded to Lyft Shared, so that passengers can pool their rides to reduce the cost. The business model has the potential to qualify as a more sustainable transportation solution than the solo ridesourcing, especially for commute trips ( 4 ) at reasonable costs, and to alleviate the heated debate on ridesourcing implications on excessive vehicle miles traveled and congestion. UberPool is said to save 120 tons of carbon dioxide emissions in San Francisco where it accounts for approximately 50% of Uber rides in the city, and to save 7.9 million driving miles in Los Angeles ( 5 ). Evidence on the potential of this shared ridesourcing model was provided by Santi et al. ( 6 ) in a simulation-based study using New York City (NYC) taxi trips, and on the environmental benefits by comparing the shared versus not-shared scenarios’ respective emissions using DiDi Chuxing trips in Chengdu, China ( 7 ). Therefore, understanding the behavior of willingness-to-share (WTS) ridesourcing trips is not only pertinent to comprehending the system from the demand side, but also to boosting and operationalizing those benefits as well.

Ridesourcing dynamics, that is, WTS trips and surge pricing schemes, remain unexplored areas in ridesourcing research. Research endeavors mostly focus on the causal forces driving both systems’ features but overlook the underlying patterns and trends that could remarkably improve our understanding of WTS behavior. To fill these gaps in the research, an explorative spatiotemporal analysis is needed on both features’ interdependencies, that is, WTS and surge pricing. Ridesourcing surge pricing needs to be analyzed and understood within a spatiotemporal framework to help agencies address equity oligopoly concerns and understand the pricing tactics and demand decision-making processes in such two-sided market. As for WTS, the market segments need to be first identified to better explain the causal forces behind the behavior. The implications of this research on behavioral market segmentation can be extended to the area of long-range transportation planning to plan ahead for technologies such as the futuristic shared unmanned autonomous vehicle (SUAV). As of now, Lyft has already surpassed 100,000 self-driving rides ( 8 ). This potential progress in self-driving places more weight on the timely need to understand WTS ridesourcing trips from spatiotemporal as well as market segmentation perspectives.

In this paper, WTS behavior is discussed with respect to its econometric and psychological aspects. Surge pricing is discussed within the classic economic theory on supply and demand dynamics, as well as other factors such as traffic conditions and trip length. For WTS behavior, recent behavior studies have yielded inconsistent conclusions on the factors governing the behavior ( 9 – 11 ), for example, travel impedance versus sociodemographic features, although they used the same data from the same geography and for the same period to analyze and model the behavior. One can attribute these inconsistent results to the difference in the granularity level of the analysis, that is, community level as opposed to census tract level. However, given that spatial effects were already asserted to be present in ridesourcing demand ( 12 ), and the suggestion from previous work to account for WTS varying disutility, that is, heterogeneity ( 13 ), there is motivation for the incorporation of spatial and temporal effects in analyzing and introspecting WTS behavioral patterns. Therefore, a behavioral market segmentation analysis will be conducted to better understand the causal forces of the behavior in a spatiotemporal context, and control for any uncaptured factor in the previous analysis. This framework will allow one to control for the spatial as well as temporal effects and explore the behavior determinants in a spatiotemporal dependency-free context.

The empirical analysis conducted in this paper will lead to findings with respect to whether a pattern of segments exists, and whether a dominant trend of that pattern can be mined. The behavior causal forces will be then explored and attested within that pattern using regression analysis. This will contribute to the equity discussion on the ridesourcing system, as WTS behavior will be analyzed with respect to the underlying sociodemographic differences. Another rationale to perform this exercise for trend mining in a spatiotemporal setting is to provide input and guidance to the following: (1) regional agencies on environmental justice and equity analysis of the ridesourcing system with spatiotemporal key performance indices; (2) futuristic SUAV hubs planning and allocation with spatiotemporal WTS profiling; (3) transit agencies on spatiotemporal operational integration with TNCs; and (4) TNCs on optimizing their fleet’s spatiotemporal allocation.

The underlying research tasks can be broken down as follows: (1) explore, analyze, and visualize the surge price and WTS potential driving factors, and the interdependencies between both system features; (2) explore whether WTS behavior portrays any forms of clusters or urban pockets, or if they are complete random processes; (3) develop a spatiotemporal analytical framework to analyze the behavior; (4) synthesize a protocol for market segmentation; (5) implement a trend mining process to temporally classify the previously separated market segments; and (6) statistically attest the causal forces governing the behavior in those separated segments.

Literature Review

There is limited body of literature on the factors affecting ridesourcing users’ WTS ( 14 ). The work conducted in the area of analyzing TNCs’ surge pricing scheme is limited, too ( 15 ). Capturing the interdependencies between surge pricing and passengers’ WTS their rides is not adequately explored ( 14 ). Nurul Habib ( 16 ) in tackling the mode choice component of ridesourcing highlighted the insufficient resources on the “surge price of Uber”. Middleton et al. (14) also emphasizes the need to thoroughly explore the “segment” and “contexts” of passengers who are more inclined to share their rides. Thus, the relations between both system components remains an unexplored area that is worth further study, especially when considering their dynamicity in the two-sided market of ridesourcing. Questioning individuals’ WTS in such a two-sided market can be discussed in two domains: (1) the psychological domain; and (2) the econometric domain, as excerpted from the available literature and explained hereinafter.

The psychology of WTS was clearly present in the analysis conducted by Sarriera at al. ( 17 ) on the social aspects of dynamic ridesharing, and the safety concerns amongst the factors affecting WTS were pointed out. Moreover, a pattern of “rider-to-rider discriminatory attitudes” caused by race and class norms existing among the respondents’ subset of those who used the service before, and an anticipated “lower willingness” to share their rides in the future were revealed by Moody et al. (18). Kang et al. (19) emphasized the role of “psycho-social latent constructs” in capturing and understanding WTS behavior. Their survey-based analysis drew closer attention to conservative ride-sharer groups that include women, older adults, and non-Hispanic/non-Latino Whites ( 19 ).

As for the econometry of WTS, Chen at al. ( 20 ) ranked the key features governing the WTS in the following order: “trip travel time,”“surge pricing ratio,”“trip fee,” and “trip distance.” However, in Hou et al.’s ( 9 ) analysis of WTS behavior in the City of Chicago TNC trip dataset, the distance, fare difference percentage, and duration ranked last in significance. Abkarian et al. ( 10 ) analyzed the same behavior using the same data from Chicago at the community level, and highlighted that features such as income, education, and race contribute more or as much as the trip-level features in understanding WTS behavior. Taiebat et al. ( 11 ) explored WTS behavior in the City of Chicago TNC trip dataset at the finer scale of census tracts. In contrast to Abkarian et al.’s ( 10 ) findings, Taiebat et al. ( 11 ) indicated that the trip-level features are more significant in terms the predictive power of the models than any other “spatial,”“temporal,”“sociodemographic,”“built environment,” or “transit supply.”

Liu et al. ( 13 ) estimated a multinomial logit model that included UberPool as a viable mode in their survey collected data and found travel time and trip cost to be significant. However, Liu et al. ( 13 ) underscored the need to incorporate “various perception-based latent factors,” for example, “variation in disutility of sharing rides.” Similar results on trip characteristics, that is, length, travel time, and pricing, being governing factors among those who are willing to share their trips, were revealed by Alonso-González et al. ( 31 ). Moody and Zhao ( 21 ) compared between the U.S.A. and Singapore with respect to the determinants of ridesourcing passengers’ WTS and found an association between a higher income population and less WTS. The authors in this study highlighted the need for more granular exploration of WTS rides in a ridesourcing context, taking into consideration the interdependencies with other context-related factors, for example, “sociodemographics” and “current transportation infrastructure and services,” and they emphasized the significance of clearly distinguishing between shared and not-shared ridesourcing services while conducting this exploration.

The case study data presented in this paper is the City of Chicago Transportation Network Providers – Trips Dataset ( 22 ). The data has the ridesourcing trip ends, that is, pick-up and drop-off, approximated to the census tract level for obfuscation purposes and privacy of passengers. This is a typical case that may entail spatial autocorrelation, as described by Wang et al. ( 23 ) and cited in Dean and Kockelman ( 24 ). Therefore, Dean and Kockelman ( 24 ) adopted a spatial regressive modeling in in their exploration of WTS behavior causal forces using the same data we use from the City of Chicago. Kelleny and Ishak ( 12 ) asserted the presence of spatial dependence in the trip ends, pick-ups, and drop-offs at the census tracts level, and Soria and Stathopoulos ( 25 ) confirmed the “presence of spatial effects” at the community level in WTS behavior in the City of Chicago TNC trip dataset. They also highlighted the positive correlation of socioeconomic disadvantage with more authorized-to-share (ATS) trips using a “social disadvantage index” ( 25 ). In addition to exploring the socioeconomic impact on WTS behavior, previous work by Bansal et al. ( 26 ) based on a 11,902-observation survey revealed the tendency in older population with higher household vehicle ownership toward not-authorized-to-share (NATS) trips in ridesourcing. Therefore, socioeconomic fabric and demographics, particularly age-specific features, can be regarded amongst the main forces shaping WTS behavior. However, they should be handled with spatial, and even temporal, curation to refrain from any exogenous effects.

To conclude, WTS and surge pricing parameters are amongst the key stochastic features characterizing the ridesourcing system from other transportation modes. The impacts of the system cannot be studied separately from those parameters. There is a current research gap on understanding both features and their relationships. Moreover, the endeavors made in the literature to explain WTS behavior are either inconsistent in their results ( 9 – 11 ) or overlook the impact of surge pricing on the behavior. To partially fill those gaps in the research, a methodology comprising two layers of analytics is proposed: (1) spatiotemporal market segmentation; and (2) spatiotemporal transformation and multiple linear regression (MLR), using the TNC trip data from the City of Chicago during the year 2019. In the next section, this data will be described, followed by a discussion on the preliminary analysis of the data and the spatiotemporal aggregation processes.

Data Description

Starting from November 2018, all TNCs operating in the City of Chicago were required by ordinance to regularly report all their trips, and the TNC trip data has been made publicly available through the Chicago Data Portal ( 22 ) and updated on quarterly basis. We chose to limit our analysis to data collected in 2019 to avoid any potential flaws in data reporting or packaging at the start of the initiative in 2018, and not to delve into odd travel behavior associated with the 2020 COVID-19 pandemic. Trips start or end in either of the airport census tracts—O’Hare International Airport and Chicago Midway International Airport—as well as external trips are all eliminated because of their distinctive nature that does not fall within the scope of this work. This truncation of the data removed 6.8 million airport trip records and left approximately 90 million trips to analyze. The data key variables and their description can be summarized as follows ( 22 ).

Trip ID: text—a unique identifier for the trip.

Trip start and end timestamps: date and time—when the trip started and ended, rounded to the nearest 15 min.

Trip seconds and miles: numbers—time and distance of the trip in seconds and miles, respectively.

Pick-up and drop-off census tracts: text—the census tract where the trip began and ended.

Fare: number—the fare for the trip, rounded to the nearest US$2.50.

Shared trip authorized: binary (yes/no)—whether the customer agreed to a shared trip with another customer, regardless of whether the customer was actually matched for a shared trip.

Data Aggregation and Explorative Analytics

To analyze WTS behavior with respect to trip characteristics, the year 2019 trip data was aggregated into bins according to the pick-up census tract and the hour of the day of the year, so that the analysis variables are obtained for each bin and compared on the same spatiotemporal basis. This aggregation approach is excerpted from the “space time cube” (see Figure 1) concept adopted in the ArcGIS Pro software ( 27 ) Space Time Pattern Mining toolbox. To elaborate, the X and Y bounding coordinates are replaced in the bins with the pick-up census tracts boundaries. Only pick-up census tracts are chosen to complete this analysis, since no intrinsic differences were observed in the top-level pattern between the pick-up and the drop-off locations, as observed in Figure 2. Using a time slice of 1 h generates a total of 8760 bins for each census tract in the 1-year period selected in the study. Not all census tracts had ridesourcing trips picked-up for each hour of the year; therefore, approximately 50% of the bins are empty. If those empty bins are analyzed collectively, without comparing ATS against NATS trips, as in our proposed market segmentation framework, they are assigned zero values and included in the analysis; otherwise, only spatiotemporally matching non-empty bins are kept for further analysis, leaving approximately 3 million bins.

Figure 1.

Data spatiotemporal aggregation bins.

Figure 2.

Percentage of authorized-to-share trips at pick-up and drop-off census tracts during year 2019 in the study area (City of Chicago, Illinois).

The distribution of trip characteristics, that is, length and duration, shown in Figures 3 and 4, respectively, shows a skewed profile. We depend on the median trip-related variables, therefore, to overcome such skewness in the data and to represent the central location of the trip-related variables. According to the findings from the literature review, the trip length could be reasonably assumed as a governing factor to consider in these explorative analytics on ridesourcing trips for the sharing authorization rate (SAR), as evident from the univariate correlation and the kernel-density estimate (KDE) visualized correlation between WTS and median trip length, shown in Figures 5 and 6, respectively.

Figure 3.

Distribution of trip length (miles) during 2019.

Figure 4.

Distribution of trip duration (minutes) during 2019.

Figure 5.

Sharing authorization rate versus median trip length (miles).

Figure 6.

Sharing authorization rate versus median trip length (miles) using kernel-density estimate—Pearson correlation = 0.17.

The mile-price in dollars is computed for all trips; thus, the surge pricing is normalized with respect to a reasonable trip variable to avoid any misinterpretation. The mile-price is predicated only on the surge pricing component of the fare, excluding other components of tipping and additional charges. The SAR is introduced as the signal to consolidate the WTS. The SAR is the ratio of the total ATS trips to the total number of picked-up trips at the bin level. Following the approach explained earlier to bin-based aggregation for trip characteristics, a comparable approach is adopted for analyzing the WTS elasticity on a pricing basis, with one key difference in that the data was split before aggregation into two subsets—ATS trips and NATS trips—and for each subset, the aggregated bins’ median mile-price in dollars was calculated. To analyze the WTS elasticity on a pricing basis, each pick-up census tract is represented by two spatiotemporal bins: one for the ATS trips and the other for the NATS ones.

The median price distribution for the two aggregated subsets (ATS trips and NATS trips) is displayed in Figure 7 after eliminating the mile-price extreme values (>US$50/mile) for bins with a median mile-price below US$20 for clarity purposes. The distribution for the median mile-price displayed in Figure 7 shows an anticipated pattern of the NATS trips taking the lead in mile-price, especially within the mode intervals. However, the distribution takes an identical shape for both bin types with a median mile-price more than US$5, which implies that certain types of trips under certain conditions are assigned the same mile-price from the provider side, no matter what type of authorization to share is willed at the demand side. This preliminary finding on pricing is interesting because Hou et al. ( 9 ), who used a segment of the same Chicago TNC trip data from the period between November 2018 and April 2019, found a minimal, yet positive, impact of pricing on influencing the WTS, that is, only 0.82% of the increase in WTS is associated with a 10% pricing increase, as cited by Middleton et al. ( 14 ). However, from this finding we have from the bin-related mile-price distribution, we see that this mile-price headway in the NATS bins diminishes with increasing mile-price. Since the density of bins with median mile-price more than US$10 is minimal, the visuals provided henceforth will be truncated to those with a median mile-price of less than US$20 in ATS and NATS trips for clarity.

Figure 7.

Distribution of the bin-level median mile-price.

The interdependencies between pricing and WTS parameters are central to understanding the ridesourcing system’s complex dynamics. TNCs adopt the surge pricing mechanism as a measure for “market correction” (Gurley [ 29 ] as cited by Battifarano and Qian [ 15 ]) to respond to an excess in demand, that is, requests, or shortage in supply of active drivers ( 30 ). Ridesourcing is a typical two-sided market but operates differently in pricing. In typical third-party hosted markets, sellers price their product as in e-commerce, or buyers bid for the product or the service in an auction-like setting, for example, e-financial services markets, and the third-party host either charges a percentage of transactions or benefits from advertisements. This is not the case for TNCs, where buyers and sellers are both subjected to the surge pricing mechanism adopted by the intermediary. TNCs price the service to incentivize more drivers to enter the market in the case of excessive demand, or to remain in the market in case of unfavorable conditions, for example, inclement weather or crashes and congestion. However, surge pricing is not entirely dependent on supply and demand dynamics, but also on trip length, where a discounted rate is offered to incentivize users to take longer trips and a base fare to penalize extremely short trips.

To verify this theory on ridesourcing pricing, trip length and the hour-of-day as a surrogate measure for prevailing traffic conditions can be reasonably assumed to be governing factors, as evident from Figures 8 and 9, respectively. The relationship between the median mile-price and the median trip length abides by classic market rules on the price elasticity of demand, as seen in the kernel-density estimated distribution in Figure 9. To explain, the price decreases monotonically with longer trips. The median price quartiles shown in Figure 9, especially those corresponding to NATS bins, can be readily explained with respect to the typical recurrent traffic conditions during peak (07:00–9:00 a.m. and 4:00–6:00 p.m.) and off-peak hours.

Figure 8.

Bin median mile-price distribution with respect to median trip length.

Figure 9.

Distribution of bin median mile-price with respect to pick-up hour of day.

To further explore interdependencies between the SAR and mile-price and reveal if an unexpected pattern exists in the bins’ mile-price distribution, we visualize, using the KDE, the ATS bin-level SAR distribution versus the respective NATS bins’ median mile-price (see Figure 10). This kind of visual is intended to reveal how the SAR in the bins aggregating passengers’ WTS responds to the surge pricing fluctuating and presumably penalizing solo riders, aggregated from the NATS bins. This trend shows an inverse, yet not remarkable, relationship between the SAR and the NATS bin median mile-price. To further understand this striking relationship, the difference in the median mile-price between the NATS and the ATS bins is visualized against the SAR. This difference is expected to be strictly positive, since the median mile-price for NATS trips is believed to be always higher than the ATS one, compared for the same pick-up location and the same hour of the day, but this turns out not to be the case here, as shown in Figure 11, in which again a striking pattern is present.

Figure 10.

Sharing authorization rate distribution versus median mile-price (US$) in not authorized-to-share trips’ bins with fitted regression line.

Figure 11.

Sharing authorization rate distribution versus difference in mile-price between not-authorized-to-share and authorized-to-share trips’ bins.

These negative differences, although thin in magnitude, support the earlier highlighted findings of Alonso-González et al. ( 31 ) on the insufficient cost savings for shared trips resulting in the low likelihood of WTS in ridesourcing trips. In fact, there is a counter argument here that can be drawn from these negative differences as one can attribute these insufficient incentives, or even a higher shared mile-price for some destinations as revealed here, to the inherent less WTS behavior presents among some segments of the market. Moreover, some destinations with less overall adoption rates make it unfavorable for drivers to accept the ride, and TNCs have to compensate, even if the ride is ATS. This underscores the significance of understanding WTS behavior from spatiotemporal market segmentation to accept or reject such arguments.

Lastly, to capture the trends in the SAR from a psychological standpoint, the hourly distribution of the SAR, aggregated using the space–time bin approach discussed earlier without distinguishing between ATS and NATS bins, is depicted in Figure 12. As previously suggested, the hour-of-day is used as a proxy for passengers to accept sharing rides with strangers, predicating on the hypothesis of individuals feeling less secure during late hour rides. These assumptions are supported by the median SAR concomitant with day hours and showing the least observed SAR at 1:00 a.m., and spikes alignedly with the typical traffic a.m. and p.m. peak periods. Moreover, one can observe a thin, yet fixed, SAR around 100% recurrent in each hour. Those captive ride-sharers showing less or no sensitivity to the hour-of-day, in accordance with the previous finding from Alonso-González et al. ( 31 ) on the lower sensitivity of the willing to share population to the “on-board discomfort associated with ride-spooling.”

Figure 12.

Distribution of year 2019 hourly aggregated pick-up census tracts’ sharing authorization rate with respect to pick-up hour of day.

Those explored trends and patterns shown through Figure 7 and Figures 10 –12 suggest the existence of a conservative ride-sharer population that is not willing to share rides regardless of the mile-price factor, and a captive ride-sharer population regardless of the hour-of-day. Moreover, the surge pricing scheme adopted by TNCs seems to not only account for supply and demand at pick-up location and hour of the day and prevailing traffic conditions, but there is clearly another factor that possibly pertains to the drop-off location. This is evident from the pattern observed in Figure 11, in which NATS bins maintained a lower median mile-price than their same spatiotemporal ATS peers, which could be explained only with respect to drop-off location disparities.

For the conservative and the captive ride-sharer population, a behavioral market segmentation analysis and trend mining framework is developed in the next section to reveal their respective cold and hot spots based on WTS behavior, that is, ATS trips. For this trend mining framework, it should be noted that aggregation bins from the split subsets, that is, the ATS trips and NATS trips, are abandoned. A collective aggregation protocol is adopted instead, in which the entire trip population is included without segregation according to the sharing authorization. The split subsets were essentially needed for exploring the interdependencies between the SAR and pricing patterns in a way that guarantees the ATS and NATS trip bins are evaluated in a spatiotemporal alignment. As for the SAR trend mining, the pricing factor is controlled as the scope is to reveal whether a spatiotemporal trend on WTS or unwillingness to share exists.

Methodology

The methodology adopted in this paper is two layers of analytics framework, as shown in Figure 13. The first layer of analytics handles the spatiotemporal analysis of WTS behavior. In this layer, a protocol for behavioral market segmentation and trend mining is proposed using Getis-Ord Gi* and Mann–Kendall statistics, and implemented in the Emerging Hot Spot Analysis module ( 32 ) in the ArcGIS Pro Space Time Pattern Mining toolbox. The protocol workflow builds on two basic concepts: (1) test statistics on spatial association, that is, autocorrelation; and (2) time-series trend mining and identification. Hotspot analysis founded by Getis and Ord ( 33 ) and known as the “Getis-Ord Gi*” ( 34 ) can provide insights into spatial heterogeneity with rigorous statistical tests on significance. In this work, Getis and Ord developed the basic statistic to test the spatial association between significantly high and low weighted values with respect to their spatial relations, that is, proximity. The Z-values essentially are the standard deviation of the Getis-Ord Gi* weighted value $G_{i} (d)$ from the mean weighted values obtained globally (see Equation 1) and test the null hypothesis that the ith tested spatial entity is not a significant hot or cold spot. A pivotal element in this analysis is the spatial weight incorporated in the test statistic and governed by how neighboring relations are defined among the explored geography ( 33 , 34 ):

Z_{i} = \frac{G_{i} (d) - E [G_{i} (d)]}{\sqrt{Var G_{i} (d)}} = \frac{\sum_{j = 1}^{n} w_{i, j} x_{j} - \bar{X} \sum_{j = 1}^{n} w_{i, j}}{S \sqrt{\frac{n \sum_{j = 1}^{n} {w^{2}}_{i, j} - {(\sum_{i' = 1}^{n} w_{i, j})}^{2}}{n - 1}}}

(1)

where $G_{i} (d)$ is the Getis weighting function of value $x$ using distance $d$ ; d, then known as w_i,_j, is a defined weighted distance between the studied entities; E and Var are the mean and the variance, respectively, of the weighted value x; $j \in {1, \dots n = 799}$ is the indexed census tract; and:

\begin{matrix} \bar{X} = \frac{\sum_{j = 1}^{n} x_{j}}{n} \\ S = \sqrt{\frac{\sum_{j = 1}^{n} x_{j}^{2}}{n} - {(\bar{X})}^{2}} \end{matrix}

For a geographic entity to be identified as a hot or cold spot, it is not sufficient for it to be characterized by a high or low signal value $x$ , that is, a high SAR, but it has to be surrounded by spatially defined neighbors exhibiting similar signal behavior, as can be interpreted from Equation 1, in which the standard deviation compares the weighted localized signal strength with the global one. High Z-values, that is, above 1.65, 1.96, and 2.58, and their respective low p-values, that is, 0.1, 0.05, and 0.01, will result in rejecting such a hypothesis and identifying the spatial entity as a hot or cold spot at confidence levels of 90%, 95%, and 99%, respectively. The signal $x_{j}$ is the pattern value in geography $j; j \in {1, \dots n = 799}$ , namely the spatiotemporal bin’s SAR. As for the $w_{i, j}$ , it is the spatial weight, defined binarily as 1 for neighbor bins and 0 for non-neighbor bins. The neighboring definition will be clarified in the next section discussing the implementation and results. This test statistic is performed at the time slice level (see Figure 1), and thus each bin is assigned a Z-value in each time slice, forming the bin time series of Z-values to be processed in the second step of the workflow on trend mining.

Figure 13.

Methodological framework.

The time-series trend mining and identification is performed by means of a univariate non-parametric test called the Mann–Kendall statistic, in which rank correlation analysis is conducted by computing the Mann–Kendall location-based statistic, as shown in Equation 2. The mean of this test statistic is hypothesized to be zero, implying that no trend exists, and the variance and the Z-score are calculated as shown in Equations 3 and 4, respectively ( 35 ):

S = \sum_{k = 1}^{n - 1} \sum_{j = k + 1}^{n} sgn (X_{j} - X_{k})

(2)

where $X$ is the time-series object, hourly SAR, and hot or cold spot Z-score time series and $S$ is the Mann–Kendall location-based statistic, with $sgn$ obtained as follows:

sgn (x) = {\begin{matrix} 1 if x > 0 \\ 0 if x = 0 \\ - 1 if x < 0 \end{matrix}

σ^{2} = [n (n - 1) (2 n + 5) - \sum_{j = 1}^{p} t_{j} (t_{j} - 1) (2 t_{j} + 5)] / 18

(3)

where $n$ is the number of observations in the time series, $p$ is the number of tied groups in the time series, and $t_{j}$ is the number of observations in the jth tied group:

z^{*} = S / σ

(4)

Note that the mean ( $E [S])$ is assumed to be zero to reflect the null hypothesis on no trend existing.

The processes can be understood as follows: the outcome of the SAR spatial association analysis, that is, Getis-Ord Gi*, is obtained for each hour of the analysis period. This outcome is basically labeling the bin category, that is, whether a certain census tract is a hot, cold, or not significant spot, in association with other neighboring census tracts at the same hour of analysis. Noting that we are analyzing the hourly SAR for one full year, we should have 799 objects, that is, the number of the census tracts of the 8760-h time series. Then those Getis-Ord Gi* outcomes stacked in that time-series fashion as shown in Figure 14 would be consumed by the first Mann–Kendall process to identify the trend category. The Z-scores on the Mann–Kendall location trend stacked in the same time-series manner is then used by another Mann–Kendall process to identify whether a trend of significant hot or cold spots exists at that location. The Emerging Hot Spot Analysis module ( 32 ) in ArcGIS Pro identifies 17 categories of patterns that exist among statistically significant hot or cold spots, and the interested reader may refer to Esri Inc. ( 36 ) for further details.

Figure 14.

Locational time-series objects consumed by the Mann–Kendall process.

The second layer of analytics is diagnostic to identify and assert WTS behavior determinants using MLR. In this layer of analytics we extend the previous research conducted by Soria and Stathopoulos ( 25 ) that explored the socio-spatial differences between “solo” and “pooled” rides by building on the spatial concept and adding a temporal dimension to the analytics. Moreover, Soria and Stathopoulos ( 25 ) explored the causal forces at the level of community areas, which are units introduced within the city’s historical geographic division system to collect, analyze, and present information and data for urban and regional planning purposes and updates. A community area comprises several census tracts. Conducting our spatiotemporal diagnostic analytics at the census tract level would improve the granularity of the analysis and provide more spatial insights.

As it is evident from previous work that the system demand and WTS behavior portray spatially heterogenous patterns, it is indispensable to incorporate spatial effects in the WTS diagnostic analytics, or this could lead to mis-specified models ( 37 ). This is typically handled using spatial econometrics, which is a well-studied area in aggregated behavior modeling, and the interested reader may refer to Kelleny ( 38 ) in which a range of spatial econometric models, for example, the spatial error model (SEM) ( 39 ), (2) spatially lagged X (SLX) ( 40 ), and (3) geographically weighted regression (GWR) ( 41 ), are studied within the scope of ridesourcing demand modeling. The core concept of this modeling approach is to lessen the impact of spatial effects, that is, spatial dependence or autocorrelation, on the modeled outcome to draw meaningful conclusions on the hypothesized determinants. This is typically pursued by means of incorporating the space either endogenously as an explanatory variable or exogenously as an error parameter.

In this paper, we propose another simple yet powerful approach to account for spatial and any potential temporal heterogenous effects of WTS behavior by conducting a spatiotemporal transformation of the modeled variable, that is, the hourly SAR. To elaborate, the z-score on Mann–Kendall location trend (see Figure 13) is used as the spatiotemporally transformed variable explaining WTS behavior. This z-score is developed from rank correlation analysis, that is, temporal transformation, of the previously attained Getis-Ord Gi*Z-scores on spatial hot/cold spots, that is, spatial transformation. The first z-score from the Mann–Kendall location trend ranges from small negative values for the significant cold spots, that is, fewer WTS trends, to large positive values for the significant hotspots, that is, higher WTS trends, and the values in between pertain to insignificant unrecognized patterns. The z-score lends itself as a very good proxy for gauging the WTS in a quantifiable manner, with the spatial and temporal effects controlled as they are already captured previously. Thus, we can pursue further evidence on the association between WTS behavior and other proxies and explanatory variables.

In previous work, a socioeconomically disadvantaged population, captured in a so-called “social disadvantage index” ( 25 ), was found to be “positively correlated” with WTS and negatively correlated with unwillingness to share. The social disadvantage index is predicated on the following proxies: (1) non-white population percentage (NonWhitePop%); (2) percentage of households with zero car ownership (Hh0Car%); and (3) percentage of low-income households, that is, less than US$k35 per year (LowIncHH%). Those variables are collected from the American Community Survey (ACS) data ( 42 ) for the year 2019. Also, the previous work by Bansal et al. ( 26 ) revealed the tendency in older population toward fewer WTS trips in ridesourcing. Therefore, those social disadvantage proxies along with age-specific groups percentages are selected for identifying the behavioral determinants of WTS. The age-specific groups were aggregated into the following respective groups: (1) the Z and Millennial generations—below or 39 years old in 2019 (Z_MillGen%); (2) X generation population—below or 54 years old but older than 39 years old in 2019 (XGen%); and (3) baby boomers—older than 55 years old in 2019 (BBoomersGen%).

Implementation and Results

In implementing the first layer of analytics in the previously discussed protocol, that is, the spatiotemporal analysis of WTS behavior, a pivotal parameter needs to be determined, which is the conceptualization of the spatial relationships. That conceptualization defines the neighboring context, for which the locations falling within it will be assigned a weight of one and the other locations falling outside will be assigned a zero value of weight and will have no influence in the process of estimating the hot and cold spots within the time slices. Experimentally, using a slicing-grid to capture the relatively largest population of census tracts (homogenous in their WTS behavior reflected in the SAR), a fixed distance (search radius) of 2.5 mi was chosen empirically, as shown in Figure 15a, to define this neighboring relation. After implementing the behavioral market segmentation protocol on Chicago’s WTS ridesourcing services explored with respect to the hourly SAR signal, at a 90% level of significance, four patterns of behaviors are revealed, as shown in Figure 15b and explained as follows.

Oscillating cold spots: “A statistically significant cold spot for the final time-step interval that has a history of also being a statistically significant hot spot during a prior time step. Less than 90% of the time-step intervals have been statistically significant cold spots” ( 43 )—concentrated in the central business district (CBD) and the surroundings in the Central Side and North Side, and extending to the Far North Side.

Oscillating hot spots: “A statistically significant hot spot for the final time-step interval that has a history of also being a statistically significant cold spot during a prior time step. Less than 90% of the time-step intervals have been statistically significant hot spots” ( 43 )—concentrated in the West Side and at the core of the four South districts.

Sporadic cold spots: “A statistically significant cold spot for the final time-step interval with a history of also being an on-again and off-again cold spot”. Less than 90% of the time-step intervals have been statistically significant cold spots and none of the time-step intervals have been statistically significant hot spots” ( 43 )—appear briefly in the Far North Side district.

Sporadic hot spots: “A statistically significant hot spot for the final time-step interval with a history of also being an on-again and off-again hot spot. Less than 90% of the time-step intervals have been statistically significant hot spots and none of the time-step intervals have been statistically significant cold spots” ( 43 )—concentrated in the South Side district.

The oscillating and few sporadic cold spots are concentrated in the CBD and the North Side and extend slightly to the Far North and Far Northwest Sides, and a few tracts in the peripheries of the city in the Southwest. As can be understood from the interpretation of the patterns, those oscillating and sporadic cold spots are census tracts that show more conservative WTS behavior during the analyzed time-steps. As for the revealed oscillating and sporadic hot spots, they are concentrated in South and West Sides of the city. Those are the census tract populations that show more propensity toward sharing their ridesourcing trips and were identified earlier as captive ride-sharers. The white space in Figure 15b shows census tracts with no pattern detected, and they are typical medium dense neighborhoods with mild demand for ridesourcing, as evident in Kelleny and Ishak ( 12 ). To add more context to these results, the spatial bivariate distribution of median age and per capita income is shown in Figure 16 for the year 2019. One can realize the spatial association between higher per capita income and lower WTS, and vice versa. In contrast, census tracts with higher median ages are associated with higher WTS. However, this latter relationship between age and WTS is less pronounced and needs further evidence.

Figure 15.

(a) Slicing-grid of 5 mi to approximate the 2019 sharing authorization rate (SAR) clusters and (b) the identified significant trend patterns of the hourly SAR in Chicago districts.

Figure 16.

Chicago 2019 spatial distribution of median age and per capita income.

To further evaluate and examine those preliminary findings with respect to income and age influence on WTS, in the second layer of analytics we conduct a regression analysis on the z-score on the Mann–Kendall location trend as the spatiotemporally transformed variable explaining WTS behavior, as explained earlier in the Methodology section. Figure 17 shows the frequency distribution of the z-score on the Mann–Kendall location trend. Higher positive z-scores pertain to more spatiotemporally observed WTS behavior, and lower negative ones pertain to spatiotemporally conservative WTS behavior. Table 1 shows the multiple regression analysis results for the z-score explained in three proxies from the social disadvantage index, namely, NonWhitePop%, Hh0Car%, and LowIncHH%. In Table 2, the regression analysis results with respect to age-specific groups indices, namely Z_MillGen%, XGen%, and BBoomersGen%, are presented.

Figure 17.

Distribution of Mann–Kendall location trend Z-scores.

Table 1.

Mann–Kendall Willingness-To-Share Location Trend z-Score Regression Analysis with Social Disadvantage Index Proxies

Regression statistics
R-square	0.812
Adjusted R-square	0.811
Standard error	0.256
Observations	798
	Coefficients	Standard error	t-stat	p-value
NonWhitePop%	0.539*	0.03	19.69	1.38E-70
Hh0Car%	0.003	0.04	0.08	9.36E-01
LowIncHH%	0.388*	0.04	11.07	1.37E-26

Significant (p-value < 0.01).

Table 2.

Mann–Kendall Willingness-To-Share Location Trend z-score Regression Analysis with Age-Specific Groups Indices

Regression statistics
R-square	0.18
Adjusted R-square	0.17
Standard error	22.39
Observations	798
	Coefficients	Standard error	t-stat	p-value
Z_MillGen%	−0.393*	0.039	−10.132	0.000
XGen%	0.300	0.156	1.924	0.055
BBoomersGen%	0.624*	0.078	8.010	0.000

*Significant (p-value < 0.01).

Discussion and Interpretation of Results

The preliminary explorative analytics revealed two ridesourcing market segments with respect to WTS behavior, namely conservative and captive ride-sharers. The results of the spatiotemporal market segmentation asserted the existence of the two populations and made a clear distinction between their urban pockets. No new hot or cold spots were revealed from the spatiotemporal analysis, which supports the earlier finding on the two market segments and how they are adhering to their WTS behavior. No persistent or intensifying spots were revealed, either.

This absence of intensifying or persistent patterns is unexpected for cold spots, that is, conservative ride-sharers, since the vast majority of trips made within those urban pockets are short in length, as concluded by Kelleny and Ishak ( 12 ), and shorter trips are typically less likely to be shared. However, in the same work by Kelleny and Ishak ( 12 ), traces of longer trips between the CBD and the outskirts of the city were revealed. Therefore, one way to explain this is that even though we are analyzing WTS behavior at the pick-up locations, those locations are not necessarily the starting point of people’s itineraries. In other words, the analyzed trip can be a returning trip to any of the captive ride-sharer destinations. Therefore, those potential ATS trips would restrain the capturing of intensifying or persistent trends in the cold spot clusters.

As for the hot spots, the absence of intensifying or persistent patterns is expected and can be explained with respect to the overall monotonical decrease of the SAR from 27% to approximately 13% during the study year. This decline in the SAR elucidates how this segment of the market, that is, captive ride-sharers, responds to the early highlighted insufficient cost savings of ATS trips. At this point, this insufficiency in the ATS trips’ cost incentives stems from TNCs’ discriminatory pricing tactics against certain destinations. However, it is not clear whether those tactics are put in place to compensate for drivers or as demand corrective measures. Further future research is needed to explore this point.

For the regression analysis results, the model for socioeconomic determinants asserts the spatial association between social disadvantage index proxies and the propensity to higher WTS behavior. With respect to goodness of fit, the socioeconomic model has a remarkable R-square and adjusted R-square of above 0.81. The non-white population percentage and percentage of low-income households exhibit a significant positive relationship with the WTS behavior proxy, that is, the z-score on the Mann–Kendall location trend. The percentage of households with zero car ownership exhibits a positive but insignificant relationship. This is interesting, because research on ridesourcing demand has revealed positive and significant relationship with zero car ownership ( 38 ). This can be interpreted as car ownership not always being indicative of social disadvantage in multimodal cities like Chicago. Further looking into the bivariate plots (see Figure 18) of the variables against the z-score reveals a consistent positive correlation with the non-white population percentage. However, for the percentage of low-income households, the correlation is weak, and the sign for zero car ownership is inflected. This is typical in regression analysis where insignificant variables are prone to what is so-called a “suppressor effect” ( 44 ) from other independent variables in the model.

Figure 18.

Mann–Kendall willingness-to-share location trend Z-score Pearson correlation analysis with social disadvantage index proxies.

The other regression model for the age-specific group indices has relatively poorer goodness of fit with the R-square of 0.18. However, the model yielded results on two significant and informative relationships: (1) a negative relationship between Z_MillGen% and the WTS behavior proxy; and (2) a positive relationship between BBoomersGen% and the WTS behavior proxy. The XGen% turns out to be insignificant. The relationships are consistent with the earlier findings on the spatial association between the younger population and conservative WTS behavior, unlike previous research findings highlighted in the literature review ( 19 ). This negative impact of a younger population on the WTS is evident, too, from the bivariate Pearson correlation analysis shown in Figure 19. The concentration of younger professionals in the hot demand areas, that is, the CBD and its surroundings, generates shorter trips ( 12 ). Individuals usually seek reliability in such mandatory weekday shorter trips, and that can explain the lower WTS-associated behavior, but further evidence is needed from a more disaggregated analysis.

Figure 19.

Mann–Kendall willingness-to-share location trend Z-score Pearson correlation analysis with age-specific group indices.

Therefore, it is evident that the captive sharers belong to the disadvantaged population. Age plays a role in shaping the behavior in millennials and baby boomers, but not in middle-aged user groups. The conservative sharers are mostly concentrated in census tracts with a more affluent population in the CBD and its surroundings. This should advise policymaking to adopt measures for promoting such sustainable travel behavior, that is, WTS, in the captive ride-sharers’ communities for more equitable ridesourcing service. Measures such as exempting ridesourcing vehicles with high occupancy from tolls on certain major roads or high-occupancy vehicle dedicated lanes can encourage TNCs to cut their ATS trip costs, and consequently promote WTS behavior. However, more transparency into the pricing mechanism should be provided by TNCs to guarantee the effectiveness of such measures.

Conclusions and Limitations

The interdependencies between ridesourcing trip length, surge pricing, and hour-of-day on the one hand and passengers’ WTS their rides on the other hand were explored using the city of Chicago’s TNC trip data. An unexpected trend was empirically revealed for the relationship between mile-price and WTS, with unwillingness to share persisting with increasing mile-price. This suggests the existence of a conservative ridesharing population that is not willing to share their rides regardless of the mile-price factor. Also, analyzing the mile-price metric predicated on surge pricing revealed another striking pattern on pick-ups of shared trips from the same location in the same time window priced at rates higher than their respective spatiotemporal not-shared trips. Negative mile-price differences were observed on a pair-wise basis between spatiotemporally aligned ATS and NATS trip bins.

The results are consistent with recent research findings on the increased mile-price of ATS trips ( 45 ) and on the insufficient cost savings ( 31 ) for shared trips resulting in the low likelihood of WTS in ridesourcing trips. However, this may also signal an internal pricing mechanism penalizing certain drop-off locations. This suggests that the surge pricing mechanism is not only governed by supply and demand or the prevailing traffic conditions at pick-up locations, but also by the destination or the drop-off location. Therefore, it would be an interesting future research direction to further explore the spatiotemporal commonalities and disparities of those drop-off locations triggering higher surge pricing. Analyzing the sharing behavior with respect to the hour-of-day as a proxy for the way ridesourcing users consider safety concerns revealed the existence of another group of captive ride-sharers, in accordance with findings from previous research on the lower sensitivity of the willing to share population to the overall discomfort associated with ATS ridesourcing trips.

A protocol for behavioral market segmentation and spatiotemporal trend mining was implemented to explore the spatial and temporal patterns of the two groups of users revealed previously, namely, conservative and captive ride-sharers. The protocol revealed a profile of higher tendency to share aligned with socioeconomically less fortunate clusters of census tracts. Lower tendency for sharing was observed in more advantaged clusters of tracts. However, the trend mined in both patterns was found to be either oscillating at most significant locations or sporadic at a few significant locations. The statistical interpretation of the oscillating locations indicates less than 90% significant time-step intervals, and for the sporadic ones, it indicates some significant time-step intervals.

No new hot or cold spots were revealed from the spatiotemporal analysis, which supports the earlier findings on captive ride-sharers and conservative ride-sharers. Nor were intensifying spots revealed either, which can be explained with respect to the overall monotonical decrease of the SAR from 27% to approximately 13% during the study year. Therefore, adopting a more in-depth quantitative analysis approach on the temporal intensity of WTS and extending the spatiotemporal analysis into the direction of origin–destination (OD) analysis could provide a better idea of the sharing behavior across OD pairs and could explain this revealed negative difference in mile-price across those spatiotemporally origin-aligned ATS and NATS trip bins.

Further spatiotemporal inferential regression analysis on social disadvantage proxies and age-specific indices revealed that the percentage of the on-white population and the percentage of low-income households were found to be significantly affecting behavior, in accordance with previous research findings ( 25 ), but this was not the case for car ownership. As for the age-specific group indices, unlike previous research findings highlighted in the literature review ( 19 ), younger generations were found to be less willing to share their rides. However, overall, the analysis revealed that the age-specific group indices are not as powerful as the social disadvantage proxies in explaining WTS behavior. Therefore, it was evident that captive ride-sharers are members of the disadvantaged population. Conservative ride-sharers are mostly concentrated in census tracts with a more affluent population in the CBD and the surroundings.

This study serves as an endeavor to understand WTS behavior in the ridesourcing transportation system. Amongst the key limitations of this study is the aggregated format of the trip data. The trips’ pick-up and drop-off locations and time were obfuscated to the respective census tract centroids and the nearest 15-min, respectively, by the data steward to protect the privacy of the passengers. This feature restrained further analysis of WTS behavior in the vicinity of transit stations and other points of interest. Therefore, future granular analysis is needed to further understand the disaggregate decision-making and choice behavior of the users. The general transit feed specification (GTFS) can be used to further understand WTS and the ridesourcing surge pricing mechanism in relation to transit supply and trip-level fares.

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: B. Kelleny, S. Ishak; data collection: B. Kelleny, S. Ishak; analysis and interpretation of results: B. Kelleny, S. Ishak.; draft manuscript preparation: B. Kelleny, S. Ishak. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Bishoy Kelleny

Data Accessibility Statement

The data used in this paper is publicly available through the Chicago Data Portal.

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