Accessibility matters: Exploring the determinants of public 1 transport mode share across income groups in Canadian 2 cities

Planning for accessibility is increasingly considered in the development of equitable plans by 3 transport agencies and it has also been shown to exert a positive influence on public transport use. 4 However, this influence has not been examined across income groups and in different geographic 5 regions of varying sizes. The present study measures the relationship between accessibility and 6 mode choice for low- and higher-income groups in eleven Canadian metropolitan regions. Our 7 results show that the impact of accessibility on public transport mode share is stronger and non- 8 linear for the low-income group especially in the largest metropolitan areas, where increasing 9 accessibility past a certain optimal value will lead to a decrease in public transport mode share. 10 However, this point occurs at the 80 th percentile of existing accessibility, so improvements in mode 11 share are nonetheless expected with improved accessibility in most areas within these regions. 12 Moreover, in regions where an optimal value is not readily observed, improved accessibility 13 throughout the region would lead to increased uptake of public transport for both the higher- and 14 to a greater extent, the low-income group. Findings from this paper can be of value to transport 15 professionals working towards meeting ridership goals around the world as comparisons between 16 groups and across regions highlight the variation in the impacts of accessibility on mode share.


INTRODUCTION
In recent years, professionals have recognized that the environmental, social and economic 20 benefits of public transport compared to personal vehicles are numerous. As such, governments in 21 North America are promoting the use of public transport and often setting goals for ridership (Ville 22 de Montréal, 2008) or mode share (City of Vancouver, 2012) in their plans. In light of these goals, 23 the use of public transport in Canada has risen slowly, from 10.1% in 1996 to 12.4% in 2016 with 24 plateaus observed in recent years (Miller et al., 2018). In some areas, mode share has decreased 25 over the same period (Statistics Canada, 2017). Considering that capital expenditure for public 26 transport projects has been rising steadily at a much higher rate since the early 2000's (Canadian 27 Urban Transit Association, 2010, Canadian Urban Transit Association, 2019), one wonders if the 28 costs of investing in public transport are appropriate to its use. Also, are these public transport 29 investments going to serve those who would benefit and use it most? The response from 30 researchers in the U.S. (Taylor and Morris, 2015) and the U.K. to these questions is "no" (Banister, 31 2018) as they argue that there has been a trend of increasing investments in rail transport that is 32 geared towards higher-income choice riders. As a result, captive riders, who generally have lower 33 income and are less likely to own personal vehicles, tend to have a limited number of travel options 34 (Dodson et al., 2007) and find themselves stranded in the face of reduced public transport services 35 (Giuliano, 2005). 36 For practitioners to begin tackling this inequality in transport, a metric must be defined for 37 which objectives can be set and progress can be tracked against. Researchers have deemed 38 accessibility is largely influenced by the built environment where regional differences in size, 1 structure and public transport system maturity can yield different patterns in accessibility and 2 subsequently, result in differences in the way accessibility affects public transport use. Previous 3 research carried out in Canada was of an exploratory nature and relied on graphical bivariate 4 analyses (Cui and El-Geneidy, 2019) to highlight the relationship between accessibility and public 5 transport use among different income groups and across different geographic regions. In this 6 previous study, a non-linear relationship was identified between accessibility and mode share and 7 was best modelled as a quadratic relationship. Non-linear relationships between aspects of the built 8 environment and commuting outcomes including commuting distance and mode choice by car 9 have also been observed in past research (Ding et al., 2018a, Ding et al., 2018b. 10 The aim of the present study is to build upon the bivariate analysis done previously to 11 confirm and to quantify the impacts of accessibility to jobs on public transport mode share among 12 low-and higher-income groups in these Canadian metropolitan regions, while controlling for other 13 determinants of public transport use. This study will add to the conversation of planning for 14 equitable transport system through accessibility by focusing on the outputs of doing so in regions 15 with different characteristics of the built environment. 16 17 Whether or not cities in North America are experiencing a public transport renaissance, one thing 18 is for certain -factors that drive public transport use have been of great interest to researchers for  23 Moreover, to capture the combined effects of these highly influential socio-demographic variables, 24 researchers have started using composite variables such as the social deprivation index (Foth et 25 al., 2013). In addition, there is consensus among researchers in Canada, the U.S. and Australia that 26 personal vehicle ownership is a major deterrent of public transport use (Boisjoly et al., 2018, 27 Manville et al., 2018, Currie and Delbosc, 2011).

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In particular, income is a widely used indicator of social exclusion, transport disadvantage 29 and social inequity (Mercado et al., 2012, McCray andBrais, 2007). With respect to mode choice, 30 it has been shown that nationally, low-income groups exhibit higher public transport use than 31 higher-income groups in the U.S. (Giuliano, 2005). In some cases, lower-income users have been 32 termed captive users as they have no choice but to use public transport (Beimborn et al., 2003). 33 On the other hand, a study that examined public transport use of low-and higher-wage workers in 34 Toronto-Hamilton found that low-wage workers as a group had lower public transport mode share 35 than higher-wage workers (Legrain et al., 2015). However, this contradictory finding could be 36 attributed to the methodology employed to segment workers into wage categories by job sector. 37 The determinants of public transport use specific to lower-income populations has also been 38 explored by researchers such as Mercado et al. (2012) where they found that among low-income 39 1 influential than residential density. Easy access to a public transport system also impacts mode 2 choice, where being closer to public transport infrastructure, such as stations or stops, increases 3 the odds of its use (Ewing and Cervero, 2010). Accessibility, as the ease of reaching destinations, 4 is used to measure the ease of accessing opportunities using the transport system, thus internalizing 5 aspects of both the built environment, namely density and location of opportunities, as well as 6 availability and quality of transport infrastructure. 7 Accessibility has also been shown to influence public transport mode share positively (Chow 8 et al., 2006). For example, researchers Owen and Levinson (2015) found, using continuous 9 accessibility to jobs, higher mode share is associated with higher average public transport 10 accessibility in the Minneapolis-Saint Paul area. Moniruzzaman and Páez (2012) found, using data 11 from Hamilton, Ontario that mode share increases as accessibility increases but the relationship is 12 not linear due their use of logit regression models. With this in consideration, and based on the 13 shift we have seen in the past years towards incorporating accessibility as an objective in transport 14 plans (Boisjoly and El-Geneidy, 2017), we identified a need to study accessibility and mode share 15 from an equity perspective to enable a comparison between its impact on public transport mode 16 share at different geographic scales and among different income groups. identified that while there are geographic differences in accessibility of the two groups, the 23 vulnerable tend to experience higher accessibility when compared to the entire population in each 24 region. Furthermore, accessibility has also been studied as a predictor of travel, such as research 25 done on the impact of accessibility on the journey to work (Levinson, 1998). In particular, 26 Canadian researchers (Cui et al., 2019a), using data for Toronto-Hamilton, Montreal and 27 Vancouver, found that the influence of accessibility to jobs as well as the presence of worker 28 competition impacts commute duration and is stronger for low-income compared to higher-income 29 groups. In addition, the distributional impact of accessibility on employment outcomes were 30 examined for the Los Angeles area where researchers identified that accessibility to jobs by car 31 positively affected the employment status of medium-to low-income groups but not for the lowest 32 income group (Hu, 2017). The geographic scope of the present study concerns eleven Canadian metropolitan regions 36 extending from coast to coast as shown in Figure 1. These regions, shown in detail in Figure 2, 37 were selected due to differences in city size, city structure, public transport system maturity, and 38 other socio-demographic factors. As a result, we hope that their inclusion would offer some insight 39 as to how the impact of accessibility differs between regions and among different income groups.  Accessibility measures used in this study are cumulative-opportunity measures which evaluate the 2 number of opportunities that can be reached from an origin point within a fixed cost, e.g.travel 3 time. As such, the generation of such accessibility measures requires two data inputs: number of 4 low-and higher-income jobs available in each census tract across the eleven regions and public 5 transport travel time between census tracts within each region. 6 The number of jobs available in each census tract was obtained from the Statistics Canada 2016 is that the data has been suppressed for confidentiality purposes. As such, this could lead to some 13 inconsistencies in the results especially where there are low numbers of commuters observed. As 14 we do not know the distribution of the jobs within the census tracts, jobs were assumed to be 15 located at the census tract centroids for which travel time information was also calculated for. 16 We chose to define the two income groups in this study as low-and higher-income rather than 17 further defining categories such as medium and high-income groups because we wanted to focus 18 on the results for the low-income group rather than exploring the impacts across an entire income 19 distribution. The low-income threshold is defined in this study as the bottom 30% of low paying 20 jobs in each metropolitan region to reflect the local wage distribution. As the Commuting Flow 21 tables categorize commuters by income brackets, the bracket closest to having 30% of the lowest 22 paying jobs is selected as the threshold. A threshold bracket of $30,000 CAD is used for all regions 23 apart from Calgary, Edmonton and Ottawa-Gatineau where $40,000 CAD is used. Subsequently, 24 the higher-income group includes commuters from all other income groups higher than the low-25 income threshold bracket. Therefore, the number of low-income jobs in a census tract is taken as 26 the sum of all commuters belonging to or below the low-income threshold bracket arriving at that 27 census tract. This was similarly done for the higher-income group.

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To compute public transport travel time between census tracts centroids within each 29 metropolitan region, General Transit Feed Specification (GTFS) data was first obtained from all 30 public transport agencies operating in each of the eleven regions. Then a joint network between 31 the public transport network and the streets was created using the "Add GTFS to network dataset" 32 toolbox in ArcGIS and a travel time matrix for an 8 a.m. departure on a Tuesday was generated 33 using fastest route calculations. Public transport travel time includes access, egress, waiting, in- 34 vehicle and transfer times as applicable. In this research we opted to calculate accessibility using 35 one departure time and at the census tract level as the imposed errors from using this method are 36 minor and value added from going into more detail by averaging multiple departures or using 37 smaller geographic areas is minor (Cui et al., 2019b) and would generally harm the transferability 38 of the findings to practitioners. 39 Separate accessibility measures were generated in this study for the two income groups being  Table 1 and are rounded to the nearest 5-minute interval for use in 2 accessibility measures. 3 Cumulative accessibility measures for the two income groups was calculated separately the 4 jobs and median travel times specific to each group in each region. The measures are formulated 5 as follows:

Model inputs and development 21
The regression model is formulated as follows: β0, β1, β2, β3, β4, β5, β6, β7, β8 = parameters to be estimated. 36 Separate models for each income group in each metropolitan region are generated since 37 different median travel times serve as thresholds to calculate accessibility. The non-linear 38 relationship described by the quadratic function between mode share and accessibility observed in 39 earlier bivariate research (Cui and El-Geneidy, 2019) are shown in the scatterplots in Figure 3. We 40 incorporated this quadratic relationship in the regression models through the addition of a squared accessibility term (higher-order term) which is the squared value of existing accessibility (lower-1 order term).

FIGURE 3 Scatterplots of public transport mode share and accessibility for both income groups in all regions (Cui and El-Geneidy, 2019)
The road network distance to the closest rapid public transport station (including Bus Rapid 1 Transit stops as well as light, heavy and commuter rail stations) from the centroid of the origin 2 census tract is used to control for the influence of higher quality transport infrastructure on mode 3 share. We defined BRTs based on the presence of dedicated right-of-way and off-board fare 4 payment systems. In addition, network proximity to the nearest highway ramp is also included as 5 the presence of car-oriented infrastructure could impact public transport use negatively (Foth et 6 al., 2014).

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Moreover, socio-demographic variables at the origin census tracts, obtained from the 2016 8 Canadian Census, are also included in the regression models. These variables have been studied 9 in previous studies as determinants of public transport use (Miller et al., 2018).We have also 10 elected to use a social deprivation index (in the model) which combines normalized values of 11 household income, unemployment rate, housing affordability, and recent immigration status which 12 has been used previously in studies (Foth et al., 2014). The social deprivation index of each census 13 tract within a metropolitan region is then divided into deciles and entered into the models, with 14 one being least socially deprived to ten being most socially deprived. As we do not have 15 information on the travel attitudes for each commuter, we were not able to control for this in this 16 study.

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Furthermore, while household vehicle ownership has been found to be influential on public 18 transport use (Miller et al., 2018), this was not available at the census tract level at time of the 19 study. As such, its inclusion in future studies of a similar nature may be beneficial. As well, early 20 trials of the models included the network distance to the city centre as a variable to correct for the 21 effects of spatial autocorrelation by controlling for similarities between census tracts at the same 22 distance from the city centre. However, it was removed from the final model as it was found to be 23 highly correlated with accessibility.  25 The mean values for the input variables (including variables that make up the social deprivation 26 index) and relevant summary statistics are presented in Table 1. 27 For the majority of the areas being studied, with the exception of London and Kitchener-28 Cambridge-Waterloo, both average and median commuting times by public transport are lower for 29 low-income groups. Public transport mode share is nonetheless much higher for low-income 30 groups across the country, as observed in past research (Giuliano, 2005). As expected, average 31 mode share is highest in the three largest metropolitan regions with the most developed rapid 32 public transport systems. However, the difference in mode share between other metropolitan 33 regions seems to be unrelated to the existence of rapid public transport systems. For example, in 34 Quebec City, a city without an LRT system, both income groups exhibit higher public transport 35 use when compared with Edmonton, one with an LRT. This confirms that the presence of high-36 quality public transport infrastructure is not the sole predictor of public transport use. Interestingly, 37 active modes are also used by a greater proportion of low-income commuters across all regions. 38 However, when considering higher-income commuters in Halifax, Kitchener-Cambridge- 39 Waterloo, and London, we observe that when averaged across each region, a greater proportion of 40 commuters use active modes compared to public transport, which is indicative of either a lack of 41 high-quality public transport infrastructure or dense city structures that facilitates the use of active London, average accessibility to low-income jobs is lower than average accessibility to higher-45 income jobs for each metropolitan region. This is in contrast to previous research (Deboosere and 1 income groups as well as using time thresholds specific to each income group.    4.1 Accessibility to jobs by public transport 12 The lower-order term of percentage of jobs (Access) accessible by public transport is positively 13 associated with mode share in most regions except for the higher-income groups in Halifax and 14 Kitchener-Cambridge-Waterloo and the higher-order term of the same variable (Access squared) 15 has a negative impact. This result indicates a relationship demonstrated by a concave parabola, 16 where mode share increases in response to increasing accessibility at a non-constant rate until the 17 optimal accessibility value, where a further increase in accessibility has a negative effect on mode 18 share. It is possible that the uptake of active modes at locations of very high accessibility by public 19 transport, which can be correlated to high accessibility by active modes, could explain this pattern. 20 A quadratic relationship also means that improvements in mode share due to a one percent 21 point increase in accessibility is different depending on the starting accessibility level. For 22 example, an increase in accessibility from 6% (the mean) to 7% for the low-income group in 23 Toronto-Hamilton will result in a mode share improvement of 2.7 percentage points (an absolute 24 increase of 2.7%, not a relative increase) compared to an improvement of 1.1 percentage points 25 when accessibility is increased from 13% (one standard deviation above the mean) to 14% in the 26 same region. Moreover, the optimal value for this model is reached when the percentage of jobs 27 that are accessible is 18% (89 th percentile) where maximum public transport mode share is 28 expected but any further increase in accessibility would cause the mode share to decrease. It is 29 important to note that 18% may seem low, but this is three times greater than the mean value of 30 6% for the low-income Toronto-Hamilton model. The optimal values for the low-income models 31 in Montreal and Vancouver are also much higher than the mean and occurs when accessibility is 32 at the 87 th and 81 th percentiles respectively.

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The lower-order accessibility term is statistically significant at 95% in most models but the areas. In contrast, the quadratic relationship between accessibility to jobs by public transport and 43 public transport mode share is not strongly observable for either income groups in Calgary, income Toronto, Montreal, Vancouver, and Winnipeg models in addition to the low-income 1 Kitchener-Cambridge-Waterloo, Ottawa-Gatineau and Quebec City models (i.e. optimal value 2 falls outside of the observed range of values), the phenomenon of decreasing mode share past the 3 optimal accessibility value may not hold true for these groups of commuters. In light of these 4 observations, it seems that the non-linear quadratic relationship is mostly applicable for the low-5 income models for the three large metropolitan regions, Edmonton and London in addition to the 6 higher-income Ottawa-Gatineau and Quebec City models.

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In addition, we observe that the coefficients for accessibility are always higher (in terms of 8 magnitude) in the low-income models compared to the higher-income ones, with the exception of 9 Halifax where the effects are similar and Kitchener-Cambridge-Waterloo where the pattern is 10 inversed. This implies that accessibility by public transport influences mode share more strongly 11 for the low-income group compared to the higher-income group while controlling for the same 12 socio-demographic and spatial variables. Specifically, this result indicates that every percentage 13 point increase in accessibility results in a greater increase in public transport mode share for the 14 low-income group than the higher-income. 15 Furthermore, it is important to note that a one percent increase in job accessibility in  Hamilton is not equal to the same percent increase in a smaller city. For example, a one percent 17 increase of low-income jobs accessible in Toronto-Hamilton is equivalent to an increase of 8,000 18 jobs whereas in London this equates to 600 jobs, which is unlikely to have impact on public 19 transport mode share. However, when the same models are run with all other variables held 20 constant but using the number of jobs accessible rather than the percentage (shown in Table 5), we 21 see that the magnitudes of the coefficients are higher in smaller regions like London where a 22 10,000 increase in jobs accessible by public transport would have a greater impact on mode share.

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The most influential control variables across all models include the social deprivation index (Social 29 Index) and the network distance to a rapid public transport station (Station). The social deprivation 30 index has a positive influence on public transport mode share (i.e. higher level of social deprivation 31 is correlated with higher use) across all models, confirming results from past research (Foth et al.,32 2014). It is clear that low-income individuals living in more socially deprived census tracts are 33 more likely to use public transport rather than high-income individuals in a similarly socially 34 deprived census tract.

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As expected, as distance from a rapid rail station increases, public transport mode share is 36 likely to decrease for both income groups . The relationship between network 37 distance to the closest highway on-ramp and mode share is mixed, as it is significant and positive 38 for the higher-income group in Calgary, Edmonton and Toronto-Hamilton but negative for both 39 income groups in Vancouver, Halifax and Quebec City, and would require further investigation.       accessibility to impact mode share, particularly for the low-income group, while demonstrating 7 discrepancies between metropolitan regions. 8 Firstly, we confirm that a greater proportion of people in the low-income group use public 9 transport as their main commute mode in all study areas, similar to past research (Giuliano, 2005). 10 Next, more socially deprived census tracts exhibit higher public transport use and shorter distances 11 to rapid public transport stations positively influence mode share. Most importantly, we find that 12 accessibility is a predictor of mode share as previous researchers have shown (Moniruzzaman and 13 Páez, 2012), although our characterization of this relationship as quadratic may not be applicable 14 to all metropolitan regions. The relationship between the two variables is more strongly observed 15 in the largest metropolitan regions. A notable result is income does moderate the relationship 16 between accessibility and mode share in that it has a higher predicting power of mode share for 17 the low-income group than higher-income groups in the majority of the studied regions. In other 18 words, public transport use by the low-income group is more sensitive to changes in accessibility 19 than the higher-income group. 20 Furthermore, while these results imply that we would expect significant gains in public 21 transport mode share for low-income groups in the largest metropolitan regions, we need to be 22 mindful that at very high levels of accessibility, increasing accessibility is not expected to lead to 23 a substantial increase in use due the non-linear relationship observed between accessibility and 24 mode share. However, since the percentage of jobs accessible in a census tract would have to be 25 in at least the 80 th percentile in these regions for this to be applicable, improvements in mode share 26 are still expected in the majority of the census tracts where the accessibility is currently below this 27 value. Moreover, for metropolitan regions where the quadratic relationship is not strongly 28 observed and there is no optimal value, we can expect an increase in mode share for the low-29 income, and to a lesser extent, the higher-income groups with improved accessibility throughout 30 the region.

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With these findings in mind, policies that would greatly improve the accessibility for low- 32 income groups would bring about a greater increase in public transport use. Doing so would also 33 mean that low-income riders who are more likely to be reliant on public transport will benefit from 34 the service improvements, which can make a greater impact to improve their quality of life. As a 35 first step, ridership profiles can be created for the public transport network in a region to identify 36 routes that are mostly frequently used by low-income commuters. These can be targeted for service 37 improvements to improve accessibility and potentially result in more public transport use based 38 on our findings. In addition, a return on public transport investments can be expected when they 39 are aimed at improving accessibility in areas of low existing accessibility rather than highly 40 accessible ones. Furthermore, the findings of our research can help policy-makers determine the 41 approximate optimal accessibility value at which public transit use may be maximized based on 42 the values of the input variables specific to a census tract and the results of the regression analysis 43 in this study.

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Further examination of the relationship between accessibility by active modes and public 45 transport mode share is necessary to confirm our hypothesis that the decline in mode share at very high levels of accessibility is attributed to the uptake of walking and cycling. Doing so could also 1 help explain the inconsistent results that were observed in the higher-income Halifax, Kitchener-2 Cambridge-Waterloo models. Moreover, while this model used a quadratic function to model the 3 non-linear relationship, understandably this may not be the best function to use to fit the data in 4 every metropolitan region but was done for the sake of comparison. Future studies can employ 5 more advanced methods to describe the relationship more appropriately. In addition, the effects of 6 temporal variability of public transport on accessibility can be addressed in the future studies by 7 using an average accessibility value to be entered in the models described in this study. As well, 8 other regressions models may be employed to model public transport use such as a binomial 9 regression model for the proportion of commuters that use public transport. 10 This study also highlights the importance of context-specific research. Namely, this study 11 raises important questions, especially with respect to smaller metropolitan regions. Firstly, the 12 quadratic relationship is not observed for all income groups and not in all the metropolitan regions.

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As such, other relationships can be explored between accessibility and mode share that may