Correlates of Cycling Flows in Hamilton, Ontario - Fastest, Quietest, or Balanced Routes?

Elise Desjardins (McMaster University)
Christopher D. Higgins (University of Toronto, Scarborough)
Darren M. Scott (McMaster University)
Emma Apatou (McMaster University)
Antonio Paez (McMaster University)

Abstract

Cycling is an increasingly popular mode of travel in Canadian urban areas, like the Greater Toronto and Hamilton Area (GTHA). While trip origins and destinations can be inferred from travel surveys, data on route choice is often not collected which makes it challenging to capture the attributes of routes travelled by people who cycle. With new algorithms for cycle routing it is now possible to infer routes. Using bicycle trip records from the most recent regional travel survey, a spatial interaction model is developed to investigate the built environment correlates of cycling flows in Hamilton, Ontario, a mid-sized city part of the GTHA. A feature of the analysis is the use of CycleStreets to compare the distance and time according to different routes inferred between trip zones of origin and destination. In addition, network autocorrelation is accounted for in the estimated models. The most parsimonious model suggests that shortest-path quietest routes that minimize traffic best explain the pattern of bicycle trip flows in Hamilton. Commercial and office locations and points of interest at the zone of origin negatively correlate with the production of trips, while different land uses and the availability of jobs at the zone of destination are trip attractors. The use of a route planner offers a novel approach to modelling and understanding cycling flows within a city. This may be useful for transportation planners to infer different types of routes that bicyclists may seek out and consider these in travel demand models.

Transportation (2021) https://doi.org/10.1007/s11116-021-10197-1.

Keywords

Cycling Spatial interaction modelling Route choice

Introduction

Cycling is an increasingly popular mode of travel in Canadian urban areas. From 1996 to 2016 the number of people commuting to work by bicycle in Canadian census metropolitan areas increased by 87.9% and the share of bicycle commute trips grew from 1.2% to 1.6% (Statistics Canada 2017). Such modal shifts have been prompted in part by the widely recognized health and environmental benefits associated with cycling. Compared to other transportation modes, travelling by bicycle is more enjoyable (Páez and Whalen 2010), and is associated with better self-perceived health (Avila-Palencia et al. 2018) and reduced risk of chronic disease (Celis-Morales, Lyall, and Welsh 2017; Oja et al. 2011). Furthermore, cycling also leads to reduced greenhouse gas emissions (Zahabi et al. 2016) and improved air and noise pollution (De Nazelle et al. 2011). These benefits serve as motivation for cities to encourage more travel by this mode, but this requires effort to put cycling on par with other modes of transportation at a policy level. For this reason, many Canadian cities have integrated cycling in their transportation plans in recent years (inter alia, see City of Calgary 2011; City of Montreal 2017; City of Vancouver 2012) and have implemented a range of interventions and strategies that have been effective in increasing cycling (Assunçao-Denis and Tomalty 2019; Verlinden et al. 2019).

The City of Hamilton, a mid-sized city located in the Greater Toronto and Hamilton Area (GTHA) urban region approximately 50 km from Toronto, has experienced an increase in cycling. Approximately one third of all trips in this area are 5 km or less, which is widely considered to be a bikeable distance. In 2016, 1.2% of all trips in Hamilton were made by bicycle according to the latest Transportation Tomorrow Survey, the regional travel survey conducted every 5 years (Data Management Group 2018). This was a two-fold increase from the 2011 survey results when the cycling mode share was only 0.6% (Data Management Group 2014). Hamilton has also been identified as a city where cycling levels could substantially increase to approximately 35% of the mode share (Mitra et al. 2016). The increase in bicycle trips in Hamilton between 2011 and 2016 occurred over the same period that cycling interventions were implemented, such as new cycling facilities and a public bicycle-share program. In other words, we suggest that Hamilton can be characterized as a developing cycling city (see Liu et al. 2020) because efforts to increase cycling have been implemented and cycling levels are growing. Recent studies in Hamilton have used global positioning system (GPS) data from the bike share program to conduct route choice analysis (Lu, Scott, and Dalumpines 2018; Darren M. Scott, Lu, and Brown 2021) and explore influences on bike share ridership (Darren M. Scott and Ciuro 2019). However, we still know relatively little about trips in this city beyond those made by bike share. To date, there has been no published research that has investigated the pattern of bicycle trips in Hamilton using data from the 2016 Transportation Tomorrow Survey. Our understanding of the spatial distribution of such trips in a mid-sized developing cycling city and the influence of the built environment is also limited.

To address these gaps in knowledge, the objective of this study is to investigate the correlates of cycling flows in Hamilton. This paper describes the development of a spatial interaction model (a component of the four-step travel model; see Dios Ortúzar and Willumsen 2011) to test the level of cycling flows against various attributes at the zones of origin and destination. Travel surveys are typically rich in terms of information about where trips start or end, but are less informative with respect to route characteristics, which often have to be inferred. For this reason, a feature of the analysis is the use of an algorithm for cycle routing, CycleStreets, to infer and compare different routes between the zones of origin and destination instead of using only the shortest-path distance. This algorithm identifies routes according to various attributes and characterizes them as fastest, quietest, and balanced routes. The distance and time from the zone of origin to destination along each inferred route serve as measures of cost in the analysis. The following two questions are addressed: 1) Which attributes at the zones of origin and destination influence cycling trip flows in Hamilton?; and 2) Which type of route best explains the pattern of cycling trip flows in Hamilton? In addition, residuals from the spatial interaction model are analyzed using a spatial autocorrelation statistic to assess the model’s compliance with the assumption of independently distributed residuals. Future opportunities for research and practice, including assessment of the built environment along select routes identified by the algorithm, are also discussed.

Following recommendations for reproducible research in the spatial sciences (see Brunsdon and Comber 2020), all data and code used in this paper are available online. The source for this paper is an R markdown document that can be obtained from the following GitHub repository:

https://github.com/paezha/Correlates-of-Cycling-Flows-Route-Types

Background

A diversity of factors influence the decision to commute by bicycle ranging from the natural and built environments to individual and household characteristics (Heinen, van Wee, and Maat 2010). Where people live, work, and play is particularly important because it influences the transport modes available to them, the destinations and amenities that they can access, and the routes they can travel to get from A to B. As such, the built environment receives a lot of attention in cycling research because factors that are known to influence cycling can be modified by urban and transportation planners to potentially shift a large number of currently motorized trips. Population-based travel surveys are useful for understanding cycling activity and patterns at the city level (Handy, van Wee, and Kroesen 2014) which can, in turn, support strategic investments where cycling levels have the potential to increase. Open source tools, such R packages and OpenStreetMap, can also assist in geographic analysis at the local level to complement and inform transport planning decisions and practice (Lovelace 2021).

The behavioral model of the environment was proposed as a theoretical framework for environmental audits to identify the determinants of walking and cycling at three different scales that make up any trip (Moudon and Lee 2003). According to this framework, all three spatial areas (i.e., the characteristics of i) the origin, ii) the destination, and iii) the route) are important and necessary to assess the influence of the built environment on walking and cycling. These modes, more so than motorized travel, allow a traveller to interact more intimately with the micro-level environment (Moniruzzaman and Páez 2012, 2016; Moudon and Lee 2003). This type of framework holds true for bicycle trip analysis as well. Winters et al. (2010) conducted a study measuring built environment variables at three different scales in Vancouver, Canada and found that the built environment around the origin and destination, as well as along the route, are indeed different and influence cycling in different ways. This emphasizes the need for travel behaviour models to capture environmental attributes along different parts of the trip, not just at the zone of origin and destination or the community-level.

Macro-Level Built Environment Factors

The urban form at the places where bicycle trips originate and end is important (Darren M. Scott and Ciuro 2019). This topic is well-documented in the cycling literature. Land use mix, whereby people can reach a variety of amenities within a distance that is comfortable to cycle, influences travel by bicycle (Cervero, Denman, and Jin 2019; Sallis et al. 2013; Winters et al. 2010; Zhao 2014). For instance, Heesch et al. (2015) found that shorter distances to destinations, including a business district with jobs and a river where there are bicycle paths, increased the odds of cycling in Brisbane, Australia. Higher densities of population (Nielsen and Skov-Petersen 2018; Nordengen et al. 2019; Schneider and Stefanich 2015; Winters et al. 2010) and employment (Le, Buehler, and Hankey 2018; Zhao 2014) are other important factors. In the case of cities with low levels of cycling, access to bicycles can make this mode more attractive. Cole-Hunter et al. (2015) report that public bicycle share stations near the residence were a significant positive determinant of commuting by bicycle. The quality of the urban environment also matters. Areas with trees and green space also associated with more cycling (Cole-Hunter et al. 2015; Le, Buehler, and Hankey 2018; Mertens et al. 2017).

In most studies, a combination of these attributes are found to influence cycling, which suggests that multiple factors are needed to create spaces that ultimately encourage people to cycle (Cervero, Denman, and Jin 2019; Handy 2020). Higher levels of cycling are typically observed in neighbourhoods with good street connectivity, supportive infrastructure, and a variety of amenities that can be reached in a short distance. However, there is variation in the relative influence of these attributes across studies and across places, which might reveal different effects that are related to contextual behaviours, or planning and transportation policies. For example, residential density (Darren M. Scott and Ciuro 2019; Zhao 2014) and the presence of cycling infrastructure (Moudon et al. 2005) are not always a significant factor. Therefore, additional analysis to determine the influence of specific attributes on cycling levels is important in developing cycling cities, where such studies have not been previously conducted, which can inform new strategies to induce the uptake of cycling.

Micro-Level Route Factors

Cycling infrastructure is often identified as an important attribute in bicycle-friendly cities. It is thought to be fundamental for encouraging more bicycle trips in cities that are predominantly car-centric (Adam, Jones, and te Brömmelstroet 2020). The provision of, or proximity to, infrastructure has been found to have an influence or association with cycling behaviour (inter alia, see Buehler and Pucher 2012; Buehler and Dill 2016; J. Dill and Carr 2003; Mertens et al. 2017; Winters et al. 2010). For example, Le et al. (2018) found that cycling facilities had a strong association with bicycle volume and traffic based on their analysis of 20 metropolitan statistical areas in the United States. Infrastructure can be very influential - a new bicycle lane in Oslo, Norway attracted trips by shifting bicyclists from other parallel routes (Pritchard, Bucher, and Frøyen 2019). Bike share users also detour from dominant routes to incorporate cycling facilities in their travels (Darren M. Scott, Lu, and Brown 2021). This suggests that it is not uncommon for preferred routes to change as new facilities are built over time and they are incorporated into daily trips. Furthermore, infrastructure can also increase perceptions of cycling safety (Branion-Calles et al. 2019) which may encourage more trips. At the very least, cycling infrastructure is a visual and physical sign that streets can accommodate people who choose to travel using this mode.

Studies examining the characteristics along routes travelled by people who cycle is limited but has grown over the past decade owing in part to the availability of new data technologies. Researchers have used a variety of methods to reveal the route preferences of people who cycle including data obtained from global positioning system (GPS) devices or smartphone applications (Pritchard 2018). In general, studies using such data confirm that people who cycle prefer routes with separated facilities over mixing with traffic (Chen, Shen, and Childress 2018; Jennifer Dill 2009; El-Assi, Mahmoud, and Habib 2017; Lu, Scott, and Dalumpines 2018; Skov-Petersen et al. 2018) and incorporate infrastructure as part of their routes (Jennifer Dill 2009; Lu, Scott, and Dalumpines 2018; Pritchard, Bucher, and Frøyen 2019; Darren M. Scott, Lu, and Brown 2021). One study conducted in Portland, Oregon using GPS data found that streets with bike lanes were comparable in attractiveness to streets with low traffic volume (Broach, Dill, and Gliebe 2012). By examining GPS data from Hamilton’s bike share program, Lu et al. (2018) found that users travel routes that are significantly longer than the shortest path distance and are more likely to use local streets with low traffic and bicycle facilities. Similarly, Chen et al. (2018) also reported that people who travel by bicycle in Seattle, Washington prefer short and flat routes with connected facilities on roads that have low traffic speeds. Their study found more variability with respect to preference for views along routes with features like mixed land use, street trees, lighting, and city features.

Cycling facilities and street connectivity have most consistently been found to be an important attribute of the built environment for promoting cycling (Yang et al. 2019). However, few studies incorporate variables at two or more spatial scales, as outlined in Moudon and Lee’s (2003) framework to capture a comprehensive view of the variability in the built environment that a bicyclist might encounter. Winters et al.’s (2010) study in Vancouver, Canada is an exception, as is a recent study conducted by Cole-Hunter et al. (2015) that took some factors at the route level into account in their analysis of cycling propensity in Barcelona, Spain. Nielsen and Skov-Petersen (2018) recently analyzed the influence of built environment attributes at three different scales on the probability of cycling in Copenhagen, Denmark which captured some of the spatial differentiation at which variables are important, however they did not include any route analysis. There is a need for more research to measure and understand the built environment attributes that affect cycling along different parts of the trip and at different spatial zones.

Methods

Spatial Interaction Modelling

We use spatial interaction methods to analyze bicycle trip flows in Hamilton, Ontario. In the form of a gravity model, this modelling approach can account for multiple spatial zones along a cycling trip, and is therefore a more holistic approach than trip generation analysis (e.g. Dios Ortúzar and Willumsen 2011, chap. 5). The Transportation Tomorrow Survey provides sufficient information to infer the zone of origin and destination of all bicycle trips in Hamilton using centroids of the traffic zones. Built environment attributes at the zone of origin and zone of destination of cycling trips can be accessed through publicly available data. Finally, new algorithms for cycle routing like CycleStreets now make it possible to infer route characteristics between origins and destinations, which can be considered when calculating the cost (i.e., in terms of distance and time) of undertaking trips.

Spatial interaction models operate on principles of propulsion, attraction, and the friction of space (Rodrigue 2020). We can assume that there are factors within a particular geographic area that contribute to producing or generating trips, such as residential or population density, and there are factors in other geographic areas that attract trips like jobs or amenities. Finally, there is the friction of space, in other words, the cost incurred in reaching a destination from an origin. Spatial interaction models are useful for estimating or explaining variation of spatial flows in a particular system or to predict them in different scenarios.

The spatial interaction model is generally represented by the following expression:

where represents the origin, represents the destination, $U_{ij}$ is the total interaction between origin and destination (i.e., for this analysis it is the number of bicycle trips recorded in the TTS), is a vector of attributes at the zone of origin (i.e., the push factors), is a vector of attributes at the zone of destination (i.e., the pull factors), and $d_{ij}$ represents the cost of making the trip (i.e., often the distance or time as a measurement of spatial separation).

Poisson regression is commonly used in the estimation of a spatial interaction model when the dependent variable is available as a count (Chun 2008; Griffith 2011; Metulini, Patuelli, and Griffith 2018). This specification of the gravity model estimates the level of flows based on explanatory variables at the origin and destination (Griffith and Fischer 2016). This regression model is also suitable for datasets that contain true zero counts (Griffith 2011), as is the case when many zones of origin and destination do not generate trips. The Poisson model is:

To estimate the model, we work with the mean function $\lambda$ :

The generalized linear version of the model uses the natural logarithm as the link function, which leads to the following log-linear specification of the mean function (see Chun 2008):

In Equation , $x = [1, V_i, W_j, d_{ij}]$ is the vector of correlates including constant term(s), variables at the origin (), at the destination (), and the cost of movement between origin and destination ( $d_{ij}$ ). These correlates are associated with a vector of estimable parameters $\theta = [\theta_0, \theta_O, \theta_D, \theta_C]$ corresponding to the constant term(s), and the variables at the origin, at the destination, and the cost.

For our analysis, bicycle trip counts serve as the dependent variable and built environment or demographic attributes known to influence cycling serve as independent variables, with and representing push and pull factors at and respectively, and $d_{ij}$ the cost or separation between the zone of origin and zone of destination .

As highlighted by numerous studies (e.g., Chun 2008; Metulini, Patuelli, and Griffith 2018), spatial or network autocorrelation can occur in spatial interaction models because of, among other things, unobservable factors at the zone of origin or destination that are not included in the model, or a misspecified cost function. Failing to account for network autocorrelation can lead to unreliable findings or misleading interpretations of the behaviour modelled (Chun 2008; Griffith and Fischer 2016). In this respect, use of Moran’s has been criticized for the case of residuals of a Poisson regression model because it is based on a normality assumption and Poisson has distributional properties that are not well known (Chun 2008). Instead the statistic (see Jacqmin-Gadda et al. 1997) is recommended for applications in spatial interaction modelling (Chun 2008; Metulini, Patuelli, and Griffith 2018).

The statistic derived by Jacqmin-Gadda et al. (1997) has the following equation:

In Equation , the term $w_{ij}$ is a weight that indicates whether, and to what extent, zones and are related in space (conventionally $0\le w_{ij}\le 1$ ); is a spatial random variable, and $\hat{\mu_i}$ is the estimated value of the variable according to a suitable model.

Study Area

Hamilton is a growing mid-sized city located in the Greater Toronto and Hamilton Area, in Canada. The city is divided by the Niagara Escarpment, which separates the lower city and downtown core in Dundas Valley from the suburban/rural parts of the city on top of the escarpment and is approximately 100m tall in many places. The population was approximately 540,000 in 2016 at the time that the Transportation Tomorrow Survey was conducted, but is expected to increase by 22.9% over the coming 15 years (City of Hamilton 2018a), indicating that transportation demand will likely also grow. The city’s current Cycling Master Plan was released in 2009 to “guide the development and operation of [the city’s] cycling infrastructure for the next twenty years” (City of Hamilton 2018c, i) and was most recently updated in 2018 (City of Hamilton 2018b). According to the City of Hamilton, approximately 46% of the planned city-wide cycling infrastructure, which includes on-street and off-street facilities, has been built as of 2019. Around 15 to 20 km of new cycling facilities are built each year, amounting to an annual increase of 1-2% for the entire network.

Data Sources

The Transportation Tomorrow Survey (TTS) is a voluntary travel survey conducted every 5 years since 1986 to collect information about urban travel for commuting purposes in Southern Ontario (Data Management Group 2018). The final dataset for the 2016 survey includes 6,424 completed surveys in Hamilton out of a total of 162,708 from the entire GTHA. The results from respondents in Hamilton serve as the primary dataset used in this analysis and were made available in Spring 2018. The TTS study employed a mixed sampling approach that was primarily address-based in response to changes in landline ownership and increasing households that only have a cell phone and no landline (Data Management Group 2018). The survey includes sampling weights to obtain population-level values of the variables (Data Management Group 2018). The survey was conducted between September and December 2016 online (64% of surveys completed) and by telephone (36% of surveys completed). Each participant was asked to provide household and demographic data (e.g., household size, number of vehicles, gender, etc.) and to describe all trips (e.g., origin, destination, transport mode, etc.) made the previous day by each member of the household aged 11 years or older. Trip data are aggregated for public use and the traffic zone is the finest level of spatial disaggregation. Hamilton has 234 traffic zones. Each traffic zone typically falls along the centre line of roads or the natural geographic boundaries, but may or may not align with municipal ward boundaries.

In total, there are 13,635 bicycle trips in the 113 traffic zones within Hamilton, after the expansion factor to make it a representative sample. The trips occurred between a total of 294 origin-destination pairs. The true origins and destinations of trips are not included in the dataset, only the number of trips produced or attracted to each traffic zone. Although cycling increased overall in the city in recent years, levels vary across different parts of the city. The geographical context for the analysis can be seen in Figure and Figure . The maximum number of bicycle trips recorded for a single trip flow was 365 trips. The zone of origin of this trip flow features the local university and ends at a neighbouring residential area. This aligns with Scott and Ciuro’s (2019) findings that the university is a major generator and attractor of bike share trips. Due to low density and few destinations within a bikeable distance, the majority of traffic zones located in the rural areas of the city generated 0 bicycle trips. An average of 46 bicycle trips occurred per traffic zone that produced bicycle trips. The minimum number of bicycle trips recorded in a traffic zone that produced any trips at all was 6. Of the 113 traffic zones that produced bicycle trips, about 25% produced more than 55 trips, likely zones that feature attributes that are conducive to greater cycling levels, such infrastructure or mixed land uses.

Objectively measured demographic and environmental attributes at the zones of origin and destination that might explain the production or attraction of bicycle trips were included in the model. These explanatory variables were selected based on their known or potential influence on cycling behaviour, as identified in the literature above, but also on our ability to access such data. For instance, residential density at the zone of origin might explain why trips begin there, and the number of jobs or services at the zone of destination could explain why trips end there. When possible, the datasets used for this analysis come from 2016 to match the year of the Transportation Tomorrow Survey results. The 2016 Canadian Census, which is publicly available information, provided population estimates at the census tract level. Land use data was accessed from Teranet Inc. and The City of Hamilton’s Department of Planning and Economic Development. The latter dataset defines all land parcels in the city as well as the type of land use for each parcel. The 2016 Enhanced Points of Interest (EPOI), produced by DMTI Spatial Inc, is a national database of over 1 million business and recreational points of interest in Canada that featured over 32,000 points of interest located in Hamilton. Finally, The City of Hamilton’s Open Data Program offered a dataset containing the number of transit stops and the number of existing and proposed cycling infrastructure segments.

Data Preparation

Hamilton’s bicycle trip records were accessed in July 2019 and exported as a contingency table with the traffic zones of origin and destination of all cycling trips. The original table containing only trip information featured 294 origin-destination (O-D) pairs of traffic zones. This table was cleaned to remove 13 isolated zones, which produced trips only to neighbouring zones and not elsewhere in the city. This reduced the number of O-D pairs in our analysis from 294 to 262. Objective demographic and environmental variables were geographically organized in two different zoning systems, and areal interpolation was performed to convert census data from the tract level to traffic zones. Similarly, spatial subsetting was performed to select and organize environmental attributes based on their known coordinates and whether or not they intersected with a traffic zone. Zonal demographic and environmental variables were then joined to the origin-destination table. Table shows the variables that were tested in the model to measure their relative and collective influence on cycling trip flows.

Demographic and Built Environment Variables Used in the Analysis

Variable	Description	Source
Population	Persons residing in each traffic zone (1,000s)	2016 Canadian Census
Points of Interest	Points of interest (e.g., health care and educational facilities, restaurants, etc.) per traffic zone (1,000s)	DMTI Spatial Inc.
Bus Stops	Municipal bus stops per traffic zone (100s)	City of Hamilton Open Data
Infrastructure Segments	Existing and proposed cycling infrastructure segments (100s)	City of Hamilton Open Data
Institutions	Institutions (e.g., schools, places of worship, government, etc.) per traffic zone (1,000s)	Teranet Inc., Hamilton Parcel/Land Use Data
Commercial	Commercial locations (e.g., general retail, recreation, and sports clubs, etc.) per traffic zone (1,000s)	Teranet Inc., Hamilton Parcel/Land Use Data
Residential	Residences (e.g., detached house, semi-detached house, apartment, etc.) per traffic zone (1,000s)	Teranet Inc., Hamilton Parcel/Land Use Data
Full-Time Jobs	Persons employed full-time, outside of the home, by zone of employment (1,000s)	Transportation Tomorrow Survey
Part-Time Jobs	Persons employed part-time, outside of the home, by zone of employment (1,000s)	Transportation Tomorrow Survey

In addition to the variables in Table , dummy variables were created to account for Hamilton’s topography. Traffic zones were classified by geographic area, namely zones in the lower city and zones on the Niagara Escarpment or the suburban/rural parts of the city. This classification was used to code O-D pairs that were in the same different geographical classes, to capture that a bicyclist would need to navigate changes in elevation and natural features when travelling across different topographies in Hamilton. If both the zone of origin and zone of destination were in the lower city, this pair was labelled with 0. If the origin and destination were in different regions (i.e., lower city and escarpment/rural), the pair was labelled with 1. If both zones were in the escarpment or rural areas, the pair was labelled with 2.

Inferring Cycle Routes

The Transportation Tomorrow Survey does not ask respondents to state the routes that they travel, so this information is unknown. For this reason, we have to infer routes using the centroids of each traffic zone polygon as a start or end point, which are then used as cost functions in the model. We use a novel routing service, CycleStreets, to this end. The algorithm relies on data that is publicly available through OpenStreetMap, which means that there are additional objectively measured environmental variables captured in the cost function. This can potentially provide more information about trip distribution than using only the shortest-path distance. The distance and time on each leg of a route can be obtained from the algorithm, and from these, the total travel distance and time for each type of route between origin and destination can be calculated.

The algorithm infers three different types of routes: fastest, quietest, and balanced. The R package used in this analysis states: “These represent routes taken to minimize time, avoid traffic, and compromise between the two, respectively” (Lovelace and Lucas-Smith 2018, 1). The documentation states that the algorithm considers the following factors when searching for a route: length of streets, signalled junctions, signalled crossings, elevation, speed, busynance, and quietness. The CycleStreets algorithm rates the quietness as a percentage score, with routes featuring cycle tracks and park paths rated as the quietest, and then decreasing to varying degrees of quietness depending on the extent that people who cycle would have to interact with other road users on. The documentation explains: “When the Journey Planner is asked to generate the ‘Quietest’ route, the effect of these percentage scores is to make the quieter routes appear to be the best option. A busy route, with a quietness of 50% will appear twice as long as a 100% quiet route. This balances quietness with distance, and in this case could mean you would have to travel twice as far as the busy route. However when there are no other choices the journey planner will sometimes be forced to pick busy routes.” Thus, the overall quietness is defined as the total length of the segment divided by the total busyness. The routes are essentially modified impedances based on distance, which would be akin to labelling approaches in route choice set generation. The algorithm tries to minimize the busyness which means that the inferred route “may not always be the quietest - but always the least busy.” However, there is a lack of transparency with respect to the speed limit used for calculating the time of each route, which the algorithm also seeks to minimize, and the specific attributes that are considered by the algorithm when minimizing busyness. Quietness scores are adjusted based on feedback from users, and therefore include what might be considered expert opinion.

Testing each type of route as an impedance factor in the model yields six different cost variables for each origin-destination pair (i.e., , , , , , and ). For the sake of comparison, we also include the simplest measure of cost, which is the Euclidean distance between origin-destination centroids (or Euclidean time, the time that it would take to travel that distance on a straight line, assuming a speed of 22.5 km/h). Each of these variables were incorporated into the spatial interaction model to test which cost variable best explains cycling flows in Hamilton. Table offers descriptive statistics of the different types of routes, after removing intrazonal trips. Table includes the average detour of the quietest and balanced routes compared to the Euclidean distance. The detour is defined as the ratio of the distance (or time) on the route to the Euclidean distance (or time) for the same origin-destination pair. For example, a detour of 1.5 means that the route is 50% longer than the corresponding Euclidean metric.

Descriptive Statistics of Inferred Routes by CycleStreets

Route	Minimum	Quartile.1	Median	Mean	Quartile.3	Max	SD
Euclidean Distance (km)	0.318	3.387	5.508	5.924	7.950	19.631	3.367
Euclidean Time (min)	0.8461	9.0188	14.668	15.775	21.172	52.279	8.968
Quietest Distance (km)	0.412	4.950	7.944	8.293	11.085	25.523	4.419
Quietest Time (mins)	1.617	22.725	37.817	40.572	54.683	133.117	4.373
Balanced Distance (km)	0.412	4.829	7.688	8.127	10.784	24.908	4.424
Balanced Time (mins)	1.617	20.837	34.825	36.752	49.462	124.567	23.091
Fastest Distance (km)	0.412	4.851	7.715	8.179	10.834	24.865	20.376
Fastest Time (mins)	1.617	20.038	32.975	34.612	46.783	110.300	18.788

Descriptive Statistics of Average Detour of Inferred Routes by CycleStreeets Compared to Euclidean Distance

Route	Min	Quartile.1	Median	Mean	Quartile.3	Max
Quietest Distance (km)	0.9861	1.2782	1.3971	1.4388	1.5187	5.4321
Quietest Time (mins)	1.058	2.108	2.403	2.661	2.982	15.943
Balanced Distance (km)	0.9861	1.2574	1.3794	1.4064	1.4893	5.4149
Balanced Time (mins)	1.058	1.960	2.182	2.421	2.689	15.791

As seen in Tables and quietest distance routes and quietest time routes are longer than the balanced and fastest route counterparts, but not by much. Most of the quietest distance routes are also 50% longer than the Euclidean distance.

Results

Spatial Interaction Models Considered

Four spatial interaction models were estimated with bicycle flows between zones of origin and destination as the dependent variable. The models are compared to show how each of the spatial zones of the behavioral model of the environment (see Moudon and Lee 2003) are necessary for spatial interaction modelling. Various combinations of zonal attributes and the distance or time of inferred cycle routes between origins and destinations were experimented with. Each of these models went through a general-to-particular variable selection process. Starting with models that included all zonal attributes in Table , variables that did not meet a significance criterion of $p \le 5$ % were removed to obtain a more parsimonious model. For comparison purposes, a base model with a constant only was estimated to serve as a benchmark. This was followed by a model with only zonal attributes (i.e., push-pull factors), then a model only with cost variables (time or distance of different inferred routes), and then finally a full model with zonal and cost variables. The selection of initial variables for each model was deliberate and meant to investigate the performance of models that considered only certain aspects of the spatial interaction process. The models are described next and the results are presented in Table .

Model 1: Zonal Attributes Only

After the benchmark non-informative model, the first estimated spatial interaction model included zonal attributes as explanatory variables that might explain the production or attraction of bicycle trips but did not include a cost variable. These were the variables that met the significance criterion of $p \le 5$ % in the general-to-particular variable selection process. Therefore, this model did not include the second spatial zone of the behavioral model of the environment.

Model 2: Cost Variables Only

This model used only cost variables, which included our geographical classes for the zones. In other words, this model includes only attributes of the second spatial zone of the behavioral model of the environment, namely the different inferred routes. We estimated this model with one cost variable at a time (e.g., topography and fastest distance, topography and quietest time, and so forth) which allowed for the comparison of how distance or time along specific inferred routes performed in each model.

Model 3: Full Model

In the final model, we combined the variables used in Models 1 and 2, to include both zonal attributes and the cost function. This model includes zonal attributes that might explain the production or attraction of bicycle trips, topography classification, and measures of cost from inferred routes. Just like Model 2, we estimated this model using each cost variable at the time (i.e., all zonal attributes with fastest distance as cost, and so forth).

Model Results

Akaike’s information criterion () is used to compare the various models. As a test for goodness of fit, it estimates the relative quality of statistical models. The model with the lowest is selected as the model that minimizes information loss, while considering parsimony of the specification.

The is calculated by Equation :

where is the number of estimated parameters and is the maximum value of the likelihood function of the model.

In addition, is used in the calculation of the relative likelihood, which is defined as:

In the above, $AIC_{min}$ is the of the model that minimizes this criterion, and is the of a competing model. This measure of goodness of fit is interpreted as the probability that the competing model minimizes information loss to the same extent as the best model. It is important to note that although comparison of from a set of models indicates the model with the best fit, it does not reveal any information about the quality of each model, which is why analysis of the residuals is important as well.

Table presents a summary of the goodness of fit of the models. For reference, the of the base model is 95,808 and the of Model 1 is 83,995. Model 1 is a significantly better fit than the base model, which indicates the explanatory power of zonal attributes as independent variables. Interestingly, as seen in the table, the use of cost as in Model 2, provides much higher explanatory power than zonal attributes. Of the different cost variables, distance along quietest routes is the cost variable that leads to the best fit, a result that is replicated in Model 3. An obvious limitation of Model 2 is that it lacks variables that might ultimately explain what is producing or attracting bicycle trips from each traffic zone. Our full model, Model 3, includes variables that might explain trips and cost variables, which ultimately provides the best fit of all models considered. As seen in Table , Model 3 with distance along inferred quietest routes provides a significantly better fit than any of the competing models, and the relative likelihood (calculated with respect to this model) indicates that the probability that any of the alternative models minimizes the information loss to the same extent is practically zero.

Model Comparison: AIC and Relative Likelihood

	Model 2		Model 3
Cost Variable	AIC	Relative Likelihood	AIC	Relative Likelihood
Euclidean Distance	71514	$	63127	$
Fastest Distance	71839	$	63365	$
Fastest Time	71969	$	63521	$
Quietest Distance	71307	$	62973	1
Quietest Time	71589	$	63132	$
Balanced Distance	71647	$	63357	$
Balanced Time	71979	$	63541	$
Note:
Relative likelihood is calculated with respect to Model 3:Quietest Distance

The results of the models are presented in Table . In addition to their goodness of fit, each of the models was tested for network autocorrelation, using Jacqmin-Gadda’s statistic (Jacqmin-Gadda et al. 1997; Chun 2008; Metulini, Patuelli, and Griffith 2018). Network autocorrelation is, in addition to a violation of the independence assumption, an indication of a model that is misspecified (either the functional form in incorrect or there are relevant variables that were omitted).

It is worth noting that the only model without residual network autocorrelation is Model 3, which signifies that this model not only provides the best fit but it is also the only one that is free from network autocorrelation. As described above, testing for network autocorrelation in a spatial interaction model is a diagnostic tool. When no network autocorrelation is detected in the residuals of the model, this is a sign that all systematic variation has been accounted for with the variables included in the model. The model can be considered a sufficient explanation of the pattern observed. We discuss the results of the analysis next.

Results of the Models

	Base Model		Model 1		Model 2		Model 3
Variable	Estimate	p-value	Estimate	p-value	Estimate	p-value	Estimate	p-value
(Intercept)	0.2099	<0.0001	0.0396	0.3735	2.4061	<0.0001	1.9826	<0.0001
Population.o			-93.5856	<0.0001			-27.3106	0.0097
Points\_of\_Interest.o			-0.6827	<0.0001			-0.7509	<0.0001
Institutions.o			30.4358	<0.0001			14.6119	<0.0001
Commercial.o			5.5309	<0.0001			-1.6004	0.0011
Industry.o			-5.8369	<0.0001			1.6853	0.0125
Office.o			-11.2755	<0.0001			-10.2228	<0.0001
Residential.o			-0.7102	<0.0001			-0.1558	<0.0001
BusStops.o			1.6269	<0.0001			1.7688	<0.0001
BikeInfra.o			0.0107	<0.0001			0.0019	0.0926
Population.d			-166.7009	<0.0001			-97.1404	<0.0001
Institutions.d			36.4256	<0.0001			24.1953	<0.0001
Commercial.d			1.5804	7e-04			-8.0098	<0.0001
Industry.d			-6.0468	<0.0001			5.3459	<0.0001
Office.d			6.8574	<0.0001			15.0947	<0.0001
Residential.d			0.1398	<0.0001			0.7039	<0.0001
BusStops.d			-1.503	<0.0001			-1.2592	<0.0001
BikeInfra.d			0.0024	0.0442			-0.0083	<0.0001
Full\_time\_jobs.d			0.1907	<0.0001			0.0796	<0.0001
Part\_time\_jobs.d			0.2368	<0.0001			0.5414	<0.0001
Topographylower city - rural					-2.53	<0.0001	-2.4021	<0.0001
Topographyrural					-0.6518	<0.0001	-0.545	<0.0001
quietest\_distance					-0.3253	<0.0001	-0.345	<0.0001
Model diagnostics
Jacqmin-Gadda z(T)	34.4011	p<0.0001	26.5433	p<0.0001	28.5666	p<0.0001	0.1576	p = 0.4374
n =		9801		9801		9801		9801
log-likelihood =		-47902.9293		-41976.9929		-35649.4031		-31463.3543
AIC =		95807.8587		83993.9858		71306.8063		62972.7087
Relative likelihood =		<0.0001		<0.0001		<0.0001		1
Note:
Jacqmin-Gadda T is converted to a z-score
Relative likelihood is calculated with respect to Model 3

Discussion

Best Fit Model

Model 3 reveals that several built environment attributes at the zones of origin and destination produce or attract bicycle trips in Hamilton, Ontario. Points of interest and commercial and office locations at the zone of origin had a negative influence on the number of expected bicycle trips. This is as expected: more destinations or amenities at the origin create more intervening opportunities that ultimately reduce the need to travel to other areas. Although population density has been found to influence cycling trips in several studies (e.g., Nielsen and Skov-Petersen 2018; Nordengen et al. 2019; Schneider and Stefanich 2015; Winters et al. 2010), in our analysis we find a negative effect of population density in terms of both producing and attracting trips by bicycle. Scott and Ciuro similarly found that population density around bike share hubs in Hamilton does not influence ridership (Darren M. Scott and Ciuro 2019). It is possible that this is due to the relatively low population density of Hamilton in general. In contrast, availability of jobs at the destination was a positive attractor of bicycle trips.

The model also uncovered a positive relationship between number of trips and different land uses at the destination: institution, industry, office, residential locations. This reflects an abundance of amenities and diversity of jobs, as well as the reciprocal trip flow to return to one’s residence. Geographical classification of the zones was found to have a negative relationship with the number of bicycle trips. This suggests relatively little interaction between the two broad regions in the city, namely lower city and escarpment/suburban/rural, and also lower interaction within the escarpment/suburban/rural compared to the lower city. The presence of the Niagara Escarpment, in particular, echoes other studies that have found that elevation at the destination or changes in slope can deter travel by bicycle (e.g., Broach, Dill, and Gliebe 2012; Cole-Hunter et al. 2015; Darren M. Scott, Lu, and Brown 2021). In the case of Hamilton, the Escarpment is a significant change in slope. The physical cost of travelling up and down an escarpment, in addition to longer trip distances, can help to explain why there are few trips between the two distinct areas of the city.

The findings from this study offer important information to transportation planners in similar mid-sized Canadian cities, particularly for making the case to enhance infrastructure that connects residential areas and business districts with a large employment. This type of geographic analysis can also provide support for the continuation or expansion of existing cycling interventions. In the case of Hamilton, our findings confirm that the city’s recent implementation of a “Mountain Climber” program, which allows bicyclists to put their bike on local buses and travel up and down the escarpment for free (Hamilton 2019, July 12), is an appropriate solution to support more cycling trips between the two broad regions in the city.

Inferred Routes

Another key contribution of this paper is the use of an open source novel routing algorithm, CycleStreets, to derive cost variables for spatial interaction modelling instead of using shortest path algorithms. To the best of our knowledge, this is the first North American study that uses the CycleStreets algorithm in combination with travel survey data to infer routes in the analysis of cycling trip flows.

The best model reveals that the quietest routes that allow bicyclists to minimize distance and interactions with other road users best explain the pattern of cycling trip flows in Hamilton. This finding is consistent with previous research that used GPS data to reveal the route preferences of bike share users in Hamilton (Lu, Scott, and Dalumpines 2018; Darren M. Scott, Lu, and Brown 2021). After quietest distance, quietest time was the closest competitor. After the identified quietest routes, there was relatively little difference between using balanced distance and fastest distance as a measure of spatial separation in the model. Intuitively, it makes sense that these two measures would have similar goodness of fit since they both involve greater mixing with traffic. If traffic interactions cannot be avoided, then taking the fastest shortest path route to arrive at the destination would likely be the next best option for many experienced bicyclists.

As previously noted, the differences between quietest routes and balanced/fastest routes are relatively small. The fact that the goodness of fit of the models using the quietest routes is significantly better suggests that there might be other factors at the micro-level of the routes that may influence cycling differently between these routes. This leaves open the question whether routes inferred by CycleStreets have attributes that support cycling, such as infrastructure or enjoyable environments, in addition to less busyness. Despite the lack of transparency about certain aspects of the algorithm (in particular the expert input used to modify the quietness scores), the algorithm makes overall sensible recommendations for quietest routes in the experience of the authors. While we cannot know with complete certainty which routes were actually used by TTS respondents, by exploring different types of routes in our models we are able to provide statistical support for quietest routes that minimize distance. Again, this finding is in line with bike share results from studies conducted in Hamilton (Lu, Scott, and Dalumpines 2018; Darren M. Scott, Lu, and Brown 2021).

Inferring the route travelled between zones of origin and destination using routing algorithms is an important method to account for route characteristics in the analysis of trip distribution, and the second spatial zone of the behavioral model of the environment. It is more informative than using the shortest path which may not reflect the true behaviour of bicyclists in Hamilton who are known to avoid direct routes and to detour for streets with infrastructure (Lu, Scott, and Dalumpines 2018; Darren M. Scott, Lu, and Brown 2021). Other studies have used GIS (Cole-Hunter et al. 2015; Winters et al. 2010), GPS data (Chen, Shen, and Childress 2018; Jennifer Dill 2009; Lu, Scott, and Dalumpines 2018; Skov-Petersen et al. 2018), or new methods using crowd-sourced data (McArthur and Hong 2019; Sarjala 2019) to measure or approximate the built environment along routes travelled by bicyclists. However, GPS data are typically available only for small samples or under limited conditions, such as with bike share trips in Hamilton, that may not cover the full geographical extent of travel by bicycle in a region. Ideally, more sophisticated spatial interaction or trip distribution models could be developed with routing algorithms that better incorporate and reflect route preferences at the local level. This is where open source tools for geographic analysis have a greater role to play.

Open source tools such as CycleStreets that interface with open data sources allow for the estimation of a cost variable in an inexpensive way when such data is generally not available from travel surveys, including the Transportation Tomorrow Survey. They do not require a proprietary license and can be used to enhance citizen participation in the transportation planning process (Lovelace 2021). Broach et al. (2012) noted that in many cases the conventional travel demand model does not address cycling well for several reasons. Cycling is often combined with walking since they are both active modes and it is often excluded after the second step of the travel demand model, meaning that route choice and network assignment are not accounted for. Chen at al. (2018) touch upon this as well by suggesting that data about route choice is needed to overcome these limitations. Common approaches of including only the shortest path route between origins and destinations when accounting for cycling in a travel demand model presents additional limitations because it excludes different built environment attributes that are known to influence route choice (Broach, Dill, and Gliebe 2012). Use of an open source routing algorithm helps, therefore, to overcome the dearth of information on actual routes and can account for variability in route characteristics depending on the availability of data.

However, there are advantages and limitations to using cycle routing algorithms. The ability to infer distance and time from different routes that a knowledgeable bicyclist would take when modelling bicycle trips using data from travel surveys is particularly efficient when GPS data are not available. Thus, cycle routing algorithms can be more practical for transportation planners because they are less demanding and expensive than collecting route data in travel surveys or creating their own network dataset. A limitation, on the other hand, is the inability to capture the variety of routes that bicyclists actually take. GPS data, when available, is more suited to capturing variations between dominant and shortest path routes (Lu, Scott, and Dalumpines 2018). However, despite some limitations, we offer that the approach outlined in this research can be replicated in other cities covered by CycleStreets and OpenStreetMap if the underlying data is of good quality and accurate. Ferster et al. (fersterUsingOpenStreetMapInventory2020?) highlight: “OSM provides a single central source to obtain a global transportation and built environment dataset.” When it comes to length of cycle infrastructure in several Canadian cities, the authors found that crowd-sourced data available on OpenStreetMap was comparable to open data that can be accessed from the cities (fersterUsingOpenStreetMapInventory2020?). This is another example of the added value of open source tools for research and practice.

Strengthening publicly available data in OpenStreetMap could be useful to measure the influence of route characteristics on travel by bicycle between different origins and destinations. Ferster et al. (fersterUsingOpenStreetMapInventory2020?) offer some considerations for making this type of data more useful for local researchers and transportation planners, including improving consistency and alignment of labelling cycle infrastructure. This could be a great learning opportunity for novice geographers (see Solís, Anderson, and Rajagopalan 2020). Open source tools can also allow citizens to add their preferred routes, and the most popular route could be used as cost functions in future trip distribution or spatial interaction models. Lovelace (2021) notes that open source tools should be used more in transportation modelling and planning practice, and we argue that our analysis provides a strong example in support of his recommendation.

Bicycle Trip Flow Characteristics According to Quietest Distance Routes

Characteristics	Percentage
Trip Flows ![\\ge](https://latex.codecogs.com/png.latex?%5Cge "\ge") 10 km	4.6%
Trip Flows ![\\ge](https://latex.codecogs.com/png.latex?%5Cge "\ge") 5 km	21.4%
Trip Flows ![\\le](https://latex.codecogs.com/png.latex?%5Cle "\le") 5 km	78.6%
Trip Flows ![\\le](https://latex.codecogs.com/png.latex?%5Cle "\le") 2.5 km	48.5%
Trip Flows Rural/Escarpment to Lower City	1.9%
Trip Flows Lower City to Rural/Escarpment	1.9%
Trip Flows Only Rural/Escarpment	16.8%
Trip Flows Only Lower City	79.4%
Trip Flows ![\\le](https://latex.codecogs.com/png.latex?%5Cle "\le") 2.5 km in Lower City	52.4%
Trip Flows ![\\le](https://latex.codecogs.com/png.latex?%5Cle "\le") 5 km in Lower City	80.8%
Trip Flows ![\\ge](https://latex.codecogs.com/png.latex?%5Cge "\ge") 5 km in Lower City	19.2%
Trip Flows ![\\le](https://latex.codecogs.com/png.latex?%5Cle "\le") 2.5 km in Rural/Escarpment Area	40.9%
Trip Flows ![\\le](https://latex.codecogs.com/png.latex?%5Cle "\le") 5 km in Rural/Escarpment Area	86.4%
Trip Flows ![\\ge](https://latex.codecogs.com/png.latex?%5Cge "\ge") 5 km in Rural/Escarpment Area	13.6%

Analysis of Residuals

The best model minimized information loss conditional on the independent variables. Informed by the work of Moniruzzaman and Páez (2012) with walking trips in Hamilton, we were curious to examine in more detail over- and under-estimated trip flows. There were a total of 4 over-estimated trip flows and 256 under-estimated trip flows. Since the model is not Gaussian, there is no assumption that the distribution of the residuals will be symmetric. We hypothesize that discrepancies between the number of observed trips and the number of expected trips are due to the built environment, namely attributes along the quietest distance route that might influence cycling but that we were not able to capture in the model. With respect to over-estimated trip flows, there may be barriers along the inferred cycle route between zone of origin and destination that deter people from cycling between the two areas. The opposite may be true for under-estimated trip flows. It is worth noting first that the majority of trip flows were under-estimated which indicates, to some extent, that there is more cycling in Hamilton than predicted by the model. This suggests that route characteristics that influence cycling may be influential and facilitating such travel. We provide a qualitative description of these trip flows next.

By plotting the negative residuals from the best model, after removing all origin-destination (O-D) pairs with zero trips, bicycle trip flows that were over-estimated were visualized in Figure . There were only 4 trip flows, 3 of which represent travel in a westward direction. The zone of destination for 3 of the 4 trip flows includes the university which is a major employment and educational institution, and thus acts as a strong push and pull factor for trips. This was identified with bike share trips in Hamilton as well (Darren M. Scott and Ciuro 2019). Schneider et al. (2015) also found that neighbourhoods with high levels of commute trips by bicycle are located near a university campus. This suggests that universities can attract a large number of trips. Upon further investigation, the Enhanced Points of Interest dataset catalogues each different building and unit within the university, meaning that there are several hundred destinations within the traffic zone. The count may have skewed the relative influence of the university by indicating more potential destinations, instead of one institution, leading to over-estimation. The zone of destination for the other trip flow was also near the university, however the over-estimation was almost negligible. When analyzing the quietest distance routes for the O-D pairs that end at the traffic zone with the university, each route would require a bicyclist to cross a major highway or travel along an arterial road. At the route level, road networks with fewer highways or arterial roads have been found to increase the likelihood of making a trip by bicycle (Winters et al. 2010; Zhao 2014). Although we were able to provide statistical support for quietest routes that minimize distance, there are still roads and intersections in Hamilton that cannot be avoided and that still feature along routes that are less busy overall.

Similarly, by plotting the positive residuals, after removing all origin-destination pairs with zero trips, bicycle trip flows that were under-estimated were visualized in Figure . Given that the majority of trip flows were under-estimated, we visualized trip flows in different maps according to their characteristics. Figure shows a map of trip flows over 5 km and Figure shows trip flows under 5 km. One fifth of under-estimated trip flows, approximately 21%, had a quietest distance route between 5 and 25 kilometres. Trip distance is an important determinant of cycling for transport (Heinen, van Wee, and Maat 2010), which suggests that the distance between origin and destination could be the reason that these flows were under-estimated. Furthermore, approximately 17% of under-estimated trip flows occurred within the suburban neighbourhoods on the Niagara Escarpment. Fewer cycling trips were expected in this area of the city because bicycle trips are typically less likely in low density areas where there are fewer destinations that can be reached in short distances, as was found to be the case in the United States (Pucher and Buehler 2006). It is also worth noting in this case that Hamilton’s suburban areas have far less cycling facilities compared to the lower city, which reinforces the car-centric design of these neighbourhoods. Finally, there is a noteworthy cluster of trip flows in the city’s downtown core of 5 km or less. Nielsen and Skov-Petersen (2018) note that built environment attributes are effective at different spatial scales. They uncovered positive effects of cycling infrastructure within 1 km of the home on the probability of cycling, providing evidence that proximity to cycling facilities can influence transport mode choices (Nielsen and Skov-Petersen 2018). We hypothesize that this cluster was under-estimated because cycling infrastructure has been built more extensively in the downtown core and is likely normalizing travel by bicycle in this area. The connectivity of such infrastructure between zone of origin and zone of destination may not have been captured in the inferred routes used as the cost function, leading to under-estimation. Likewise, the downtown core features a higher density of destinations within a 1-5 km distance that people could comfortably reach by bicycle, compared to residential-only neighbourhoods.

Analyzing the residuals of trip flows can be a helpful practice for transportation planners to evaluate how well the existing cycling network meets the needs of bicyclists. This is particularly useful in developing cycling cities, like Hamilton, where local geographic analysis is needed to better inform future investments in infrastructure to better support mobility. Transportation planners can use the residuals to identify flows that are not well served by cycling facilities and uncover gaps in the network.

Limitations

Although there was no network autocorrelation in the final model, which indicates that it sufficiently explains the observed pattern, the findings may overemphasize the trip patterns of experienced bicyclists. Hamilton’s cycling mode share is 1.2% which means that it’s highly likely that bicyclists in the city at this time are “strong and fearless” or “enthused and confident” riders (see Geller 2006). This hypothesis is supported by the finding that approximately 21% of under-estimated trip flows were between 5 and 25 kilometres, which is longer than the conventional bikeable distance. New or inexperienced bicyclists would probably be uncomfortable travelling for such long distances. The CycleStreets documentation acknowledges that routes inferred by the algorithm “emulate the routes taken by a knowledgeable cyclist.” This means that the inferred routes used as a cost variable in our model may only be appealing to bicyclists who are experienced and potentially more comfortable navigating a developing cycling city with a fragmented cycle network. In this respect, the quietest-distance routes that best explained the pattern of cycling flows in Hamilton may not represent routes that would be considered “quiet” or safe enough by groups that are often underrepresented in cycling such as women, children, and older adults.

CycleStreets can infer a maximum of six routes that are rated fastest, quietest, and balanced using either distance or time. While the quietest distance routes best explained the pattern of cycling trip flows, these are not the only attractive or preferred routes between zones of origin and destination. There are other routes or combinations of routes that incorporate existing infrastructure which reflect individual tolerance mixing with traffic or infrastructure preferences. Routes travelled by the “strong and fearless” are not necessarily the same as routes travelled by the “interested but concerned.” Therefore, one of the limitations of using an open source routing algorithm is that it does not currently consider route preferences of bicyclists in Hamilton. However, it does give streets with infrastructure a higher quietest percentage score, and we know from the literature that bicyclists prefer separated and protected infrastructure (Buehler and Dill 2016). In another forthcoming paper, we used photo elicitation to explore whether some of the inferred routes were known to local bicyclists in Hamilton and confirmed that the algorithm does select routes that are indeed commonly travelled [Desjardins et al. 2020b submitted for publication].

Conclusion

The objective of this study was to address the following questions: 1) Which attributes at the zones of origin and destination influence cycling trip flows in Hamilton?; and 2) Which type of route best explains the pattern of travel by bicycle in Hamilton?. The use of a spatial interaction model is methodologically more holistic than trip generation analysis, an approach often used in the cycling literature (for instance, see Noland, Smart, and Guo 2016), because it considered attributes at the zones of origin and destination, as well as route characteristics to estimate bicyclist travel. Use of a routing algorithm like CycleStreets also constitutes a novel approach to overcome the limitation of travel surveys. CycleStreets enabled us to experiment with different types of routes that knowledgeable and experienced bicyclists may seek out. The model revealed that shortest-distance quietest routes that allow bicyclists to avoid traffic best explain the pattern of cycling trip flows in Hamilton. In addition, the availability of jobs and different land uses and destinations at the end of the trip were positive attractors of bicycle trips. Commercial locations and other destinations at the zone of origin, as well as topography, had a negative influence on the number of expected bicycle trips. Other important practical findings include that the misspecification in the analysis of bicycle trip flows is evident in the form of network autocorrelation - this has been known for other types of flows, but as far as we know, has never been reported in the cycling literature. By testing for network autocorrelation, we are confident in the final model, which not only accounts for various pull-push factors and cost measures, but also indicates that the model sufficiently describes the pattern observed. Finally, analysis of the model residuals to identify under- and over-estimated trip flows was also suggestive in terms of other information about potential cycling routes.

The approach adopted in this research also presents future opportunities to systematically investigate the built environment along the inferred routes. For instance, shortest-path quietest routes may have attributes that promote travel by bicycle, such as infrastructure or a large proportion of residential streets, which leads to more cycling than expected from the model. To test this assumption, environmental audits were conducted along quietest routes for a selection of origin-destination pairs that were under-predicted in order to document the presence or absence of features that may influence cycling (a similar approach was employed in Moniruzzaman and Páez 2012). The documentation of built environment attributes would contribute to our understanding of what bicyclists experience as they travel through a developing cycling city like Hamilton, as well as validate whether the inferred routes match where bicyclists do indeed travel. This is the topic of another forthcoming paper [Desjardins et al. 2020b submitted for publication].

Acknowledgments

The authors wish to express their gratitude to Yongwan Chun and Roberto Patuelli for sharing their R code for the Jacqmin-Gadda’s test. The authors would also like to thank the three anonymous reviewers for their constructive feedback. In addition, the following R packages were used in the course of this investigation and the authors wish to acknowledge their developers: cyclestreets (Lovelace and Lucas-Smith 2018), ggthemes (Arnold 2019), kableExtra (Zhu 2019), knitr(Xie 2014, 2015), rticles (Allaire et al. 2020), sf (Pebesma 2018), spdep (Bivand, Pebesma, and Gomez-Rubio 2013), tidyverse (Wickham et al. 2019), units (Pebesma, Mailund, and Hiebert 2016), and zeligverse (Gandrud 2017).

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