i
Sacramento’s Fix I- 5 Project:
Impact on Bus Transit Ridership
By
RACHEL A. CARPENTER
B. S. ( California Polytechnic State University, San Luis Obispo) 2008
THESIS
Submitted in partial satisfaction of the requirements for the degree of
MASTER OF SCIENCE
in
Civil and Environmental Engineering
in the
OFFICE OF GRADUATE STUDIES
of the
UNIVERSITY OF CALIFORNIA
DAVIS
Approved:
_____________________________________
Chair H. Michael Zhang
_____________________________________
Patricia L. Mokhtarian
_____________________________________
Alexander Aue
Committee in Charge
2010
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ACKNOWLEDGEMENTS
I would like to thank my committee chair and advisor, Professor Michael Zhang, for his
guidance, suggestions and financial support.
I would like to thank my committee members, Professor Patricia Mokhtarian and
Professor Alexander Aue, for their advice and constructive comments on my thesis.
I would like to show gratitude to my student colleagues Zhen ( Sean) Qian, Yi- Ru Chen,
and Wei Shen for their ever- present willingness to help, and also for their friendships.
Finally, I would like to thank my parents, Linda and Dave, and sister, Molly, for their
continued support and patience during my studies at UC Davis.
This research was funded by the Cal EPA.
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CONTENTS
Chapter 1 INTRODUCTION ............................................................................................... 1
1.1 Purpose ...................................................................................................................... 3
1.2 Analysis Scope .......................................................................................................... 3
1.3 Gap in Knowledge ..................................................................................................... 4
1.4 Response to the Event ............................................................................................... 5
1.4.1 City of Sacramento Traffic Operations Center ................................................... 5
1.4.2 Government Media Outreach ............................................................................. 7
1.4.3 Private Media Outreach ...................................................................................... 9
1.4.4 Transit Agency Outreach and Preparation ........................................................ 10
1.5 Organization of Analysis ......................................................................................... 11
Chapter 2 LITERATURE REVIEW .................................................................................. 13
2.1 Time Series .............................................................................................................. 14
2.1.1 Background ....................................................................................................... 14
2.1.2 Trend Components ........................................................................................... 17
2.1.3 Seasonal Components ....................................................................................... 19
2.2 Goodness- of- fit Tests .............................................................................................. 21
2.3 Multicollinearity ...................................................................................................... 23
2.4 Lagged Variables..................................................................................................... 24
2.5 Box- Jenkins ( ARMA) Models ................................................................................ 25
2.6 Intervention Analysis .............................................................................................. 27
2.7 Review of Relevant Past Studies ............................................................................. 29
2.7.1 Predicting Transit Ridership Using Multiple Regression ................................. 31
2.7.2 Transit Ridership and Intervention Analysis .................................................... 32
2.8 Summary of Literature Review ............................................................................... 34
Chapter 3 DATA DESCRIPTION ..................................................................................... 35
3.1 Methods of Data Collection .................................................................................... 35
3.2 Data Sample ............................................................................................................ 36
3.2.1 Regional Transit ............................................................................................... 37
3.2.2 Yolobus ............................................................................................................. 39
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3.2.3 Roseville Transit ............................................................................................... 40
3.2.4 North Natomas TMA ........................................................................................ 41
3.2.5 Yuba- Sutter Transit .......................................................................................... 42
3.3 Data Filtering........................................................................................................... 42
3.3.1 General Procedure ............................................................................................ 42
3.3.2 Special Modifications to General Procedure for Regional Transit................... 44
3.4 Independent Variables ............................................................................................. 45
3.5 Data Quality ............................................................................................................ 47
3.5.1 Automatic Passenger Counting Devices ........................................................... 48
3.5.2 Electronic Registering Fareboxes ..................................................................... 49
3.5.3 Manual Counts by Route Checkers .................................................................. 50
3.5.4 Manual Counts by Bus Drivers ........................................................................ 51
3.5.5 Additional Data Quality Considerations........................................................... 52
3.6 Data Cleaning .......................................................................................................... 53
3.7 Descriptive Statistics for Transit Ridership ............................................................ 57
3.7.1 Measures of Central Tendency ......................................................................... 57
3.7.2 Measures of Dispersion .................................................................................... 62
3.7.3 Discussion ......................................................................................................... 63
Chapter 4 MODEL BUILDING ........................................................................................ 65
4.1 Multiple Regression ................................................................................................ 65
4.1.1 Bus Transit Ridership and Gas Prices .............................................................. 66
4.1.2 Bus Transit Ridership and Unemployment Rates ............................................. 67
4.1.3 Bus Transit Ridership and Gross Domestic Product ........................................ 69
4.1.4 Bus Transit Ridership and Transit Fares .......................................................... 70
4.2 Sinusoidal Decomposition....................................................................................... 72
4.3 Intervention ............................................................................................................. 72
Chapter 5 RESULTS.......................................................................................................... 75
5.1 Eliminating Trends: Details of Multiple Regression............................................... 75
5.2 Eliminating Seasonal Components in the Data: Details of Sinusoidal
Decomposition .............................................................................................................. 81
5.3 Intervention Analysis: Details of the Fix I- 5 Impact............................................... 85
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5.4 Significance of Results ............................................................................................ 87
5.5 Discussion ............................................................................................................... 90
5.6 Implications for Transit Agencies for Future Road Closure Work ......................... 93
5.7 Threats to Validity ................................................................................................... 94
Chapter 6 CONCLUSIONS ............................................................................................... 96
6.1 Summary ................................................................................................................. 96
6.2 Future Work .......................................................................................................... 102
REFERENCES ................................................................................................................ 104
APPENDICES ................................................................................................................. 111
A. City of Sacramento Traffic Operations Center Visit, August 21, 2008 ................. 111
B. Original and Cleaned Transit Agency Ridership Data Sets ................................... 118
1. North Natomas TMA AM Ridership ................................................................... 118
2. North Natomas TMA PM Ridership ................................................................... 119
3. Roseville Transit AM Ridership .......................................................................... 120
4. Roseville Transit PM Ridership .......................................................................... 121
5. Yolobus Ridership ............................................................................................... 122
6. Yuba- Sutter AM Ridership .................................................................................. 123
7. Yuba- Sutter PM Ridership .................................................................................. 124
8. Regional Transit AM Ridership .......................................................................... 125
9. Regional Transit PM Ridership ........................................................................... 126
C. Independent Variable Data Sets ............................................................................. 127
1. Gas Price Independent Variable .......................................................................... 127
2. Unemployment Rate Independent Variable ........................................................ 127
3. Gross Domestic Product Independent Variable................................................... 128
D. Holiday and Limited Service Imputation Dates ..................................................... 129
1. Year: 2006 ........................................................................................................... 129
2. Year: 2007 ........................................................................................................... 131
3. Year: 2008 ........................................................................................................... 132
E. Ad Hoc Data Imputation Method Details ............................................................... 135
F. Histograms for Each Transit Agency ...................................................................... 136
G. Multiple Regression Model Selection .................................................................... 138
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H. Transit Agency Periodograms ................................................................................ 143
1. Yuba- Sutter AM Periodogram ............................................................................. 143
2. Yuba- Sutter PM Periodogram ............................................................................. 143
3. Yolobus Daily Periodogram ................................................................................ 144
4. Roseville Transit AM Periodogram ..................................................................... 144
5. Roseville Transit PM Periodogram ..................................................................... 145
6. North Natomas AM Periodogram........................................................................ 145
7. North Natomas PM Periodogram ........................................................................ 146
8. Regional Transit AM Periodogram ..................................................................... 146
9. Regional Transit PM Periodogram ...................................................................... 147
I. Intervention Analysis Model Results ....................................................................... 148
J. Goodness- of- fit Tests............................................................................................... 152
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TABLE OF FIGURES AND TABLES
Figures
Figure 1.1: The Fix I- 5 Construction Area ......................................................................... 2
Figure 1.2: City of Sacramento T. O. C. ............................................................................... 6
Figure 1.3: The Fix I- 5 Website Encouraged Transit ......................................................... 7
Figure 1.4: Informational Documents Regarding Fix I- 5 Closures .................................... 8
Figure 3.1: Plots of Original Roseville Peak- Period Ridership Data................................ 53
Figure 3.2: Roseville and Yuba- Sutter Transit Histograms .............................................. 59
Figure 5.1: Yuba- Sutter Transit AM Peak Periodogram .................................................. 82
Tables
Table 3.1: Data Collection Details .................................................................................... 36
Table 3.2: Transit Lines Servicing the Downtown Core .................................................. 43
Table 3.3 AM Peak Period Definitions of Each Data Set ................................................. 43
Table 3.4: PM Peak Period Definitions of Each Data Set ................................................ 43
Table 3.5: Sample Size of Each Data Set ......................................................................... 44
Table 3.6: Independent Variable Details .......................................................................... 46
Table 3.7: Fare Pricing Details ......................................................................................... 47
Table 3.8: Percent Imputed Data ...................................................................................... 56
Table 3.9: Measures of Central Tendency: Mean and Median ......................................... 58
Table 3.10: Yearly Means and Medians for Transit Agencies with Data Spanning 2006-
2008........................................................................................................................... ....... 59
Table 3.11: Means by Season for 2006, 2007 and 2008 ................................................... 61
Table 3.12: Means by Construction Period for 2008 ........................................................ 62
Table 3.13: Variance and Standard Deviation for Each Transit Agency .......................... 63
Table 4.1: Ridership- Gas Price Correlation Coefficients ................................................. 67
Table 4.2: Ridership- Unemployment Correlation Coefficients ........................................ 69
Table 4.3: Ridership- Fare Correlation Coefficients.......................................................... 71
Table 5.1: Adjusted R2 With and Without the GDP Independent Variable...................... 78
Table 5.2: Statistically Significant Predictors of Bus Transit Ridership .......................... 80
Table 5.3: Means by Construction Period for 2008 After Detrending Data ..................... 81
Table 5.4: Statistically Significant Periodic Components for Each Agency .................... 83
Table 5.5: Intervention Analysis Final Model Results ..................................................... 87
Table 5.6: Final Model Significance ................................................................................. 88
Table 5.7: Interpretation of Model Significance ............................................................... 90
Table 6.1: Significant Periodic Components of Each Transit Agency ............................. 99
Table 6.2: Intervention Model Summary ................................................................... 101
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ABSTRACT
The Fix I- 5 project was an engineering project that rehabilitated drainage and pavement
on Interstate 5 in downtown Sacramento, from May 30, 2008 to July 28, 2008. In order to
alleviate congestion, media outreach alerted commuters about projected traffic conditions
as well as advised alternative modes or routes of travel. The construction schedule
included complete closures of north or southbound portions of Interstate 5. This study
analyzed the impact of the Fix I- 5 project closures on peak period bus transit ridership of
five transit agencies serving the downtown Sacramento core.
The results indicated that gasoline prices and unemployment rates were statistically
significant predictors of transit ridership, with increased gasoline prices and
unemployment related to increased bus transit ridership. All agencies had overall
increases in mean ridership during the study period, but there were also seasonal
variations in mean ridership. Removal of trend and seasonal components in the bus transit
ridership data sets was accomplished using multiple regression and sinusoidal
decomposition. Time series intervention analysis then estimated that the Fix I- 5 project
had little impact on mean number of bus riders for all five transit agencies. Bus transit
agencies with main service areas closest to the Fix I- 5 project were most affected, with
ridership increases of about three percent or less attributable to Fix I- 5. This study did not
analyze the impact of Fix I- 5 on other modes of transportation, which may have been
more affected than bus transit ridership.
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CHAPTER 1 INTRODUCTION
Interstate 5 ( I- 5) is a major interstate that runs north- south, connecting Mexico to Canada
through California, and was started in 1947 by the Federal Highway Administration. The
downtown Sacramento portion of I- 5 was completed in the 1960’ s and is nicknamed the
“ Boat Section” because it was constructed below the water level of the Sacramento River,
which runs adjacent to the freeway ( Caltrans, 2008). In order to construct the boat section
of the freeway, Caltrans had to initially drain this section, and engineer a drainage system
of pipes and pumps. The boat section was manually monitored during each winter season
to ensure pumps were working properly.
After over 40 years and without major renovation, pavement cracking and sediment
accumulation required the boat section to undergo repair, and an opportunity was
provided for drainage system upgrades. The California Department of Transportation
( Caltrans) Engineers’ Estimate projected that the rehabilitation of drainage and pavement
of Interstate 5 in downtown Sacramento, dubbed “ Fix I- 5,” would take 305 working days
at a cost of more than $ 44 million ( C. C. Myers, Inc., 2009). On February 2, 2008, a
Rancho Cordova- based engineering firm, C. C. Myers, Inc., won the Fix I- 5 project bid
with a proposed 85 working days and 29 night and weekend schedule at a substantially
lower cost of $ 36.5 million, with financial incentives for earlier completion ( Caltrans,
2009). Aggressive and compressed construction schedules are not novel for C. C. Myers.
Their resume includes more than 17 emergency projects for the State of California,
including emergency work on the San Francisco Bay Area’s 2007 MacArthur Maze
meltdown ( C. C. Myers, Inc., 2009). Although not emergency work, the Fix I- 5 project
specifically included a reconstructed six- inch pavement slab, an upgraded drainage
system, new de- watering wells, and installation
( Solak, 2008). The project was completed in a shorter period than predicted, from May
30, 2008 to July 28, 2008 in 35 days and 3 weekends
The Fix I- 5 construction schedule
portions of Interstate 5 through Sacramento
emergency construction.
Sacramento each day ( Schwarzenegger, 2008).
periods, traffic congestion could increase nineteen times (
closure periods, traffic was detoured to arterial streets and other freeways.
alleviate congestion, media outreach alerted commuters about projected traffic conditions
as well as advised alternative modes of travel. Employers, including
government which is one of the largest employers in the area with 75,000 commute
encouraged employees to use alternative modes of travel (
Figure 1.1: The Fix I- 5 Construction Area
of electronic monitoring equipment
. using full unidirectional closure
periodically closed entire northbound or southbound
Sacramento, a relatively new technique for non
Approximately 200,000 vehicles travel on Interstate 5 in
mento Reports projected that during closure
Schwarzenegger, 2008
California state
Schwarzenegger, 2008
2
closures.
, non-
2008). During
In order to
commuters,
2008).
3
1.1 Purpose
The main objective of this analysis is to examine the effect that the Fix I- 5 project had on
commuters' mode choices, more specifically bus transit ridership ( supplementary studies
are examining the impact of Fix I- 5 on other modes of travel). This objective includes the
determination of whether the Fix I- 5 project caused changes in mean bus transit ridership
levels, whether this effect on ridership was permanent or temporary, and the magnitude
of the effect. This research includes not only those statistics, but also provides
information for service changes for bus transit agencies that need to prepare for future
planned construction work, which includes freeway closures such as Fix I- 5, and also for
unplanned events which force closures.
1.2 Analysis Scope
The primary focus of media outreach was to suggest alternate transportation for those
who commute on I- 5. State governments and other employers with a large number of
employees in the downtown Sacramento core urged employees to use alternate
transportation during the Fix I- 5 period. Consequently, this study analyzed bus transit
agencies’ data from the morning ( AM) and evening ( PM) peak periods. The boundaries
of the downtown core were defined as follows: the south boundary defined by the 50/ 80
freeway, the north boundary defined by Richards Blvd, the west boundary defined by the
Sacramento River and the east boundary defined by the Business 80/ 99 freeway. Bus
stops directly below freeway boundaries were considered part of the downtown core.
This corresponds to other transit agencies’ definitions of downtown Sacramento. Since
this analysis focused on commute behavior, only inbound ridership was considered for
the AM peak period, while outbound ridership was considered for the PM peak period.
4
Inbound trips are defined as those trips with a final destination within the downtown core,
while outbound trips originate within the downtown core but have a final destination
outside it. The AM peak period is the primary morning commute period, but specific
hours varied by transit agency. The PM peak period is the primary afternoon commute
period and also varied by transit agency. In general, the peak periods occurred between
the hours of 5: 00AM to 9: 00AM, and 3: 00PM to 7: 30PM. In order to accurately assess
bus transit ridership in the downtown Sacramento area, this analysis employed bus transit
ridership counts for five transit agencies which provide commute service to the
Sacramento downtown core, including: Yuba- Sutter Transit, Yolobus, Roseville Transit,
North Natomas Transportation Management Association ( TMA) and Sacramento
Regional Transit.
As state workers comprise 75,000 commuters in Sacramento, and many state agencies
have headquarters in the downtown core, the commute choices made by that group likely
had a sizable impact on this study’s data sets.
1.3 Gap in Knowledge
In general, many studies have examined transportation- related data using time series
methods, although not many have examined bus transit ridership. Few time series studies
have analyzed bus transit ridership affected by an outside event ( an intervention) using
intervention analysis. To date, there are no known studies that examine the intervention
of construction work on bus transit ridership.
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1.4 Response to the Event
Many public and private agencies united to publicize, prepare and provide for public
safety for the Fix I- 5 project. These measures included public outreach, intercity and
interagency partnerships including the City of Sacramento, City of West Sacramento,
Sacramento Area Council of Governments, Downtown Sacramento Partnership, and the
Old Sacramento’s Merchant’s Association. Other efforts included announcements via
changeable message signs and highway advisory radio, and California Highway Patrol
enforcement in the construction area. Much media outreach was done to warn commuters
about traffic conditions and suggest alternative modes of travel. Additionally, various
media sources made information about up- to- date information regarding the Fix I- 5
project’s progress easily available to the general public. The Governor’s Executive Order
( S- 04- 08) cited Assembly Bill 32, the California Global Warming Solutions Act of 2006,
and advised alternatives to widely used single- occupant vehicle commuting including
telecommuting and public transit. Some of the private entities that provided information
included News 10, the Sacramento Bee, Sacramento Region 511, and Capital Public
Radio, as well as some private business websites. Transit agencies responded to the Fix I-
5 project by media outreach that advertised the convenience and availability of transit.
1.4.1 City of Sacramento Traffic Operations Center
An operational tactic for traffic management is the use of traffic operations centers
( TOC). The City of Sacramento’s single jurisdiction, single agency TOC is operated by
the City of Sacramento Traffic Engineering Services Department and funded by Measure
A, the gas tax. The goal of their TOC is twofold; first, they must make Sacramento City’s
6
transportation network efficient for all transportation modes, and second, they must make
the system reliable. Many steps were taken by the TOC in order to ensure their
responsibilities were fulfilled during the Fix I- 5 project. Planning steps included ( City of
Sacramento, 2008):
• Identification of potential problem corridors
• Signal maintenance
• Construction of Synchro ( transportation modeling software) Model
• Modified signal timing plan
• Coning & striping plan
The TOC makes use of many tools for
network monitoring and operation,
especially useful during the Fix I- 5 project,
including ( City of Sacramento, 2008):
• Closed- circuit television ( CCTV)
• Advance signal control systems
• Sacramento Police Department Helicopter
• Sacramento Police Officers
• Signal and signage crews
• Traffic cameras ( 8 Cameras in 2 streams)
• Multi- agency Construction Advisory Team ( CAT)
• Traffic Alerts
• Media Contacts
Figure 1.2: City of Sacramento T. O. C.
7
A more detailed summary of the City of Sacramento TOC, based on a field visit on
August 21, 2008, is provided in Appendix A.
1.4.2 Government Media Outreach
Although all of the sources provided useful
information, the official Fix I- 5 website, supported by
Caltrans, was the most comprehensive and accessible
( although no longer active circa August 2008). This
website included daily updates ranging from
construction updates to detours. It included sections
on current work and a history of the portion of I- 5 to
be repaired ( the Boat Section). It also included useful links such as 511 Travel Info, Live
Traffic Cameras, and Commute Alternatives. It also provided links to many downtown
area businesses, some offering specials to entice people to stay downtown and avoid peak
period travel.
Caltrans also hosted three public meetings regarding Fix I- 5 in Downtown Sacramento,
Natomas and South Sacramento. They gave numerous presentations to audiences
including state and local government agencies, residential organizations, private
businesses and public officials, and reached an estimated 10,000 people.
In addition to the Fix I- 5 website and public meetings Caltrans provided public
informational documents. They sent out an email to all Sacramento Personnel
Departments which included recommended alternatives to normal work days, including
Figure 1.3: The Fix I- 5 Website
Encouraged Transit
8
revised work schedules, telecommuting and public transportation. Caltrans provided
paycheck stuffers to Sacramento Area employers through Public Outreach Contractors.
This document advised departments to reschedule or postpone meetings and events that
draw people to downtown. It also informs about a Cal EPA hotline set- up for state
workers who needed commute assistance during the Fix I- 5 project. Caltrans outreach
contractors made information cards available to Sacramento businesses located in the
downtown area. These cards provided basic facts about the Fix I- 5 project, as well as
provided the Fix I- 5 website address.
Figure 1.4: Informational Documents Regarding Fix I- 5 Closures
Additionally, Assembly member Dave Jones' office sent out a letter to his constituents
warning them about the Fix I- 5 project, and traffic delays they might encounter. He also
encouraged alternate forms of transportation during construction, as well as encouraging
shopping or dining with downtown merchants during peak hours.
Although not as comprehensive as the official Fix I- 5 website, the City of Sacramento
website provided information about the Fix I- 5 project. The City of Sacramento also
provided parking promotions for six of their parking garages for most of the duration of
the Fix I- 5 project.
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1.4.3 Private Media Outreach
Many private agencies also provided information regarding Fix I- 5. In general, these
postings included general and up- to- date information about the Fix I- 5 Project, but some
businesses provided unique information. The News 10 website allowed people to
“ comment, blog and share photos;” an option not available on the Fix I- 5 website. This
feature allowed users to share alternate routes through blogs. It also provided Sacramento
travel times, as well as easy- to- read color- coded maps that showed lane closure
information. The Sacramento Bee provided coverage regarding the Fix I- 5 project,
through their newspaper publication and website, which provided mobile alerts, a blog
jam, and a complete listing of the Fix I- 5 stories which were published in the Sacramento
Bee newspaper. The Sacramento Region 511 website permanently provides information
about traffic, transit, ridesharing and bicycling. They provided minimal coverage
regarding the Fix I- 5 project, but links to information on transit providers, finding
carpools and vanpools, and a guide to bicycle commuting may have been particularly
useful to downtown commuters. Capital Public Radio’s website provided information
about Fix I- 5, including a clever ‘ Jam Factor’ scale on their website showing congestion
levels on Sacramento area freeways including both north and south bound I- 5. Additional
Sacramento area businesses posted information about the Fix I- 5 project including the
NBA Sacramento Monarch’s Basketball team, Natomas Racquet Club, California State
University Sacramento, Talk Radio 1530 KFBK, and YouTube.
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1.4.4 Transit Agency Outreach and Preparation
To prepare riders for the Fix I- 5 construction, Regional Transit ( RT) posted a press
release on their website encouraging people to take transit during the construction period.
With additional funding from Caltrans, RT was able to provide supplemental bus and
light rail services that increased both capacity and reliability during their peak commuting
hours. RT kept ten buses on standby during the construction period and advised
passengers to take earlier buses when possible. RT also reminded the public of the 18
park- and- ride lots available throughout Sacramento.
To prepare for the I- 5 construction, Yolobus provided an I- 5 Construction Options guide
in their newsletter. The guide warned passengers of delays and advised them to take
earlier morning buses to avoid these delays. Yolobus also took several measures to
alleviate overcrowding and delays during the construction period. They had up to two
supplemental buses on standby in case other buses were running behind. Yolobus added
two morning and two afternoon express trips to both route 45 ( service between
Sacramento and Woodland) and to route 43 ( service between Sacramento and Davis). In
addition, Yolobus sold discounted Capitol Corridor train tickets in order to encourage
drivers to take transit during the construction period.
To accommodate for the Fix I- 5 construction, Roseville Transit posted information on
their website regarding the Governor’s Executive Order urging government employees to
take transit during the construction. Roseville Transit encouraged new commuter
passengers and listed on their website the AM and PM commuter routes with available
seating.
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In preparation for the Fix I- 5 construction, North Natomas T. M. A. posted information in
a specific Fix I- 5 email newsletter about service changes for the construction period,
including loop and route changes that went into effect on June 2, 2008. Additionally,
supplemental shuttles and drivers were provided to ease the impact of the anticipated
higher ridership during the construction period. The T. M. A. was able to provide
additional shuttles with extra funds provided by Caltrans for the construction period, but
were required to provide daily counts of AM and PM shuttle riders for each loop. North
Natomas T. M. A. also created a special shuttle hotline for passengers to call for up- to- date
information about route changes and delays during this period.
In addition to the supplemental schedules, Yuba- Sutter took several other measures to
accommodate for the I- 5 construction. Route or schedule changes were not made with the
exception of minor detours during northbound I- 5 closures. Second, Yuba- Sutter had
additional buses on call in the event that any early morning buses became overcrowded.
Third, Yuba- Sutter used all buses during the construction period, whereas they normally
keep three buses non- operational. And finally, Yuba- Sutter closely monitored traffic
conditions, which was made possible by improved connections with Caltrans, the City of
Sacramento, and Regional Transit.
1.5 Organization of Analysis
The organization of the analysis is as follows. Chapter 2 provides an overview of
important concepts in time series which is used in this analysis. It also describes past
studies analyzing bus transit ridership, and more specifically those few that used
intervention analysis to analyze the impact of an intervention on a time series data set.
12
Chapter 3 describes the transit agency data, including details of each agency’s samples
and collection methods, as well as data quality considerations. It also includes
information about data cleaning, which was needed to adjust for holidays and limited
service days. Finally, data exploration is presented in two sections: measures of centrality
and measures of spread for the transit agencies’ data sets. Both sections begin by briefly
defining the statistics included in that section. Chapter 4 describes the methodology for
eliminating trends and cyclic components, and the intervention analysis which examined
the impact of the Fix I- 5 construction on bus transit ridership. Chapter 5 presents the
results of the intervention analysis for each agency, in addition to implications for bus
transit agencies for future freeway closures. To conclude, Chapter 6 summarizes the
analysis methods and results, and gives recommendations for future work.
13
CHAPTER 2 LITERATURE REVIEW
Many studies have been conducted analyzing variables that impact transit ridership,
primarily using two statistical methods of analysis; time series, and multiple regression.
Some, categorized as econometric studies, use those two statistical methods with a focus
on economic theory.
Time series is used to analyze a series of data points, to understand the underlying order
or context of the data. A review of the literature ( Cryer, 1986; Shumway and Stoffer,
2006; Brockwell and Davis, 2002; Anderson, 1976; Kendall, 1973; Kyte et al., 1988)
identified a host of different methods used to model time series data, including but not
limited to univariate and multiple time series models and transfer function models.
Simple regression is used to analyze the change in a dependent variable as an
independent variable changes or is manipulated, while multiple regression uses multiple
independent variables ( Mann, 2004). However, all regression models assume that the
error terms, and therefore response variable observations, are uncorrelated ( Kutner et al.,
2005). In contrast, time series data often contains observations which are serially
dependent ( Box and Tiao, 1975). Additional regression methods have been developed
that are used for autocorrelated time series data. They employ typical regression
techniques, but model the error term using time series models ( Tsay, 1984).
Econometrics uses statistical methods to study economic principles ( Tinbergen, 1951).
The primary focus is the evaluation of economic theory using statistical methods.
Discussions of strict and weak stationarity, autoregressive models, and lag structures are
found in both econometric time series literature and statistics time series literature.
14
However, a standard tool in econometrics is to use the structural econometric time series
approach ( SEMTSA), which uses Box- Jenkins methods but imposes a priori restrictions
on the equations based on economic theories ( Christ, 1983). Further, this approach is
commonly simplified to vector autoregression models ( VAR) which omit the moving
average polynomial of the ARIMA model ( Zellner and Franz, 2004).
Time series was the primary method of analysis used in this study, as autocorrelation was
likely to be present in the transit ridership data. Time series analysis encompasses a wide
range of models which can handle multiple scenarios within data sets. Time series
intervention analysis was used, which provided a methodology to determine the effects of
one event on a series. This study used the ARIMA class of time series models, which
specify only causality and invertibility as restrictions on the parameters, a feature that
was an advantage over models which place additional assumptions on the parameters.
Regression was also used to analyze the relationship between multiple independent
variables and transit ridership, and for eliminating trends related to independent variables
in the transit ridership data sets.
2.1 Time Series
Because time series is a method less commonly used in the field of transportation
engineering, a brief overview is given in the following sections.
2.1.1 Background
A time series ( xt) is a sequence of observations collected over time for one variable. Time
series can be either continuous or discrete depending on how the observations have been
collected. A time series is continuous if observations are taken continuously over time
15
whereas the series is said to be discrete if observations are taken at specific times
( Chatfield, 1975). Time series is concerned with chronologically ordered observations of
time. Data that is observed over time, both discrete and continuous, is common across
many disciplines. In the field of engineering, some examples include series observed over
time such as traffic counts and water quality measures. There are many examples in
economics, including profits, interest rates, as well as overall economic indicators such as
gross domestic product and unemployment rates. In meteorology, a common observation
that constitutes a time series is temperature.
Because future observations could be hard to predict, a time series ( xt) is more technically
a realization ( sample function) of a stochastic process ( Xt), which is a family of random
variables ( Brockwell and Davis, 1987). Time series analysis focuses on studying a time
series realization ( xt of Xt) in order to gain insight into the stochastic process ( Xt) ( Aue,
2009). In practical time series analyses, much of the work is devoted to transforming a
nonstationary time series into a stationary process ( Fuller, 1976). Conceptually,
stationarity is similar to equilibrium within a system. A time series is strictly stationary if
its probability structure is not affected by time ( Anderson, 1971). In other words, the joint
probability distribution of xt… xt+ n, is equivalent to the joint probability distribution of
xt+ h… xt+ h+ n for all t,..., t + n  T and h such that t + h,… , t+ h+ n  T. ( Montgomery et al.,
2008).
A typically less strict definition of stationarity ( for cases where the variance is finite) is
called weak stationarity, and is often used because distribution functions are commonly
unknown. In order for a time series to be weakly stationary there are two conditions
( Shumway and Stoffer, 2006; Brockwell and Davis, 2002):
16
1. The first moment of xt is independent of time, t, and is constant.
2. The autocovariance function, defined as       	 
    ,      , which
depends only on lag h, and is independent of t.
One important example of a stationary process is called white noise. White noise is
commonly denoted     ~    0,    , where Zt is a sequence of uncorrelated random
variables with zero mean and finite variance, σ 2 ( Shumway and Stoffer, 2006). White
noise is an important building block in time series analysis, as it is the foundation for
many more complex processes ( Cryer, 1986). It is interesting to note that term white
noise is derived from white light which is composed of a continuous distribution of
wavelengths with the implication that white noise is composed equally of oscillations at
all frequencies ( Shumway and Stoffer, 2006). Furthermore, if the series of shocks
generated are not just uncorrelated ( a white noise process), but are independent and
identically distributed, the sequence is called i. i. d., denoted     ~     0,    ( Anderson,
1976). Further, if the series is normally distributed, it is both white noise and i. i. d.. Often,
a time series ( Xt) can be well- explained by a trend component ( mt), a seasonal component
( st), and a zero mean, random error component ( Yt) ( Chatfield, 1975). The process can be
represented in the form
           .
The following provides a short description of each component, although it should be
noted that a time series model may exhibit any combination of these components:
The trend component ( mt): Encompasses long run changes in mean. Trends can
have many underlying causes including, but not limited to, changes in economic
17
conditions, technological changes and changes in social custom ( Farnum and LaVerne,
1989).
The seasonal component ( st): Encompasses cycles at any recurrent period. This
component can include obvious seasonal or annual cycles, or less apparent cycles
occurring at any fixed period such as a daily, weekly, or quarterly basis.
The noise component ( Yt): A zero mean, random error component.
There are multiple methodological approaches to the analysis of time series data, more
specifically to the removal of trend and seasonal components, including the use of both
the time and frequency domains. Analysis in the time domain bases inference on the
autocorrelation function, while analysis in the frequency domain pertains to inference
based on the spectral density function. Both domains can be used to eliminate seasonal
components, while trend components can only be eliminated in the time domain. In this
study a decomposition method was used which identified and separately removed the
trend and seasonal components from the series. The removal of trend components used
methods associated with the time domain, and the removal of seasonal components used
methods associated with the frequency domain.
2.1.2 Trend Components
Analysis in the time domain includes methods for removal of both the trend and seasonal
components including least squares estimation, smoothing with moving averages,
differencing, small trend methods, and moving average estimation ( Aue, 2009).
Additionally, trend components can be removed using regression techniques ( Yaffee,
2000). Aue ( 2009) provides a detailed description of each method. This study used
18
multiple regression to remove trend components. The multiple regression method is
discussed below, in addition to differencing which is referred to in later sections:
Multiple Regression: When there are four predictor variables,    ,   ,  ! ,  " as in
this analysis, the model is formulated as
   # $  #        #      # !  !   # "  "   %  .
In this study, the combination of the predictor variables ( #        #      # !  !   # "  "  )
constitutes the trend component, while the regression error term ( %  ) constitutes both the
seasonal and error terms ( st + Yt). As discussed previously, standard linear regression
models assume that the error terms, %  , and therefore, response variable observations,   ,
are uncorrelated ( Kutner et al., 2005). Time series data, on the other hand, often contains
observations which are serially dependent ( Box and Tiao, 1975). Therefore,
modifications to standard linear regression would be necessary, including modeling the
error terms as time- series autoregressive moving average models ( Tsay, 1984; Ostrom,
1978).
Differencing: Applies the difference operator to the original series in order to
create a new, stationary series. The lag & difference operator ( ' ) is defined as ( Shumway
and Stoffer, 2006):
' ( x *  +  , +  - . .
In practice, it is common to denote the use of the difference operator by using the
backshift operator, B. In this case,
' ( x *  +  , +  - .   1 , 0  . + 
19
2.1.3 Seasonal Components
This study’s decomposition method removed the trend components using multiple
regression, and removed seasonal components from the series using a frequency domain
approach. The frequency domain, also referred to as the spectral domain, pertains to
inference based on the spectral density function. A time series can be decomposed into
periodic components, each of which contains variation at that period’s frequency, whose
variations combine together to cause the overall variation in the time series. Therefore, a
time series can be well represented as the sum of significant periodic components
( Chatfield, 1980):
+   1 A 3 cos 7 2πω 3 t :  ;
< =   B 3 sin 7 2πω 3 t :   
where Aj and Bj are uncorrelated random variables with mean zero and variances both
equal to σ 2 and A    B
, where d is the period of the cycle. For example, if there is an
annual cycle and the data set contains monthly data points, one period, d, could be 12.
Exploratory analysis using the periodogram can help to determine genuine periodic
( seasonal) components within the time series, Xt. The definition of the periodogram for
{ X1,…, Xn} is given below ( Brockwell and Davis, 2002):
  A   2 C 1 D E 1 X * e H * ω
I
 =   E

where ω is the frequency. The periodogram is the graph of A and   A  and is an
estimation of the power spectral density function. Although the periodogram is not a
consistent estimator of the spectral density because the variance of   A  does not
20
decrease as the sample size, n, increases, it will be used in this analysis to determine
periodicities, which is a common practice ( Chatfield, 1975). If the periodogram is
constructed for , π P ω P π the area under the periodogram represents the variance of
the time series ( Brocklebank, 2003). Therefore, peaks in the periodogram generally
indicate frequencies that can explain a significant part of the total variance. For example,
a periodogram that displays a large peak at frequency A  0.25, indicates a period,
S  4, which for quarterly data indicates an annual cycle. If a periodogram does not
display any obvious peaks, all frequencies are contributing to the series’ variance, and the
series may even be a white noise process. The variance by cycles can be decomposed as
follows ( Aue, 2009),
 7 A < :  S U 7 A < :  2 S V 7 A < :
where S U 7 A < :   
√ I Σ   cos  2 C A < Y  I 
=   and S V 7 A < :   
√ I Σ   sin  2 C A < Y  I 
=   . As
discussed, the periodogram can help to determine seasonalities and peaks in the
periodogram can signify a genuine periodic component which explains a large portion of
the variance in the time series. However, it is possible that peaks may occur because of
random fluctuations in the sample ( Priestley, 1981).
This study used spectral analysis of variance to determine whether peaks in the
periodogram explain a larger portion of the variance than is expected with sequences
such as white noise and ARMA processes.
21
2.2 Goodness- of- fit Tests
Ideally, after trend and seasonality are removed, the remaining series will be a white
noise process. There are many goodness- of- fit tests to determine whether the residuals
are white. For an extensive review of diagnostic checks, refer to Li ( 2004). For the
purposes of this study, four goodness- of- fit tests will be utilized, including the sample
autocorrelation function ( ACF), the portmanteau test ( Ljung- Box modification), the rank
test, and a test of normality including the squared correlation ( R2) based on a qq plot. An
explanation of the four goodness- of- fit tests is described below:
1. The sample autocorrelation function ( ACF): The autocorrelation function
and sample autocorrelation functions at lag h are defined as ( Anderson, 1976):
ρ Z     $ ρ [ Z   [   [ $
For a series, Y1,…, Yn, with a large sample size, n, the sample autocorrelations are i. i. d.
with zero mean and variance   I
( Brockwell and Davis, 2002). Therefore, in order to test
for randomness, a plot of the sample autocorrelation function for any amount of lags h
should show should that 95% of those lags fall within the bounds \   . ] ^
√ I if the process is
i. i. d. ( Aue, 2009).
2. The portmanteau test ( Ljung- Box modification): In order to test for
randomness, originally, Box and Pierce ( 1970) suggested the portmanteau test, and
developed the statistic, Q, as
Q( _ ̂   D Σ _ ̂   a   <
=  
22
where _ ̂ is defined as the autocorrelation function. Ljung and Box ( 1978, p. 298) suggest
that the Box- Pierce methodology produces “ suspiciously low values of Q( _ ̂  …” and
propose a modified version as
Q( _ ̂   D  D  2  Σ  
I - < _ ̂   a   <
=  
where Q can be approximated as a chi- squared distribution with h degrees of freedom.
The hypothesis that the residuals are i. i. d can be rejected at the level α, if b c d    - e   
( Brockwell and Davis, 2002).
3. The rank correlation test: The rank test is a test of randomness, to
establish whether there remains any systematization in the residuals. For a time series, a
trend can be determined by the correlations between the rank order of the time series
observations and their time values ( Kendall, 1955). In total, there are   b 
  
n  n , 1  pairs, where P designates the number of positive correlations, and Q
designates the number of negative correlations. P is represented by Kendall’s τ, called the
coefficient of rank correlation:
τ  f  g h i
I  I -   
The coefficient of rank correlation ranges between 1 ( perfect positive correlation) and - 1
( perfect negative correlation), with τ  0 representing an independent, white noise
process. Refer to Kendall ( 1955) for further explanation.
4. R2 based on a qq plot: In order to assess the normality of the residuals, the
squared correlation ( R2) value can be calculated based on a quantile- quantile plot ( qq
plot). A qq plot is a graph that compares the quantiles of two distributions. For this study,
the first data set is the ordered residuals from the fitted model assuming a mean zero,
23
variance one process denoted as Yj. The second data set is ordered statistics from a
random normal sample with mean μ, variance σ 2 denoted as nj. If the model residuals are
normally distributed, the pairs ( nj , Yj) should have a linear relationship ( Shumway and
Stoffer, 2000). Hence, perfect normally distributed residuals would display an R2 value
equal to one. If the R2 value is too small ( based on the level α), then the assumption of
normality must be rejected. More specifically, the R2 value can be computed as follows,
noting that Φ 3 represents the normal distribution:
R   k Σ  D < , l <  Φ 3 I <
=   m 
Σ  D < , l <  I <
=    Σ Φ 3 I <
=   
Refer to ( Shapiro and Francia, 1972) for the critical values of R2.
For residual testing in this study, lag h = 20 was used which is commonly used in time
series residual testing ( Shumway and Stoffer, 2000).
2.3 Multicollinearity
Multicollinearity occurs when independent variables are highly correlated in a multiple
regression model ( Kutner et al., 2005). This means that the two correlated variables are
not providing independent information which helps to predict the dependent variable.
Severe cases of multicollinearity must be corrected, because the result can be unstable
regression coefficient estimates. Further, multicollinearity is often indicated by very large
standard errors, even though the coefficients are still the best linear unbiased estimators
( BLUE) ( Washington et al., 2003). If two independent variables are highly correlated, it
is difficult to determine which variable is explaining more variation in the dependent
variable ( both variables’ standard errors will become large). Another test for the presence
24
of multicollinearity is the comparison of correlation coefficients to regression
coefficients. If their signs are different (+/-) then multicollinearity should be further
investigated ( Kutner et al., 2005). Two methods for detecting multicollinearity are the
variance inflation factor and the condition index.
1. The variance inflation factor ( VIF) is defined as  n  o  p  q i  r s t

 q t  i where
# p t are the estimated standardized regression coefficients and   t   is the variance of the
error term1for the correlation transformed model ( also called the standardized regression
model). The multiple regression model discussed previously was    # $  #       
#      # !  !   # "  "   %  , while the standardized regression model is   t  #   t    t  
#  t   t   # ! t  ! t   # " t  " t   %  t . If the mean of the VIF values is greater than 1, serious
multicollinearity may exist ( Kutner et al., 2005).
2. The condition number ( κ) is defined as the largest condition index ( CI). It
is defined as u  v w x y z w x { | where λmax is the largest eigenvalue, and λmin is the smallest
eigenvalue of the  }  matrix. Condition numbers between 5 and 10 indicate some
dependence, while CI values of 30 and above signify strong dependencies ( Belsley et al.,
1980).
2.4 Lagged Variables
In time series regression models, it is often the case that time lags need to be included
( Ostrom, 1978). For example, there is a time lag associated with exposure to carcinogenic
substances and the development of cancer. If there are time lags between a change in the
1 In this study, the error term ( when testing for multicollinearity) includes a seasonal and noise term ( st +
Yt).
25
independent variable and the effect on the dependent variable, a lag term should be
included in the regression model. In this study, the explanatory variables were unleaded
regular gas prices, unemployment rates, gross domestic product and transit fare prices,
each of which could have a time lag with transit ridership. However, a time series study
of Portland, Oregon transit ridership between 1971 and 1982 focusing on factors that
affect ridership show that neither gas price ( aggregation level unspecified) nor county
employment rates show a time lag for bus transit ridership ( Kyte et al., 1988). However,
Kyte et al. found a time lag between transit fare prices and ridership. The authors stated
that the largest response in ridership to the fare increase occurred almost immediately,
and then decayed at a measurable rate for three months. Prior studies have not determined
a set of independent variables that consistently predict bus transit ridership. The effects
of GDP on ridership have not been studied.
2.5 Box- Jenkins ( ARMA) Models
In the time domain, linear filters are often used to transform one time series into another,
under the assumption of linearity, and can be defined as:
Y *  1 Ψ 3
∞
< = - ∞ X * - 3
where Ψ 3 ′ s are weights for each X * , and X * and Y * are the input and output time series,
respectively ( Chatfield, 1975; Montgomery et al., 2008). There are many types of linear
filters which can be applied to white noise to obtain a more complex linear time series. In
general, there are three major classes of linear filters, including autoregressive, moving
average and autoregressive- moving average filters. They are described below:
26
1. Autoregressive Process, AR( p): An autoregressive process can be
represented as:
        -    €      -     .
The equation’s conceptual interpretation is that the current time series observation is a
linear weighted combination of the p most recent past values of the same time series, plus
an error term ( Montgomery et al., 2008). The autoregressive polynomial is defined as
     1 ,     ,     , € ,     .
The roots of the polynomial      0    must lie outside of the unit circle to ensure that
an AR( p) process is stationary; a condition commonly referred to in time series literature
as causality ( Box et al., 2008).
2. Moving Average, MA( q): An moving average process can be represented
as:
     , ‚     -   , € , ‚ ƒ   - ƒ .
Observably, a moving average model assumes the current value is a linear weighted
combination of q lagged white noise terms. Further, a condition called invertibility is
imposed on the weights, θ 3 , to ensure a unique MA process for an autocorrelation
function ( Chatfield, 1980). The moving average polynomial is defined as
‚     1  ‚          €   ƒ  ƒ .
An MA( q) process is invertible if the roots of    ‚  0    are outside the unit circle
( Box et al., 2008). Invertibility and stationary are two separate conditions; an MA( q)
process will always be stationary.
3. Autoregressive- Moving Average, ARMA( p, q): An autoregressive- moving
average ( ARMA) model assumes that the current observation is a linear weighted
27
combination of the p most recent past observations from the same time series ( the AR( p)
portion), as well as q lagged white noise terms ( the MA( q) portion). An autoregressive-moving
average process ARMA( p, q) can be represented as
        -    €      -     , ‚     -   , € , ‚ ƒ   - ƒ .
An ARMA ( p, q) process is causal if the roots of the polynomial      0    lie outside
of the unit circle, and is only invertible if the roots of    ‚  0    are outside the unit
circle ( Box et al, 2008). The coefficients for causality are computed from the
expression Ψ     …  † 
‡  †  , while the coefficients for invertibility computed from the
expression Ψ     ‡  † 
…  †  .
2.6 Intervention Analysis
Gene Glass ( 1972, p. 463) coined the term intervention and described it as follows:
“ Observation of a variable Z at several equally spaced points in time yields the
observations ˆ   , ˆ  ,…, ˆ Š . Suppose that an intervention ( T) is made at some point in time
before time N into the process presumed to be controlling Z. The time- series is said to be
interrupted at a point in time, say D   less than  : ˆ   ,…, ˆ I h , Œ , ˆ I h    ,…, ˆ Š .” Box and
Tiao ( 1975) used the term intervention and constructed an analysis method to determine
the effect of an intervention, occurring at a known time in a time series. Their
intervention model is based on the basic transfer function model,
  ,   1  <
∞
< = $   - < ,     
where Xt, 1 represents the input series, while Xt, 2 represents the output series, which
constitutes common notation in transfer function modeling. In intervention analysis, it is
28
more common to replace Xt, 1 with Xt, and also to replace Xt, 2 with Yt. The basic
intervention model can be described:
   1  <
∞
< = $   - <   
where Xt and Yt are the input ( pulse/ step) and output ( ridership, after removal of trend
and seasonal components) series of the model respectively,  < is a linear filter and Nt
represents a noise sequence.  < is defined as
 <  Ž    a    /  
where Ž   is the cross- correlation between Xt and Yt, and σ 2 is the variance of each series.
In the case of intervention “ Œ  0   Σ  < ∞ < = $ 0 < is simplified with a rational operator of
the form T( B)  ’ “ ”  ’ 
•  ’  " where b is the delay parameter, and W and V help to provide
coefficients to represent more complicated indicator series built upon a step or pulse
function ( Brockwell and Davis, 2002, pp. 340- 341). The intervention term is
then Π 0    . For a series that might be best represented as an intervention causing a
temporary change in the response variable, a pulse indicator variable would be most
appropriate:
   — 01 ˜ ˜ ™ ™ Y Y  š Œ Œ ›
where t is time, and T is the period of the intervention. For a series that might be best
represented as an intervention causing a permanent change in the response variable, a
step indicator variable would be most appropriate:
29
   — 01 ˜ ˜ ™ ™ Y Y œ  Œ Œ › .
In general, the Box and Tiao intervention analysis methodology follows a five- step
process ( Box and Tiao, 1975):
1. Eliminate trend and seasonal components from the original time series
( Xt). This study eliminated trend components from the series through a multiple
regression, and eliminated seasonal components using sinusoidal decomposition with
cycles determined by the periodogram and cycle significance based on spectral ANOVA.
2. Use ordinary least squares ( OLS) regression to obtain a initial estimate of
 < , which represents the transfer model.
3. Model the residuals from the OLS regression as an ARMA( p, q) process,
which will represent the noise model. For model diagnostics, analyze the residuals using
goodness- of- fit tests.
4. Minimize the sum of squares, Σ ž ‡ Ÿ    ¡ 
… Ÿ    ¡  ¢   W, V, ¥ ¦ , θ ¦  I  = ¨ t    , where
m*= max ( p2 + p, b + p2 + q), in order to obtain final parameter estimates of both the noise
and transfer models.
5. Analyze the final model residuals using goodness- of- fit tests. This study
used the Sample ACF, qq plot, Ljung- Box test and rank test.
2.7 Review of Relevant Past Studies
Previous studies involving multiple regression and time series analysis are discussed.
Many studies have examined transportation- related time series data and used time series
methods to analyze the data. Kyte et al. ( 1988) reviews previous work in transportation
30
related time series, other than bus transit ridership. For example, Atkins ( 1979) analyzes
the effect of speed limit changes on traffic accidents in British Columbia in the 1970’ s
using intervention analysis. Additionally, studies that use vehicle miles travelled ( VMT)
forecasting models show that VMT can be predicted by independent variables that are
similar to those used to predict transit ridership. Common predictors include, but are not
limited to, gasoline price ( Schimek, 1996 ( 1521 and 1558); Goodwin et al., 2004; Gately,
1990) and income ( Schimek, 1996 ( 1521 and 1558); Goodwin et al., 2004; Gately 1990).
Dahl ( 1986) summaries previous research on gasoline consumption demand, VMT and
miles per gallon ( not just VMT), finding negative elasticities for price, and positive
elasticities for income. Elasticities measure the responsiveness of one variable to change
in another variable. Mokhtarian et al. ( 2002) analyzed induced demand with respect to
highway capacity expansion, and listed predictors of induced vehicle travel as changes in
population, demographics, the economy, mode and land use, but not highway capacity
expansion. Rose ( 1982, 1986) examines rail transit ridership using time series and
multiple regression techniques. Rose ( 1986) studies Chicago Transit Authority rail
ridership, more specifically, 11 years of monthly average weekday data. He used fares,
weekday service miles, cost of car trips ( including gas prices), and weather changes and
found that gas prices and service levels were significant predictors of rail ridership. But,
there are few studies that analyze bus transit ridership with time series models, a fact that
was confirmed by librarians at the Physical Science and Engineering Library at UC
Davis, and the Institute of Transportation Studies Library at UC Berkeley. Those
pertaining to transit ridership ( defined as both bus and rail, or just bus) are discussed
below.
31
2.7.1 Predicting Transit Ridership Using Multiple Regression
A number of studies use multiple regression techniques to determine factors that affect
bus transit ridership. Those studies take into account autocorrelation in the residuals to
ensure valid model results. The following presents studies which use multiple regression
as the primary analysis method. Agrawal ( 1981) analyzed Southeastern Pennsylvania
Transportation Authority’s City Transit Division’s annual full- fare adult ridership
between 1964 and 1974. Using multiple regression, he found that three factors were
statistically significant in affecting ridership and produced a multiple correlation
coefficient of 0.9985. The three significant predictors included average fare ( adult riders),
jobs in Philadelphia, and bus miles of service, while number of vehicles owned was not a
significant predictor. Lane ( 2009) applied regression techniques to monthly bus and rail
transit ridership data from nine US cities between January 2002 and April 2008, and
found that gasoline prices were a statistically significant predictor of changes in transit
ridership, while service characteristics and seasonality were not significant predictors.
Wang and Skinner ( 1984) analyzed fares, gas prices and monthly ridership data from
seven transit authorities across the United States, and using regression techniques, found
that as real gasoline prices increased, transit ridership increased, although by a small
amount. Also, they found that as real fares increased, ridership decreased. Taylor et al.
( 2009) analyzed transit ridership from 265 urban areas using 22 independent variables to
and show that the majority of transit ridership variation can be explained by variables
within the categories of regional geography, metropolitan economy, population
characteristics and auto/ highway system characteristics. They found a positive correlation
between ridership and gas prices, and a negative correlation between ridership and
32
unemployment levels. Gomez- Ibanez ( 1996) reported an increase in Massachusetts Bay
Transportation Authority ( MBTA) bus transit ridership in Boston, in part due to service
improvements such as phased station modernization and bus replacement, and transit
fares which increased less than the inflation rate. Their study also included income,
Boston employment, fares, and vehicle miles. Kitamura ( 1989) showed a causal
relationship between car ownership and transit use, more specifically that an increase in
car ownership leads to a decrease in transit use, using Dutch National Mobility Panel
weekly travel diary data. Cervero ( 1990) provides a broad overview, and summarizes
multiple empirical studies which show that there are many factors affecting transit trips,
including characteristics of the traveler such as age, income, auto access, trip purpose,
trip length, and also characteristics of the operating environments, such as land use and
location settings. Although each study used a different set of independent variables to
predict transit ridership, most of the studies that used multiple regression included gas
prices, fares, and economic indicators such as unemployment rates.
2.7.2 Transit Ridership and Intervention Analysis
In terms of transit ridership and intervention analysis, there is a scarcity of previous
studies. Kyte et al. ( 1988) use Tri- County Metropolitan Transportation District of Oregon
bus transit ridership on various aggregation levels ( system, sector and route levels)
between 1971 and 1982 to show that service level, transit fares, gasoline price, and
employment are statistically significant predictors of bus transit ridership. They also note
that to fully explain ridership demand, many more independent variables should be
considered. Kyte et al. ( 1988) used intervention analysis to model changes in bus transit
33
ridership resulting from eleven separate cases of changes in their predictor variables
including increased fares, system- wide service changes, and route- level changes, and
they observed that the occurrence of multiple events at one time makes it difficult to
isolate the impact of any single event on ridership. Their results showed that for the four
cases of fare increases, the result in terms of ridership is varied. The separate
interventions of system- wide service changes and gasoline supply shortages combine to
produce an intervention output of an additional 8,400 bus transit riders. Kyte et al. use
elasticities greater than one to determine significance of intervention results. Narayan and
Considine ( 1989) use intervention analysis to analyze two cases of fare increases, in April
1980 and April 1984, and their effects on monthly upstate New York transit ridership,
assuming that ridership could be decomposed into a trend, seasonal, intervention and
noise term. They assume that the intervention term is best represented as a step function;
an “ abrupt and permanent change” in ridership ( Narayan and Considine, 1989, p. 248).
Their methodology differs from the original Box and Tiao intervention analysis
methodology, as their model isn’t based on the transfer function model, but on regression
with correlated error terms, and eleven indicator variables for seasonality, indicator
variables for the two fare price increases, and an error term which they claim “ correct[ s]
for autocorrelated errors” ( Narayan and Considine, 1989, p. 249). However they didn’t
use ARMA models for the noise, and it is unclear how they corrected for correlation,
because they used t tests which require the removal of serial dependence, nonstationarity
and seasonality. Both fare interventions produced significant ridership decreases.
Considine and Narayan ( 1988) use data from Chattanooga, Tennessee and intervention
analysis to examine the affect of market changes on total ridership, total operating
34
revenues, the ratio of total operating revenues to total revenue miles, and the ratio of total
passenger trips to total revenue miles. They slightly modify the Box- Tiao methodology
by first using the entire sample to model the noise term, then separately estimating the
intervention term, and then minimizing all parameters. They use t statistics to test for
significance. They show that marketing does significantly affect transit ridership.
2.8 Summary of Literature Review
An extensive literature review identified a number of past studies using transportation-related
data. Fewer studies used both multiple regression ( taking into account
autocorrelation) and time- series methods for the analysis of predictors for transit
ridership. There were still fewer time series studies that analyzed transit ridership
affected by an intervention, using intervention analysis. To date, there are no known
studies that examine the impact of the intervention of construction work on bus transit
ridership.
35
CHAPTER 3 DATA DESCRIPTION
This chapter describes the data used in this analysis. A brief description of methods of
ridership data collection is given. Each bus transit agency is described, with their
ridership data, and the methods they use to collect ridership data. Data filtering that was
required to construct a data set for this analysis is described, with information regarding
data imputation for missing data. An analysis was performed on each of the ridership data
sets to determine if any independent factors played a significant role in ridership changes
during the period of analysis. Data quality with relation to methods of data collection is
discussed.
3.1 Methods of Data Collection
Four methods of ridership data collection were used among the five transit agencies that
provided service to the downtown core. Those methods included automatic passenger
counters ( APC), electronic fareboxes, manual counts by route checkers, and manual
counts by bus drivers. A description of each method is provided below:
1. Automatic Passenger Counters ( APC): APC devices are often door-mounted
and use infrared beam technology to automatically count boarding and alighting
riders. Many use GPS technology to associate collected data with a time and location.
2. Electronic Fareboxes: Electronic fareboxes are devices that collect
ridership information. Typically, a bus driver enters a number corresponding to rider type
into a key pad on the electronic farebox which stores the data until it is uploaded to a
network. Usually, electronic fareboxes do not provide location information.
36
3. Manual Counts by Route Checkers: Route Checkers take manual counts of
passengers boarding and alighting at each stop, and the arrival and departure times of
these stops.
4. Manual Counts by Bus Drivers: Bus Drivers take manual counts of
passengers boarding and alighting at each stop, and the arrival and departure times of
these stops.
3.2 Data Sample
This section describes the data samples provided by each of the five bus transit agencies.
The section is divided into five sub- sections, one for each agency. Each sub- section
includes a brief background of each bus transit agency, ridership data collection methods
employed by each agency, and the data provided by each agency. Unless otherwise
stated, all information regarding each transit agency was obtained through personal
correspondence as listed in Table 3.1:
Table 3.1: Data Collection Details
Transit Agency Contact
Contact's Official
Position Title
Type of Personal
Correspondence
Regional Transit James Drake Assistant Planner e- mail, phone, mail, in- person
Yolobus Erik Reitz Transit Planner e- mail, phone, mail, in- person
Roseville Transit
Teri Sheets
Alternative
Transportation
Analyst
e- mail
Elizabeth Haydu
Administrative
Technician
e- mail, phone, in- person
North Natomas
TMA
Sarah Janus
Program
Coordinator
e- mail
Yuba- Sutter
Transit
Dawna Dutra Analyst e- mail, phone
37
3.2.1 Regional Transit
The Sacramento Regional Transit District ( RT) operates bus and light rail transit serving
418 square miles of the greater Sacramento metropolitan area ( Regional Transit, 2009).
They are the largest provider of public transportation within the City of Sacramento,
operating 256 buses servicing 97 bus routes with more than 3,600 bus stops which
operate from 5 A. M. to 11: 30 PM, 365 days per year ( Regional Transit, 2009).
RT uses all four data collection methods described in Section 3.1. Regional Transit is the
only transit agency within our study that collects ridership data using APC devices, which
have been installed in half of the RT bus fleet. Electronic farebox devices are installed on
all RT buses, and is the method that RT uses for annual reporting. But because electronic
fareboxes don’t keep track of location or alighting passengers, this data was not suitable
for this study. The ridership data for RT consisted of APC data even though it is not used
for official reporting. It records boarding and alighting riders, as well as time and
location stamps for each record, which was necessary for filtering purposes. APC devices
are still in testing stages. The FTA’s National Transit Database requires that two random
bus trips must be sampled per day by route checkers, which is why RT also employs this
ridership collection method ( Drake, 2007). Finally, RT makes use of manual counts by
driver for its specialized Community Bus Service ( now called Neighborhood Ride) which
offers intraneighborhood service within certain communities while also servicing seniors
and the disabled.
Because of the expansiveness of RT, total ridership counts are nearly impossible to
obtain. On a normal weekday, the RT bus system makes 3,000 trips. As mentioned,
38
approximately half of its bus fleet is equipped with APC devices, which results in the
collection of data for 1,500 trips per day. The data is wirelessly uploaded to the RT
network, where it undergoes filtering which uses by a relaxed set of rules to remove
faulty data. The core set of rules that determine the filtering include:
• The difference between total riders on and total riders off for a bus must be 10% or
less,
• The difference between total riders on and total riders off for a block must be 10% or
less ( a block is a schedule for one physical bus each day),
• The difference between total riders on and total riders off for a trip must be 10% or
less,
• The number of stops counted must be “ pretty close” to the actual number of stops on
the route,
• Records showing obvious technology malfunctions.
As filtering occurs, records are deleted from the database. After the filtering process is
complete, about 400 records per day remain. The original raw data only remains as the
output from the APC device in the form of a text file. It is difficult to accurately assess
RT’s total bus ridership because the data is not a random sample, which is a result of the
filtering process and the fact that bus lines are not randomly chosen. Because total
ridership data by route is not easily obtained with filtered APC data, the raw APC data
was also provided but was not used due to data quality concerns. In addition, data from
General Farebox Inc. ( counts from the fareboxes on the buses), Parking Lot, Cash, and
fare vending machine count data was provided. That additional data was not useful as it
39
provided system- wide information, and was not specific to only those bus lines serving
the downtown area.
The APC daily data, including weekdays and weekends, spans from January 7, 2008 to
December 30, 2008. Initially, the APC data was a count of boarding and alighting riders
of a randomly chosen number of stops within the entire RT service area, allowing for the
filtering of bus lines serving the downtown area. The data also contained the time and
date of the observation as well as the bus stop identifier and route schedule identifier. RT
defined the AM peak period to be 6: 30- 9: 00AM, and the PM peak period to be 3: 00-
6: 00PM. Although the RT sample only contains 49 weekly ridership counts, Cherwony
and Polin ( 1977) used daily bus transit ridership data from Albany, New York to show
that only 30 days of transit ridership data is needed to develop a valid travel- forecasting
model.
3.2.2 Yolobus
Yolobus is operated by the Yolo County Transportation District and serves Yolo County
and surrounding areas including Davis, Sacramento, Winters, and Woodland among
others. Unlike RT, Yolobus also provides service to the Sacramento International Airport.
Yolobus uses electronic farebox devices as well as manual counts by bus driver to collect
ridership information. Yolobus separates its services into three types: regular, commute,
and express. Regular services run every day of the week whereas commute and express
services only run Monday through Friday. The agency operates 365 days of the year.
Since Yolobus offers different types of services to the downtown core, the operating
times of those services vary. Regular bus routes ( 40, 41, 42A/ B, 240) collectively run all
40
day from 4: 37 AM to 11: 48 PM during the week. The commute and express services,
which only run Monday through Friday, only run during peak commuting periods. The
commuter routes ( 39, 241) collectively run from 5: 35 AM to 8: 30 AM and 3: 35 PM to
6: 34 PM. Similarly, the express routes ( 43, 44, 45, 230, 231, 232) collectively run from
5: 55 AM to 8: 32 AM and from 4: 03 PM to 7: 17 PM. Yolobus restricts passenger travel in
downtown Sacramento by not allowing passengers to both board and alight in downtown
Sacramento. Instead, passengers are requested to utilize Sacramento RT for local services
within downtown Sacramento.
The Yolobus ridership data set contains the total daily ridership counts that span the
three- year period from January 2006 to December 2008. The data set is missing two days,
July 30, 2006 and July 31, 2006.
3.2.3 Roseville Transit
Roseville Transit is operated by the City of Roseville and mainly serves the City of
Roseville, but additionally serves Sacramento commuters. Roseville Transit runs specific
commuter routes that serve the Sacramento downtown core, including AM Routes 1- 8
and PM Routes 1- 8. The commuter routes only run Monday through Friday between the
morning peak commute hours of 5 – 9 AM and the afternoon peak commute hours of
3: 30 – 7: 30 PM. Roseville Transit uses manual counts by bus driver to collect ridership
information. Its daily, peak- period, ridership data was provided for the entirety of 2006,
2007, and 2008, including separation by commuter route.
41
3.2.4 North Natomas TMA
The North Natomas “ Flyer” is operated by the North Natomas TMA, serving Natomas as
well as downtown Sacramento commuters. The Flyer runs between 20 and 28 passenger
buses through several North Natomas neighborhoods, and although there are no timed
stops, time points are listed on the schedule ( the bus will stop wherever there are
passengers waiting). In downtown Sacramento, there are timed stops at set locations. The
Flyer includes three routes that serve the downtown core: the Eastside Route, the
Westside Route, and the Central Route. In September of 2008, North Natomas TMA
began running a Square Route; however, those ridership counts were excluded from the
daily totals because that route was added after the construction period had ended and
there was no pre- construction or construction data to use for comparison. The Flyer
operates Monday through Friday except on certain holidays. North Natomas TMA runs
peak period scheduled routes between Natomas and downtown Sacramento. The Eastside
Route has three morning and three afternoon loops that run from 5: 54 AM – 9: 04 AM
and from 3: 35 PM – 6: 54 PM, respectively. The Westside Route has two morning and
two afternoon loops that run from 6: 00 AM to 7: 44 AM and from 4: 30 PM to 6: 30 PM,
respectively. The Central Route also has three morning and three afternoon loops that run
from 6: 03 AM – 9: 04 AM and from 4: 07 PM – 7: 06 PM, respectively.
North Natomas TMA uses manual counts by driver as well as farebox counts to collect
ridership information. Manual counts were also provided by volunteer riders during the
duration of the Fix I- 5 project. Their daily peak- period ridership data, collected using
both manual and automated collection methods, spans the complete 2008 year and is
separated by route.
42
3.2.5 Yuba- Sutter Transit
Yuba- Sutter Transit is operated by Sutter and Yuba Counties and the Cities of Marysville
and Yuba City and provides service to Yuba City, Marysville, Linda, Olivehurst, East
Nicolaus and Sacramento. Only the Sacramento Commuter Express provides Sacramento
downtown commuter service ( via Highways 70 and 99). The commuter service runs on
weekdays, but not on certain holidays. Yuba- Sutter currently provides nine commuter
schedules for each of the peak periods that operate from 5: 20 AM to 8: 00 AM and from
3: 45 PM to 6: 50 PM.
Yuba- Sutter Transit uses manual counts by the drivers to collect all ridership information.
Their daily, peak- period ridership data is for the Sacramento Commuter Service for the
years 2005, 2006, 2007, and 2008. This data was broken down by day and further
separated by route. 2008 data was provided in the same format but in an electronic
version.
3.3 Data Filtering
In order to modify ridership data provided by each transit agency a four- step procedure
was followed for each agency.
3.3.1 General Procedure
Step 1: Filter data to include ridership only for lines which provide service to the
Sacramento downtown core, as previously defined by cordon. Table 3.2 provides a list of
each transit agency and their bus transit lines that provide service to the downtown:
43
Table 3.2: Transit Lines Servicing the Downtown Core
Transit Agency Downtown- Servicing Lines
Regional Transit 2,3,6,7,11,15,29,30,31,33,34,36,38,50E, 51,62,63,67,68,86,88,89,109
Yolobus 39,40,41,42A, 42B, 43,44,45,230,231,232,240,241
North Natomas Eastside Route, Westside Route, and Central Route
Roseville Transit AM Routes 1- 8, PM Routes 1- 8
Yuba- Sutter Transit Sacramento Commuter Express
Step 2: Filter data according to Table 3.3 to include inbound ridership for the AM peak
period, as defined by agency.
Table 3.3 AM Peak Period Definitions of Each Data Set
Transit Agency AM Peak Period Definition
Regional Transit 6: 30- 9: 00
Yolobus Daily Data
North Natomas Route: Eastside: 5: 54- 9: 04, Westside: 6: 00- 7: 44, Central: 6: 03- 9: 04
Roseville Transit 5: 00- 9: 00
Yuba- Sutter Transit 5: 20- 8: 00
Step 3: Filter data according to Table 3.4 to include outbound ridership for the PM peak
period, as defined by agency.
Table 3.4: PM Peak Period Definitions of Each Data Set
Transit Agency PM Peak Period Definition
Regional Transit 3: 00- 6: 00
Yolobus Daily Data
North Natomas Route: Eastside: 3: 35- 6: 54, Westside: 4: 30- 6: 30, Central: 4: 07- 7: 06
Roseville Transit 3: 30- 7: 30
Yuba- Sutter Transit 3: 45- 6: 50
Step 4: Filter data to include only Tuesday, Wednesday and Thursday ridership. Because
modified work schedules are widely used, Monday and Friday are not representative of
typical ridership.
44
The final model ridership is a combination of ridership across bus lines for a given
agency, so that a single data point represents total ridership on all lines serving the
downtown core. The sample size for the final data sets for this analysis is described in
Table 3.5:
Table 3.5: Sample Size of Each Data Set
Transit Agency Time Period Aggregation Sample Size
Regional Transit 2008 Weekly, Peak Period 49
Yolobus 2006- 2008 Daily 441
North Natomas 2008 Daily, Peak Period 147
Roseville Transit 2006- 2008 Daily, Peak Period 441
Yuba- Sutter Transit 2006- 2008 Daily, Peak Period 441
3.3.2 Special Modifications to General Procedure for Regional Transit
RT data required more manipulation in order to perform the necessary filtering. The
details are described. The main objective was to use the APC data to obtain the total
weekly demand within the downtown core for all 52 weeks in 2008. More specifically,
the goal was to obtain this weekly demand data for buses entering the downtown during
the AM peak ( 6: 30 AM – 9: 00 AM) and for buses leaving the downtown during the PM
peak ( 3: 00 PM – 6: 00 PM). Because RT ridership data is not collected for every
passenger or trip, more complex methods were needed for RT. All of the bus stops within
the downtown core were identified using RT generated identifying numbers. RT uses 325
bus stops in the downtown. Then the number of boarding and alighting riders associated
with those bus stops during each peak period was obtained. Although the daily APC data
is incomplete, it covers almost half of the stops within the downtown area every day. We
can assume that the total data collection for one week ( Monday through Friday) covers all
45
of the stops within the downtown area and that the sample size for each bus stop is
sufficient ( Drake, 2007).
Next, using the APC data, the daily average of alighting riders during the AM peak
period and the daily average of boarding riders during the PM peak period was
calculated. Using the RT bus schedule, the frequency of stops at each bus stop during the
peak hours was determined. This frequency is a fixed number every day for a certain
schedule. RT had four different schedules throughout 2008; however, comparison
between schedules shows that the frequency of the downtown bus stops did not change
for the downtown core for 2008. Therefore, this study used the frequencies from the first
schedule, Schedule 20, valid between January 6, 2008 through April 5, 2008, for both the
AM and PM peak periods. The following equations were used to calculate total ridership:
Y 	 Y © & _ ˜ S l _   ˜ ª « I ¬ ­ ® I B  1 © 
 l _ © ¯ l " 	 ™ ™  " ª l _  Y 	 ª t ™ _ l ° ± l D ² ³ 	 ™  Y 	 ª  © Y ´ ±   Y 	 ª ˜ S ± _ ˜ D ¯ µ ¶ ª l © · !  ¸
« =  
Y 	 Y © & _ ˜ S l _   ˜ ª ­ ®  ¬ ­ ® I B  1 © 
 l _ © ¯ l " 	 D  " ª l _  Y 	 ª t ™ _ l ° ± l D ² ³ 	 ™  Y 	 ª  © Y ´ ±   Y 	 ª ˜ S ± _ ˜ D ¯  ¶ ª l © · !  ¸
« =  
3.4 Independent Variables
A multiple regression analysis was performed on each of the nine ridership data sets to
determine if any independent factors played a significant role in ridership changes during
the period of analysis. The regression was performed for all agencies ( and all peak
periods) using four independent variables: GDP, unemployment rates, gas prices, and fare
prices. The smallest period of data aggregation available was used for each independent
variable. Table 3.6 describes the final independent variable data:
46
Table 3.6: Independent Variable Details
Independent
Variable
Source Aggregation Location Contact
Contact's
Official
Position Title
Gross
Domestic
Product
Bureau of
Economic
Analysis
Quarterly National
Lisa
Mataloni
Economist
Gasoline
Prices
AAA Monthly Sacramento City
Michael
Geeser
Media and
Government
Relations
Representative
Unemployment
Rates
Bureau of
Labor
Statistics
Monthly
Sacramento/ Arden-
Arcade/ Roseville
Website
Fares
Yuba-
Sutter
Transit
Daily Agency
Dawna
Dutra
Analyst
Roseville
Transit
Elizabeth
Haydu
Administrative
Technician
In terms of GDP data, seasonally unadjusted data was used because the adjustment of
GDP data is outsourced, and the Bureau of Economic Analysis doesn’t provide or have
access to unadjusted GDP data. Additionally, state and metropolitan area GDP is only
available on an annual basis and the lowest level of aggregation is national GDP provided
on a quarterly basis. GDP was included as a measure of overall economic health. Hoel
( 1971), in his discussion of linear regression, gave the example of a 0.98 correlation
coefficient between teacher’s salaries and liquor consumption, noting that in general the
economy was doing well and upward trends were common. He warned about spurious
correlations which must be considered in correlational studies.
Gas price data was the unleaded gasoline price per gallon averaged for the city of
Sacramento between 2006 and 2008. Finally, fares were used for two transit agencies
who were affected by changes in basic fare rates namely Yuba- Sutter Transit and
47
Roseville Transit, with one increase for the three year period ( 2006- 2008) for both
agencies. Table 3.7 describes the fare pricing for each agency:
Table 3.7: Fare Pricing Details
Transit Agency Single Ride, Adult Fare
Regional Transit $ 2.00
Yolobus $ 1.50
North Natomas $ 1.00
Roseville Transit 11/ 1/ 2003 – 6/ 30/ 2007: $ 2.75, 7/ 1/ 2007 – 12/ 31/ 2008: $ 3.25
Yuba- Sutter Transit 8/ 1/ 2002 – 6/ 30/ 2007: $ 3.00, 7/ 1/ 2007 – 12/ 31/ 2008: $ 3.50
For data aggregated on levels other than daily, the monthly or quarterly average value of
the independent variable was repeated for all Tuesdays through Thursdays that existed for
that month or quarter ( based on the information from the data manipulation section).
Consequently, there is a single value for every day of ridership data that represents that
month’s average of the independent variable. For weeks that straddled two months, the
two monthly averages were averaged. For example, Week 17 of 2008 includes April 29,
April 30 and May 1, and the unemployment rate for April 2008 is 5.9% while May’s
unemployment rate is 6.3%. The unemployment rate for this week is calculated as
[( 2* 5.9) + 6.3] / 3 = 6.03333%.
3.5 Data Quality2
This section describes data quality considerations, including sub- sections describing
quality concerns related to the four ridership data collection methods employed by the
five transit agencies, as well as additional data quality concerns. The four collection
methods consist of automatic passenger counting ( APC) devices, electronic registering
2 Sections 3.5.1, 3.5.2, 3.5.3, and 3.5.4 use information from a report prepared by Jessica Seifert, under the
author’s direction.
48
fareboxes ( ERFs), manual counts by route checkers, and manual counts by bus drivers.
Each section will briefly discuss the collection method, concerns related to data quality
and which agencies use that method. All agencies ridership data sets were shortened to
Tuesday, Wednesday, and Thursday data sets which did not contain any missing data.
The two missing values for Yolobus, discussed previously, July 30, 2006 and July 31,
2006, fell on Sunday and Monday.
3.5.1 Automatic Passenger Counting Devices
APC devices automate ridership data collection by tracking boarding and alighting riders,
in addition to including a time and location stamp for each count. RT is the only transit
agency within the study that utilizes APC devices, supplied by Clever Devices, Inc.
( Drake, 2009). This technology uses an infrared beam to count boarding and alighting
riders, and is mounted above the bus doors ( Poggioli, 2009). The Clever Devices APC
correlates the ridership data to GPS coordinates and scheduled routes so that the data may
be viewed on a per- bus, per- door level ( Clever Devices, 2009).
Clever Devices, Inc. claims that their APC system demonstrates over 95% accuracy,
though they do not provide information on their website that would account for the 5%
error ( Clever Devices, 2009). Boyle ( 1998), referring to all APC systems, stated that
typically the most common problems are related to software, as transit agencies often
have to upgrade their analytical programs, and secondarily hardware problems ( device
failure and durability). But for the Clever Devices APC system, in large part, the 5%
error can be attributed to mechanical malfunctions as well as door bunching, carrying a
child, carrying large bags, drivers getting on and off the bus, non- riders making inquiries
49
to bus drivers, and misalignment of sensors ( Poggioli, 2009). In addition to technical
problems, Boyle ( 2008, p. 18) defines a “ debugging” period in which employees must
familiarize themselves with the new technology. From the survey Boyle conducted in
1998, the average debugging period for APC devices was 17 months ( Boyle, 2008). The
accuracy of APC systems can be evaluated by comparing its ridership data to manual
counts, although manual counts may also have data quality problems ( see Sections 3.5.3
and 3.5.4) ( Boyle, 2008).
As mentioned, RT is the only agency that uses APC devices to collect ridership
information. RT was unable to provide APC ridership data for all of the buses that serve
the downtown Sacramento region, because APC devices were not installed on the entire
bus fleet and because the data was heavily filtered to remove data with obvious errors
( see Section 3.2.1 for filtering rules). Also, RT’s APC system is still in testing phases
which could indicate that the devices are also within the debugging period ( Drake, 2009).
3.5.2 Electronic Registering Fareboxes
Electronic registering fareboxes ( ERFs) are devices in which bus drivers enter a number
corresponding to rider type into a key pad that connects to an electronic farebox ( Boyle,
1998). The drivers are also required to enter a value to indicate the route and run number
at the beginning of each trip ( Boyle, 1998). ERFs do not collect location information, so
ridership data is only available at the trip level ( Drake, 2009). As is done with APC
devices, the data collected from electronic registering fareboxes can be “ validated” by a
comparison with manual counts or by comparison with the revenue collected from fares
( Boyle, 1998).
50
There are four problems that may be encountered when using electronic registering
fareboxes: mechanical problems, operator compliance, software problems, and accuracy
of data ( Boyle, 1998). The bus operators must enter the correct codes at the beginning of
each route and trip and the correct code for the type of passenger ( Boyle, 1998). Boyle’s
survey ( 1998) indicates that some transit agencies experienced difficulties when adding
these additional responsibilities to the bus drivers’ duties, although the most successful
agencies were the ones that provided continuous ERF training to their drivers. Ultimately,
the quality of the data collected from ERFs is affected both by human and software
errors.
The transit agencies within this study that used ERF are RT, Yolobus, and North
Natomas TMA. RT has electronic fareboxes installed on all of their buses except for the
community buses.
3.5.3 Manual Counts by Route Checkers
Most transit agencies utilize manual counts either as their primary method of data
collection, or for comparison against electronic methods ( Boyle, 1998). Route checkers
ride the transit vehicle and take manual counts of passengers boarding and alighting at
each stop ( Boyle, 1998). They typically have preprinted forms or handheld units that
contain all of the stops on that route, with the sole responsibility to count passenger and
record bus stop arrival and departure times ( Boyle, 1998). Manual counts are the most
well- established method of ridership data collection ( Boyle, 1998).
The following problems are associated with manual counting by route checkers: accuracy
of data, consistency of data, labor intensiveness, reliability of route checkers, and cost of
51
manual counting ( Boyle, 1998). Problems with accuracy and consistency of the data are a
result of the training and reliability of the route checker, as well as transcription of the
handwritten record to an electronic version ( Boyle, 1998).
RT and Natomas TMA were the only transit agencies within the study that used manual
counts by route checkers to collect ridership data. It should be noted that Natomas TMA
used untrained volunteer riders to provide manual counts.
3.5.4 Manual Counts by Bus Drivers
Manual counts by bus drivers are another method of ridership collection. Manual
counting by bus drivers is concerned with many of the same problems as manual
counting by route checker, including the labor intensiveness and reliability of the counter.
But because bus drivers also have many other responsibilities such as driving the bus,
monitoring passengers and collecting fares, they may be less focused on counting
passengers than route checkers.
All five of the transit agencies within the study use manual counts by bus drivers as either
their primary method of data collection or in combination with another technique.
Roseville Transit and Yuba- Sutter Transit exclusively use manual counts by bus drivers
to collect ridership information, while North Natomas TMA and Yolobus use manual
counts by bus driver in addition to electronic registering fareboxes. RT uses manual
counts by bus driver in addition to the other three techniques.
52
3.5.5 Additional Data Quality Considerations
As discussed above, the RT data was heavily filtered and manipulated prior to being
obtained by this study. Although quantification of data quality is not possible, RT data is
probably the least reliable of the five agencies analyzed. RT ridership data was only a
sample of total ridership ( unlike all other agencies), and further the collected data was not
a random sample. Additionally the system was still in a testing phase. Furthermore, this
analysis did not separate riders who board and alight within the downtown core.
According to RT, ridership that fell within these categories was less than 5% of total
ridership for commute periods, but other ridership data was not available to verify this.
Although the Yolobus data was probably more reliable than RT, their daily ridership
totals included regular bus routes ( 40, 41, 42A/ B, 240) which operated all day during
weekdays, in addition to commute and express services which only run Monday through
Friday during peak commuting periods. The Yolobus ridership sample therefore included
some non- commute data.
Since the data from RT and Yolobus was received in an electronic format, there is a
possibility of transcription errors on the part of the transit agency. The data from Yuba-
Sutter Transit, Roseville Transit, and North Natomas T. M. A. was received in a hardcopy
format. There was also a possibility of transcription errors in entering that hardcopy data
into data sets used by this study, although all data entry was verified for accuracy by a
second person.
53
3.6 Data Cleaning
The data sets provided by each of the five agencies contained only two cases of actual
missing data, both for Yolobus ( July 30, 2006 and July 31, 2006). Although cases of
missing data were rare, plots of the data that was provided by each agency indicated that
some data manipulation would be necessary to account for holidays and limited service
days. As an example, Figure 3.1 below displays the original data for Roseville Transit:
Figure 3.1: Plots of Original Roseville Peak- Period Ridership Data
Plots of each agency’s original data set and imputed data set including Tuesday,
Wednesday and Thursday ridership can be found in Appendix B. The drops in the plots
represent transit holidays and limited service days as well as state holidays. Although not
technically missing data, because agencies had provided data for all observations, the
buses and the riders ( assumed to be workers in downtown Sacramento) were “ missing”
54
and therefore ridership was zero ( or very low) for transit and state holidays, and
unusually low for limited service days. Those occurrences were treated as missing data.
For some missing observations, the missing data could be considered missing completely
at random ( MCAR). MCAR occurs if missing observations are distributed randomly over
all observations, including that variable and any others, and can therefore be considered a
simple, random subsample ( Allison, 2002). The missing data in this analysis are MCAR,
although not ignorable. As discussed in the Literature Review, discrete time series data
assumes that the time series is observed at equal intervals. More complex methods are
necessary if the observations are not equally spaced, and therefore the missing data in this
analysis had to be imputed. There are multiple methods to deal with missing data. Some
conventional methods, excluding listwise and pairwise deletion, include dummy variable
adjustment, and imputation. A basic dummy variable regression was first used, but an ad
hoc imputation method was ultimately used because of the detailed information about the
missing value cases and their likely “ true” values.
Prior to any data imputation, it was necessary to identify days with no transit service,
limited transit service days, and full transit service days that coincide with state holidays
for each of the five transit agencies for 2006, 2007 and 2008. Those dates are considered
missing observations, and are identified in Appendix D.
From Yolobus data exploration, in general, there was low variation from the mean for
Tuesday, Wednesday and Thursday ridership for any given week. However, it also
appeared that there was low variation from the mean for the same weekday ridership for
55
three consecutive weeks. For example, the second Tuesday in a month showed similar
ridership to the first and third Tuesdays in that month. Therefore, two methods for
imputing data for “ missing” observations were compared. The methods were tested using
Tuesday, Wednesday, and Thursday Yolobus ridership data. The same set of holidays
was used to test both methods. The two methods are described below, and the detailed
calculations are given in Appendix E:
o Method 1 used the same week that the holiday falls in but different days.
T1 is defined as the ridership of the first non- holiday day in the holiday week, and T2 is
defined as the ridership of the second non- holiday day in the holiday week. For example,
if the holiday fell on a Wednesday, T1 was the ridership on Tuesday and T2 was the
ridership on Thursday, whereas if it fell on Tuesday, then T1 applied to Wednesday and
T2 to Thursday of the same week. Then the absolute value of the difference, | T1- T2|, was
calculated. The differences for all of the holidays were summed and divided by the total
number of holidays, giving the average difference. This difference was found to be equal
to 152.33.
o Method 2 uses the weeks prior to and after the holiday week but the same
day. T1’ was defined as the ridership on the same day of the week before the holiday, and
T2’ was defined as the ridership on the same day of the week after the holiday. For
example, if the holiday fell on a Tuesday, T1’ was the ridership of the previous Tuesday
and T2’ was the ridership of the following Tuesday. Then the absolute value of the
difference, | T1’- T2’|, was calculated. The differences for all of the holidays were summed
and divided by the total number of holidays, giving the average difference. This
difference was found to be equal to 154.17.
56
Since the average difference of Method 1 was smaller than the average difference of
Method 2, Method 1 was used for this study. More specifically, the average of T1 and T2,
which lie in the same week as the day with the holiday, was used to impute the missing
day’s ridership. In addition, there were no problems with Method 1 when holidays
occurred in consecutive weeks, for example, Christmas Day and New Year’s Eve. Data
imputation was done using Method 1 for the days that each transit agency ran limited or
no services as well as state holidays when they ran full services. Finally, Thanksgiving,
Christmas, and New Year’s Eve weeks were eliminated from the data as those entire
weeks showed extremely low ridership.
The formula used for percent data imputed is % Imputed = ( Number of Days
Imputed/ Total Number of Days) x 100. There were no differences between holidays, or
limited service days, so the percent of data imputed for agencies with separate AM and
PM peak data sets was constant. Table 3.8 shows that the amount of imputed data for any
given agency is at most 2%, and usually much less. This is considered an acceptable level
of imputation.
Table 3.8: Percent Imputed Data
Transit Agency Percent
Roseville Transit 0.91%
Yuba- Sutter Transit 0.91%
Yolobus 0.68%
North Natomas T. M. A. 1.36%
Regional Transit 2.04%
57
3.7 Descriptive Statistics for Transit Ridership3
The statistical methods discussed in the literature review are considered parametric
statistical methods. Parametric methods make assumptions about the population
parameters, more specifically probability distributions are usually assumed to be normal
( Mann, 2004). The statistical tests used in this study, including the regression and time
series analyses presented later, use parametric methods. The following discussion
provides a general statistical overview of each transit agency’s ridership data, based on
the cleaned data sets, prior to in- depth time series analysis. Both measures of center
tendency and measures of dispersion will help to describe the data and its distribution.
This section will present statistics, but leaves the interpretation of the statistics to Chapter
5.
3.7.1 Measures of Central Tendency
Measures of center value describe the center of the distribution of a variable. The mean is
an arithmetic average which is commonly used to describe distributions. However, the
mean statistic is sensitive to extreme values, also known as outliers ( Ross, 2005). The
median is also a measure of center value, and describes the middle value of the data
without being as affected by outliers ( Ross, 2005). In order to describe the center values
of each data set, Table 3.9 lists the mean and median ridership for each transit agency’s
data sets.
3 Section 3.7 makes use of calculations and tables created by Jessica Seifert.
58
Table 3.9: Measures of Central Tendency: Mean and Median
Transit Agency Data Aggregation Mean Ridership Median Ridership
Roseville
Transit
AM 213.9 208.0
PM 200.4 198.0
Yuba- Sutter
Transit
AM 239.2 226.0
PM 237.5 222.0
Yolobus Daily 3499.5 3383.0
North Natomas
TMA
AM 116.8 127.0
PM 96.36 96.0
RT
AM 15498.4 15314.0
PM 13639.6 13641.0
A comparison of the median and the mean provides insight into the shape of the data sets
distributions. If the median and mean have similar values, then the distribution is
probably symmetric; otherwise, the data may be to some degree skewed ( Ross, 2005).
The data for this analysis shows that the medians for each agency are similar to their
means. This indicates that the distributions of the ridership data are fairly symmetric.
More specifically, the medians for Roseville Transit, Yuba- Sutter Transit, Yolobus, and
Regional Transit are slightly less than their means, indicating that the distributions may
be skewed to the right. Part of the skew in the histograms of Roseville Transit ( AM peak
period), Yuba- Sutter Transit, and Yolobus can be attributed to slightly higher ridership on
Tuesdays compared to Wednesdays and Thursdays. The Roseville and Yuba- Sutter
histograms are shown in Figure 3.2, confirming that expectation. The histograms of all
data sets are given in Appendix F.
59
Figure 3.2: Roseville and Yuba- Sutter Transit Histograms
Roseville Transit, Yuba- Sutter Transit, and Yolobus that have data sets spanning the
period of 2006 to 2008. All three agencies experienced increased ridership in both 2007
and 2008. In particular, Yuba- Sutter Transit experienced high ridership increases; from
2006 to 2007, average AM ridership increased by 15.2% and from 2007 to 2008, it
increased by 31.5%. Similar changes were seen in Yuba- Sutter Transit’s PM ridership
during those years. The medians in Table 3.10 are much closer to their means. In fact, all
agencies display this tendency, indicating that the yearly distributions are much more
symmetric than the distributions of the entire data sets.
Table 3.10: Yearly Means and Medians for Transit Agencies with Data Spanning
2006- 2008
Roseville Transit AM Ridership
( a) Ridership
Frequency
100 150 200 250 300 350
0 10 20 30 40 50 60
Roseville Transit PM Ridership
( b) Ridership
Frequency
100 150 200 250 300 350 400
0 10 20 30 40 50 60
Yuba- Sutter Transit AM Ridership
( c) Ridership
Frequency
150 200 250 300 350 400
0 10 20 30 40
Yuba- Sutter Transit PM Ridership
( d) Ridership
Frequency
150 200 250 300 350 400
0 10 20 30 40
Transit
Agency
Data
Aggregation
Mean Median
2006 2007 2008 2006 2007 2008
Roseville
Transit
AM 194.9 205.6 241.2 196.0 203.0 240.0
PM 189.1 192.5 219.6 190.0 194.0 217.0
Yuba- Sutter
Transit
AM 195.6 225.4 296.5 195.0 226.0 300.0
PM 189.9 223.0 299.5 189.0 222.0 302.0
Yolobus Daily 3175.1 3346.1 3977.2 3188.0 3360.0 3932.0
60
3.7.1.1 Ridership Means by Period
Since not all data sets span multiple years, the means of the data were also calculated
seasonally for the year 2008. The calculations were made based on the following seasons:
• 1st quarter: January – March
• 2nd quarter: April – June
• 3rd quarter: July – September
• 4th quarter: October – December
RT was excluded as its data is observed weekly. All of the agencies experienced
increased ridership between the first and second quarters of 2008. North Natomas TMA
ridership increased the most during this period, with a 41.6% increase in AM ridership
and a 24.9% increase in PM ridership. Similarly, all agencies saw an increase in ridership
between the second and third quarters of 2008, with North Natomas TMA again showing
the largest increase. However, opposite changes occurred between the third and fourth
quarters of 2008. Almost all of the agencies experienced a decrease in ridership during
this period; Yolobus was the only agency that saw an increase in ridership ( 1.7%). The
means for each quarter of 2006, 2007 and 2008 are displayed in Table 3.11. In general, it
appears that transit ridership decreased in the first and fourth quarters.
61
Table 3.11: Means by Season for 2006, 2007 and 2008
Transit Agency
Roseville
Transit
Yuba- Sutter
Transit Yolobus
North
Natomas
TMA
Data
Aggregation AM PM AM PM Daily AM PM
2006
Mean
Ridership
1st 190.3 182.4 189.7 182.9 3270.0
2nd 203.2 190.7 190.7 184.9 3185.0
3rd 197.2 196.2 201.9 196.2 3090.6
4th 187.3 186.0 200.6 196.0 3161.8
2007
Mean
Ridership
1st 195.1 191.4 213.4 206.8 3333.8
2nd 200.3 192.6 219.9 214.1 3269.8
3rd 201.0 188.6 229.0 225.0 3385.3
4th 228.6 198.1 240.8 248.8 3403.5
2008
Mean
Ridership
1st 226.3 199.6 253.9 257.2 3423.9 77.9 74.8
2nd 235.1 213.3 288.8 292.3 3782.8 110.3 93.4
3rd 266.0 234.6 333.8 335.7 4326.6 146.8 114.7
4th 234.5 231.3 307.2 310.8 4399.9 130.8 101.3
Means and medians were also calculated based on the Fix I- 5 construction period. The
three periods in Table 3.12 represent the time before the construction ( January 1, 2008 –
May 30, 2008), the time during the construction ( May 31, 2008 – July 27, 2008), and the
time after the construction ( July 28, 2008 – December 31, 2008). All of the agencies
experienced increases in mean ridership between the pre- construction and construction
periods, but the changes in the ridership from the construction to post- construction
periods varied by agency and by peak period within agencies. However, these differences
are confounded with seasonal differences, as the previous table had shown.
62
Table 3.12: Means by Construction Period for 2008
* RT AM and PM peak period ridership represents weekly ridership counts.
3.7.2 Measures of Dispersion
But measures of central tendency do not give a complete picture of the data’s
distribution; measures of dispersion are also included as descriptive statistics and include
the standard deviation. The sample variance, s2, is the average of the squared deviations
from the sample mean,  ¹ , while the sample standard deviation, s, is the square root of the
variance ( Ross, 2004). The relative size of the standard deviation can provide information
about how tightly clustered the data are about the mean. Smaller standard deviations
indicate that the data are tightly clustered whereas larger standard deviations indicate that
the data are relatively more dispersed ( Mann, 2004). The standard deviation, together
with the mean, can be used to calculate a range in which a certain percentage of the data
can be expected to lie: the confidence interval ( Ross, 2005). This range provides values in
terms of the original data’s units that indicate how much of the data are “ normally”
contained in that range. Standard deviations ( s) by construction period are given in Table
3.13.
Transit
Agency
Data
Aggre-gation
Mean Ridership Median Ridership
Pre During Post Pre During Post
Roseville
Transit
AM 228.2 253.8 249.8 229.0 250.5 246.0
PM 204.3 226.0 233.2 204.0 230.5 230.0
Yuba- Sutter
Transit
AM 265.8 314.0 321.8 262.0 311.5 316.5
PM 268.8 317.2 324.8 268.0 318.5 320.5
Yolobus Daily 3563.1 4023.5 4393.5 3589.0 3973.0 4447
North
Natomas TMA
AM 85.2 146.2 138.1 82.0 148.5 138.5
PM 76.6 124.3 106.0 75.0 127.0 104.5
RT
AM* 14785.9 15525.8 16235.7 14990.4 15132.5 16423.0
PM* 13361.6 13907.5 13824.4 13221.9 14188.6 13966.6
63
Table 3.13: Variance and Standard Deviation for Each Transit Agency
Transit
Agency
Data
Aggregation
Standard Deviation ( s)
º » ± Pre During Post s º » ± 2s º » ± 3s
Roseville
Transit
AM 20.54 24.91 24.46
( 186.0,
241.8)
( 158.1,
269.7)
( 130.2,
297.6)
PM 15.49 20.17 23.49
( 177.7,
223.1)
( 155.0,
245.8)
( 132.3,
268.5)
Yuba- Sutter
Transit
AM 29.14 16.33 21.38
( 191.4,
287.0)
( 143.6,
334.8)
( 95.8,
382.6)
PM 33 19.7 23.02
( 185.7,
289.3)
( 133.9,
341.1)
( 82.1,
392.9)
Yolobus Daily 240.38 209.77 229.1
( 3043.5,
3955.5)
( 2587.5,
4411.5)
( 2131.5,
4867.5)
North
Natomas
TMA
AM 12.14 11.65 12.48
( 86.7,
146.9)
( 56.6,
177.0)
( 26.5,
207.1)
PM 8.75 12.37 12.42
( 75.2,
117.6)
( 54.0,
138.8)
( 32.8,
160.0)
RT
AM 992.62 1265.84 1119.38
( 14238,
16759)
( 12977,
18019)
( 11717,
19280)
PM 687.33 1043.77 793.33
( 12824,
14455)
( 12009,
15270)
( 11193,
16086)
According to the empirical rule, the following percentages of approximately normal data
lie in these respective ranges: 68% in the range  ¹ ± s, 95% in the range  ¹ ± 2s, and
99.7% in the range  ¹ ± 3s ( Ross, 2005). These ranges were calculated for the data sets
and are displayed in Table 3.13. The  ¹ ± 3s range covers 100% of the data in all but two
cases ( with Roseville Transit AM and PM data sets containing points that lie outside of
the  ¹ ± 3s, 99.7% range), indicating that the data sets are approximately normal.
3.7.3 Discussion
All agencies had overall increases in mean ridership during the study period, but there
were also seasonal variations in mean ridership. An informal analysis of data dispersion
indicated that the data sets were approximately normal, with minor skews. Although this
study’s data failed usual tests of normality, slight departures from normality do not cause
serious issues ( Kutner et al., 2005) With the possible exception of RT, this study’s data
64
sets are random samples with a sufficiently large number of observations. Their
populations were considered approximately normally distributed, and parametric methods
were justified.
The next Chapter, which uses multiple regression and time series analyses, studies the
transit agency data sets to identify independent variables that correlate with increased
ridership and which can be used in predictive models to explain the change in ridership
means during the Fix I- 5 project.
65
CHAPTER 4 MODEL BUILDING
This chapter describes the methodology that was used to create the time series
intervention models for each agency’s transit ridership data. The first two sections
present the steps taken to transform each of the nine data sets into stationary processes,
including detrending using multiple regression analysis, and eliminating seasonal
components using sinusoidal decomposition. The last section explains the intervention
analysis methodology.
4.1 Multiple Regression
The nine time series plots shown in Appendix B show an overall increasing trend in
ridership. As discussed in the Literature Review Section, there are multiple methods of
removing trend components in the time domain including least squares estimation,
smoothing with moving averages and differencing, as well as regression techniques ( Aue,
2009; Yaffee, 2000). Regression techniques allow the modeler to eliminate trends using
independent variables. As discussed earlier, each previous study used a different set of
independent variables to predict transit ridership, but most of the studies that used
multiple regression included gas prices, fares, and economic indicators such as
unemployment rates. The following sections describe the relationships between bus
transit ridership and each independent variable used in this multiple regression. Plots of
each independent variable can be found in Appendix C.
66
4.1.1 Bus Transit Ridership and Gas Prices
Many studies have shown that gas prices significantly affect ridership, and that the
ridership- gas price correlation is positive. Lane ( 2009) showed that gasoline prices are a
statistically significant predictor of positive changes in transit ridership, with positive
ridership- gas correlations. Wang and Skinner ( 1984) used data from seven transit
authorities in the U. S. and showed that as real gasoline prices increase, transit ridership
increases significantly. In a cross- sectional study, Taylor et al. ( 2009) analyze transit
ridership from 265 urban areas using regional fuel prices provided by the Bureau of
Labor Statistics as an explanatory variable and hypothesized a positive correlation. They
found that fuel prices were a significant external factor positively influencing aggregate
transit ridership. Kyte et al. ( 1988) shows that gasoline price is a statistically significant
predictor of bus transit ridership, explaining that increasing the cost of automobile travel
( i. e. gas prices) would motivate a mode change to transit. They find that gasoline prices
show a negligible lag in their influence on ridership. For the previous work presented
above, those studies that used gas prices in their analysis found them to be significant
independent variables.
This study’s data found strongly significant and positive Pearson’s correlations between
bus transit ridership and gas prices ranging between 0.18 and 0.6 for eight of the data
sets. The Pearson’s correlation coefficient, r, is defined for pairs ( xi, yi) as ( Ross, 2005):
r  Σ  ¼ ½ - ¼ ¹ ¾ ½
¿ h   À ½ - À ¹ 
 Á -    Â Ã Â Ä .
The data sets with the highest correlations ( Roseville Transit, Yuba- Sutter Transit and
Yolobus) are those having the longest time series, suggesting that perhaps the impact of
67
higher gas prices was beginning to level off by 2008 ( i. e. those who were susceptible to
the effect of higher prices had already changed earlier than 2008), or possibly that the
intervention of the Fix I- 5 project and other anomalies of 2008 ( economic conditions,
serious regional fires during the summer) disrupted the previously regular relationship
between gas prices and ridership. Also, the highest correlations between ridership and gas
price were for bus transit agencies farthest from the Sacramento downtown core ( Yuba-
Sutter Transit, Roseville Transit and Yolobus) indicating that commuters with longer
commute distances may have been more sensitive to rising gas prices, and therefore,
more inclined to use bus transit. The RT AM peak has a counterintuitive negative
ridership- gas correlation of - 0.2. The ridership- gas Pearson’s correlations are shown in
Table 4.1.
Table 4.1: Ridership- Gas Price Correlation Coefficients
Transit Agency Peak Period
Pearson's Ridership- Gas Price
Correlation Coefficient
Regional Transit AM - 0.20***
Regional Transit PM 0.18***
Yolobus Daily 0.39***
North Natomas AM 0.25***
North Natomas PM 0.28***
Roseville Transit AM 0.60***
Roseville Transit PM 0.43***
Yuba- Sutter Transit AM 0.59***
Yuba- Sutter Transit PM 0.59***
***: p < 0.001
4.1.2 Bus Transit Ridership and Unemployment Rates
A small number of previous studies have examined the effects of labor statistics,
specifically employment, on transit ridership. Agrawal ( 1981) showed that jobs in
68
Philadelphia were highly significant positive predictors of transit ridership. Surprisingly,
he showed th