RSS and rail commuting Nested logit analysis.pdf

UC Berkeley
Earlier Faculty Research
Title
Residential Self Selection and Rail Commuting: A Nested Logit Analysis
Permalink
https://escholarship.org/uc/item/1wg020cd
Authors
Cervero, Robert
Duncan, Michael
Publication Date
2002-12-01
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University of California

Residential Self Selection and Rail Commuting:
A Nested Logit Analysis
Robert Cervero and Michael Duncan
Department of City and Regional Planning
Institute of Urban and Regional Development
University of California, Berkeley
Working Paper
University of California Transportation Center
Berkeley, California
Original: December 2002
Revised: June 2008

1
Note
An error was discovered in the original Table 1 of this study. Notably, the Inclusive
terms for the upper-nest model were incorrectly calculated thus the theta terms were in
error. This revised working paper corrects this error. Also, the corrected upper nest
model has a slightly different specification than originally shown in Table 1 in order to
satisfy the condition that the theta values lie between 0 and 1. Some additional text is
added to the original working paper regarding the new upper level model, however none
of the substantive findings or conclusions of the research change as a result. The
additional variables added to the upper nest model reveal that low automobile ownership
levels tended to be associated with transit-oriented living. We acknowledge that
automobile ownership likely both influences and is influenced by transit-oriented living,
thus the coefficient on the automobile ownership variables could be subject to
endogeneity bias. The revised equation also shows that controlling for other variables in
the equation, having individuals 55 years of age and above in a household reduced the
likelihood of living near transit. It is also noted that the estimated coefficients in the
lower nest binomial logit models for predicting rail commuting (shown in the right-hand
panel of Table 3) are unchanged from the original Table 3.

2
Abstract
Past studies show that those living near train stations tend to rail-commute far more often
than the typical resident of rail-served cities. Some contend this is largely due to self-
selection, marked by those with an affinity to transit riding consciously moving into
neighborhoods that are well-served by transit. This article explores the self-selection
question by constructing a nested logit model that jointly estimates the probability
someone will reside near a rail stop and in turn commute by rail transit, using year-2000
travel data from the San Francisco Bay Area. A multinomial logit model is also used to
predict car ownership levels. The research reveals that residential location and commute
choice are jointly related decisions among station-area residents. A comparison of odds
ratios among those living near and away from transit, controlling for the influences of
other factors, suggests that residential self-selection accounts for approximately 40
percent of the rail-commute decision. These findings suggest that supportive zoning
should be introduced and barriers to residential mobility should be eliminated to allow
the self-selection process to occur naturally through the marketplace.

3
1. TRANSIT-BASED HOUSING AND RESIDENTIAL SORTING
The inventory of housing near train stations is rapidly expanding in many of
America’s rail-served cities. In California, over 12,000 apartment and condominium
units were built between 1998 and 2001 within ½ mile of stations along the Tasman light-
rail corridor in Santa Clara County, the Mission Valley Trolley line in San Diego, the
Walnut Creek-Concord axis served by the Bay Area Rapid Transit (BART) system, and
Los Angeles Metrorail’s Westlake-Hollywood subway corridor. At the Ohlone-
Chynoweth light rail station in San Jose, 194 apartment and condominium units were
constructed atop what only a few years ago was a surface park-and-ride lot.
Transit-based housing, some contend, promote a number of public-policy goals
(Calthorpe, 1993; Cervero, 1993; Bernick and Cervero, 1997). One, increased transit
ridership enhances urban mobility and relieves peak-hour traffic congestion. Surveys of
residents of multi-family complexes near suburban BART stations from the early 1990s
showed upwards of 45 percent took rail-transit to work, much higher than the regional
average of 9 percent (Cervero, 1994). Studies from metropolitan Washington, D.C. and
Toronto found even higher transit market shares (up to 65 percent of commutes) among
apartment-dwellers living near rail stops (Stringham, 1984; JHK and Associates, 1987,
1989).
Other benefits assigned to transit-based housing included increases in the supply
of affordable units and improved air quality. Housing is more affordable, proponents
maintain, because those living near rail transit stops own fewer cars and spend less
money on private mobility, therefore freeing up money for housing consumption.
Indeed, a central premise of Location Efficient Mortgage (LEM) programs, currently
under way in Los Angeles, Chicago, Seattle, San Francisco, and Salt Lake City, is that
prospective home-buyers can more easily qualify for home mortgages when living in
transit-served settings since they usually spend smaller shares of their disposable incomes
on transportation (Holtzclaw, et al., 2002). A string of studies have correlated living in
compact, mixed-use, transit-served neighborhoods with lower automobile ownership
rates and reduced automobile travel, providing empirical support for the LEM concept
(Holtzclaw, 1994; Cervero and Gorham, 1995; Cervero, 1996; Schimek, 1996;
Holtzclaw, et al., 2002). Air-quality benefits accrue from transit-based housing to the

4
degree rail access trips switch from park-and-ride to walk-and-ride. From an air-quality
standpoint, transit riding does little good if a car is driven to reach a station. This is
because disproportionately large shares of tailpipe emissions occur over the first mile of
travel (due to inefficient cold engines) (Barry and Associates, 1991). Thus the emissions
of a typical 3-mile park-and-ride trip are not too much different than those of a typical
10-mile solo commute (Cervero, 2001).
How much of the ridership bonus assigned to transit-oriented living is due to
spatial proximity or the nature of people who opt to live in these settings? Might many
residents of transit-based housing still be riding transit even if they lived away from a rail
station? Boarnet and Crane (2001) argue that travel patterns are partly a result of the
decision on where to live and this needs to be accounted for when studying how urban
design, including transit oriented development (TOD), influences travel behavior. Self-
selection – i.e., the tendency of those with a predisposition toward transit to reside in
areas well-served by transit – could be occurring for any number of reasons: to reduce the
stress of driving to work, to save time and money, or to express one’s support of “green”
transportation. Voith (1991) suggested that residential sorting largely explained ridership
gains during the 1980s along commuter rail lines in Philadelphia’s middle-class suburbs,
though no statistical evidence was presented. Several California surveys provide some
empirical support for the self-selection argument. A 1992 survey of 27 housing projects
near rail stations in northern and southern California asked residents how they got to
work at their prior residence (for those who previously lived in the same metropolitan
area but beyond one mile of a station and whose work sites remained unchanged). The
study found 42.5 percent and 13.7 percent previously commuted by rail and bus,
respectively – some four to five times higher than regional averages (Cervero, 1993;
1994). Another study found those living near Santa Clara County’s light-rail line
patronized transit as their predominant commute mode five times as often as residents
countywide; self-selection was evident in that 40 percent of the respondents who moved
close to rail stops said they were influenced in their move by the presence of light rail
(Gerston & Associates, 1995).
This article examines the influence of transit-based housing on rail commuting in
the San Francisco Bay Area, focusing on the self-selection question. Past research has

5
modeled mode choices among residents of transit-based housing using single logit model
structures (Cervero, 1994) or regression models based on highly aggregate data
(Pushkarev and Zupan, 1977; Bernick and Carroll, 1991; Parsons Brinckerhoff Quade
and Douglas, Inc., et al., 1995). Under a logit formulation, factors like travel times of
competing modes and demographic characteristics of trip-makers are used to predict
probabilities residents opt for rail transit to reach their workplaces. This research aims to
improve upon model specifications by rooting the analysis more firmly in urban location
theory – namely, by expressing mode choice as a derivative of peoples’ decision to reside
near a rail station. The decision to commute by rail, it is hypothesized, is significantly
explained by residential choice.
Using year-2000 travel data from the Bay Area, a nested logit model is estimated
that expresses the decision to live near a rail station as an antecedent to the decision to
commute via transit. Those whose workplaces are well-served by transit, and especially
those who live in less traditional, smaller households, are thought to be drawn to
residences that are well-served by transit. Transit-oriented living in turn is thought to
lower automobile ownership levels, further inducing transit ridership.
Besides improving model specification, framing mode choice as part of the
residential sorting equation can aid policy-making in several ways. One, transportation
planners can use the results to improve forecasts of ridership impacts (and related
mobility and air-quality benefits) of transit-based housing -- e.g., in testing a transit-
oriented development (TOD) scenario using a integrated land-use and transportation
modeling, such as the recently done in Sacramento (Hunt et al., 2001). Two, evidence on
rail usage among residents of transit-based housing can be used to establish credits and
off-sets against transportation impact fees. In the Bay Area, the Santa Clara County
Congestion Management Agency presently recommends a 9 percent reduction in
estimated trip generation levels when setting impact fees for new housing projects that lie
within 2,000 feet of a light rail or commuter rail station. Research can also help inform
policy initiatives like LEM programs by shedding light on the commuting cost savings of
transit-based housing. And for the growing legion of developers who are building
housing near rail stations, research on self-selection can throw light on the kinds of
households who are most inclined to move to station areas.

6
The demand for transit-based living, proponents argue, will likely increase on the
heels of America’s smart growth movement. One contributor to transit-based housing
could be changing demographics – e.g., baby-boomers reaching retirement age, forming a
market of empty-nesters who are apt to be more receptive to transit-oriented living;
increases in the share of non-traditional and childless households; and the steady influx of
foreign immigrants, some who bring with them a heritage of transit-oriented living
(Cervero, et al., 2002). Such trends underscore the value of studying the mechanisms that
shape mode choice among those living near rail stops.
2. ANALYTICAL FRAMEWORK
A conceptual three-tiered model of residential sorting, vehicle ownership, and
mode choice is shown in Figure 1. In this tree diagram, residential location is expressed
in binary terms: either one lives near (i.e., within ½ mile) of a rail station or not.
Residential location in turn influences car ownership levels, expressed in the figure as
zero, one-, and two-plus car households. The lowest level of the tree, mode choice, is
represented as a product, in part, of car-ownership. This nested model structure is
hierarchical and sequential, treating the influences of proximity to transit on mode choice
as indirect – i.e., channeled through the car ownership variable.
Multinomial logit (MNL) equations of the following form could be used to model
choice sets at each branch of the tree – i.e., residential, vehicle ownership, and commute
mode choices:
Pn,i = exp(Vn,i)/[Σj∈Cn exp(Vn,j)] (1)
Pn,i = probability person n chooses option i
Cn = choice set available to person n
Vn,i = measurable component of utility for person n choosing option i.
In the case of mode choice, the equation predicts the probability someone will choose a
private car, public transit, or some other travel means as a function of differences in
utilities among competing modes as well as attributes of the traveler, drawing its logic
from consumer choice theory (McFadden, 1974; Ben-Akiva and Lerman, 1985). The
utility of an alternative is a function of the explicit terms in the utility expression (Vn,i),
unknown parameters, and an additive, Gumbel-distributed error term. The assumption

7
that error terms are identically and independently Gumbel-distributed leads to a tractable
estimation of the model’s parameters. Whenever inter-related hierarchical relationships
exist, as in Figure 1, however, the assumption of independence breaks down, producing
potentially biased parameter estimates. This is because some of the alternatives are more
related to each other than others (e.g., zero-car households are more strongly a function
of transit-oriented living than 2+ car household). It is the relatedness among subsets of
utilities that violates the MNL model’s assumption of independence. Nested logit (NL)
models that explicitly account for interdependence among alternatives are preferred to
MNL under such circumstances (Sobel, 1980; Hensher and Green, 2002). Nested logit
has been used extensively to estimate mode choice wherein a lower level choice (e.g., bus
or rail) is a derivative of an upper level choice (e.g., transit), thereby accounting for the
correlation of utilities and unobserved effects. Past studies by Lerman (1976) and Anas

8
(1986) have adopted a similar model structure for estimating travel demand as a
consequence of residential location choice. Our study is, as far as we know, the first to
apply this approach to jointly model mode and residential location choices among those
residing near rail transit.
2.1 Case Context
The San Francisco Bay Area was chosen as a case context for this research for
several reasons. One, according to the Texas Transportation Institute, the Bay Area has
among the worst traffic congestion in the United States, ranking second in terms of
annual person-hours of delay in 2000 (Lomax and Schrank, 2002). Congestion
increases commuting costs, which in turn likely draws households to rail-served locations
that wish to economize on travel costs. Two, the Bay Area has among the highest
housing prices in the United States, prompting many households to give up private
single-lot living for smaller, more affordable units, some of which have been built by not-
for-profit housing corporations around rail stations (Bernick and Cervero, 1997; Parker et
al., 2002). Third, the Bay Area features a variety of inter-city rail services that are
intensively used for commuting, and each of the main systems serves a different
geographic setting – BART, which serves the East Bay plus the city of San Francisco; the
Valley Transit Authority’s (VTA) Light Rail Transit (LRT) system, serving the city of
San Jose and other communities in the Silicon Valley; and three commuter rail systems:
CalTrains (spanning San Mateo County between the cities of San Jose and San
Francisco); Altamont Commuter Express (ACE, connecting San Jose to pockets of
affordable housing in California’s central valley); and the Capitol Corridor Express (that
runs from the coastal areas of the East Bay to the city of Sacramento). Last, fairly recent
travel data were available from the Bay Area that supplied sufficient numbers of cases
and suitable variables to support the analyses.
2.2 Data Base and Sample Frame
The chief data base used to carry out this research was the 2000 Bay Area Travel
Survey (BATS) which contains up to two days of daily activity information for members
of 15,066 randomly selected households in the nine-county San Francisco Bay Area.
Trip records were extracted from the household activity survey, providing information on
the purpose, mode, longitudinal-latitudinal coordinates of origins and destinations, and

9
other features of the journey. Records were then extracted for commute trips (for
journeys in the home-to-work direction) that began in cities that have one or more rail
stations within their jurisdictions, excluding the city of San Francisco. We focused solely
on journeys to work since classic location theory holds workers trade-off commuting and
housing costs when choosing a residential location (Alonso, 1964). San Francisco
residents were excluded since residential sorting is thought to hold mainly for non-central
locations where high levels of transit services are limited to rail corridors. In dense cities
like San Francisco, residential sorting becomes less relevant since high-quality transit is
fairly ubiquitous. Also, we examined only commutes by motorized means since
residential location is mainly influenced by regional transportation systems, like
highways and rail transit, as opposed to neighborhood-scale bicycle and pedestrian
facilities.
To each trip record, we appended information about trip-makers (e.g., occupation)
and their households (e.g., vehicle availability) from the BATS personal and household
data files. Several additional sets of variables were also linked to each record. One set
consisted of 0-1 dummy variables that designated whether a traveler’s residence was
within ¼, ½, and one mile radii of an inter-city rail station in the San Francisco Bay Area.
(Rail systems that operate within a single city, like San Francisco Municipal Railway’s
light rail, trolley, and cable car services, were excluded since they do not provide regional
connectivity; this was necessary given that residential location choices were studied for
non-San Francisco residents.) Variables were also created to denote whether a traveler’s
workplace was within ¼, ½, or one mile distance rings of stations. Geographic
Information Systems (GIS) tools allowed us to pinpoint locations given longitudinal-
latitudinal coordinates. GIS was also used to estimate job accessibility indices via both
highway and transit networks, expressed as cumulative counts of year-2000 employment
(across traffic analysis zones) within 15, 30, 45, and 60 minute isochrones of residences.
GIS was likewise employed to measure neighborhood attributes, like densities and
median household incomes, for one-mile radii of residences and workplaces using year-
2000 census data and employment estimates maintained by the Association of Bay Area
Governments. Additionally, comparative network travel times for highway and transit
were assigned to each trip record using the Metropolitan Transportation Commission’s

10
1099x1099 work-trip travel-time matrices. In all, 14,285 observations were available
for estimating commute choice as well as residential location (near or not near rail
stations) and car ownership levels.1
We note that our research focuses on location and mode choices solely with
respect to inter-city rail systems as opposed to bus lines or other forms of mass transit.
This is because exclusive-guideway rail is generally more time-competitive with the
private automobile than conventional bus services and thus confers significant regional
mobility benefits, especially during congested peak periods. While residents plausibly
locate near rail stations to reduce commuting costs, it is hard to imagine many being
drawn to a bus route for this reason.
2.3 Model Structure
The three-tiered hierarchical model shown in Figure 1 suggests a sequential
selection process, however there is no a priori reason why this should be the case. The
decision to live near transit and reduce the number of cars in the household might be
jointly made, and indeed, the decision to routinely take rail to work might be bundled
with these choices as well. Absent any theoretical or empirical basis for modeling the
process sequentially, a simultaneous-nested logit procedure was chosen (using full
information from the lower nests to affect the scaling parameters of the upper nests).
More problematic in simultaneously modeling residential location, car ownership,
and commute-mode choice using year-2000 BATS data was the shortage of cases for
some of the choice sets at the lowest level. Notably, there were only 23 cases (less than
two-tenths of one percent of the sample) of persons who rail-commuted, lived within ½
mile of a rail stop, and owned no cars, rendering discrete choice modeling impractical
given so few degrees of freedom (Greene, 1997). Only a slightly larger share of the
sample consisted of rail commuters living near a station from households with two or
more cars.
In view of these degrees of freedom problems, a more parsimonious two-tier
model was estimated instead, with the upper tier gauging the binary choice of whether to
live near rail transit or not and the lower level indicating whether or not rail was taken to
work. Nested logit estimation occurred by weighing lower-level factors influencing rail

11
mode choice in the estimation of upper-level residential location choice. Nested
estimation acknowledges that the subset of utilities of mode alternatives is not
independent of the utilities that explain transit-based tenancy.
The two-tiered nested logit model used in our analysis took the form:
Pn,i│k = exp(Vn,i │k)/[Σj∈Cn exp(Vn, j │k)] (2)
Pn,k = exp(Vn,k + ΘkIk)/[Σj∈Cn exp(Vn, j │k + ΘkIk)] (3)
where, for the kth
branch of the upper tier, the inclusive term, Ik, is:
Ik = ln Σj∈Cn exp(Vn, j │k) (4)
Pn,i │k = probability person n chooses mode option i (e.g., rail) given
location choice k (e.g., near rail station)
Pn,k = probability person n chooses location choice k
Cn = choice set available to person n
Vn, j │k = measurable component of utility for person n choosing mode
option i given location choice k
Vn,k = measurable component of utility for person n choosing
location k
Θk = estimated coefficient on inclusive term for location choice k.
The expression ΘkIk captures feedback between the lower level (commute mode choice)
and upper level (residential location choice) of the nested model, where feedback is
presumed to occur simultaneously. The inclusive value parameter, theta (Θ), measures
the correlation among the random errors due to unobserved attributes of commute-mode
choice. Also referred to as a “coefficient of similarity”, significant theta values close to
one are suggestive of strong unobserved similarities between residential location and
commute choice whereas lower values connote weak similarities and negatives ones
suggest dissimilarities.
Among variables entered into the utility expression of residential location choice
model were workplace location (within a mile of a rail stop, expressed as a 0-1 dummy),
job accessibility via highway and transit networks, household characteristics (such as
whether or not a traditional two-adult household), vehicle ownership, and personal
attributes of adult members (such as race and profession). It is noted that a separate
multinomial model was estimated and is also presented. Both residential and workplace

12
location as well as job accessibility indicators and household socio-demographic
attributes were used to predict whether a household had zero, one, or 2+ cars.2
The
lower tier of the nested model in Table 1, estimated separately for those living near and
away from transit, included information on workplace location and car ownership levels
in addition to other conventional predictors of mode choice like travel-time ratios (over
the transit versus highway network for each origin-destination pair), neighborhood
densities, and personal attributes of trip-makers.
The dummy variable denoting whether a workplace was near rail, we note,
appears in both upper and lower tier models. Its presence in the residential choice model
is in keeping with theories on commute-cost minimization advanced by Alonso (1964)
and empirically tested by Giuliano and Small (1993) and others. The workplace location
variable appears in the lower nest, in part, as a refined metric of comparative travel times
via transit versus highway for origin-destination pairs. As commonly used in mode
choice modeling, we computed travel-time ratios using average peak-period centroid-to-
centroid durations over regional networks. This resolution of analysis, however, is too
coarse to reflect the potential door-to-door travel-time advantages of using transit when
one’s workplace is within walking distance of a train station. Thus more as a metric of
travel-time benefits and convenience at the egress end of a trip, dummy variables
denoting whether workplaces were within a 0 – ¼ mile ring and within a ¼ - ½ mile ring
of a station were used to better capture the utility of rail commuting.
Our decision to model location and mode choices binomially was based not only
on sample-size considerations but also a desire to frame the analysis so as to best support
public policy-making. As discussed earlier, recent policy interest in transit oriented
development (TOD) has focused almost exclusively on rail transit systems. In the United
States, TODs usually comprise a mix of retail, office, and housing development that
spans between ¼ mile and one-mile of rail stations (Calthorpe, 1993; Ewing, 1996;
Cervero et al., 2002). Thus, given that TODs are conceived as geographic entities with
boundaries and edges, their planning and design tends to be binary in nature – i.e., either
land lies within the TOD sphere or not. And given that the chief public benefit of TOD is
transit riding, travel demand is also best treated as binary as part of an integrated analysis
of residential location and commute choice. Furthermore, in the analysis that follows,

13
there were too few bus transit trips among those living near rail stops to support a tri-
modal model of motorized commute choice. Thus, bus trips were excluded from the final
analysis. The lower-tier model presented in the next section therefore represents mode
choice between rail transit and automobile (drive alone and shared-ride) alternatives.
3. EMPIRICAL RESULTS
Among the 11,369 cases with complete data for variables used in the nested logit
analysis, most individuals (91.4 percent) lived beyond ½ mile of a BART, light rail, or
commuter rail station. More than 90 percent of those in the sample, moreover, got to
work by private car. Simple statistics suggests that living near rail stops strongly
influenced commuting. Among those residing within ½ mile of a station, 19.6 percent
got to work by rail transit; among those living beyond the ½ mile radius, the share was
8.6 percent (Chi-Square = 157.1, probability = .000). The flip-side of this is that more
than 80 percent of those living within a walking distance of a Bay Area rail station drove
to work! Such simple cross-tabulations, of course, fail to control for other factors, like
comparative travel times, that explain mode choice, not to mention overlooking the
interdependence of residential location and commuting behavior.
Nested logit results are presented in Table 1. Full information maximum
likelihood estimation was used in deriving estimates. Variables were included in models’
utility expressions on the basis of theory as well as statistical fits. Partly because of
smaller sample sizes but also because more variables were available for specifying
commute-mode choice than residential location, better statistical fits were obtained at the
lower than upper level.
3.1 Residential Location Choice
The upper-level model, shown on the left-hand side of Table 1, predicts whether
someone lives within ½ mile of a rail station. Models were attempted for ¼ and one mile
radii as well, however the best-fitting and most interpretable statistical results were
obtained for the ½ mile radius. The literature is unclear as to what radius best constitutes
a comfortable walking distance to a station. Our nested structure, accounting for the

14
interdependence between residential location and mode choice, suggests a ½ mile radius
is most strongly associated with ridership.
The model results reveal that working within a mile of station induces households
to reside near transit, all else being equal. The one-mile workplace radius provided
much better statistical fits than the more restrictive ¼ and ½ mile radii, suggesting that
being within not only a walking distance but also a convenient feeder bus connection of a
work site weighs into residential location choices. Also instrumental in the choice to live
near transit is job accessibility via both highway and transit networks. The more jobs that
are within a 45-minute isochrone by car over the highway network or within 30 minutes
over the rail-bus network, the more likely one is to reside near a rail stop. The positive
association with transit accessibility stands to reason, however why might highway
accessibility also positively explain transit-based residency? We suspect this is
attributable to the fact that many rail stations in the Bay Area have good freeway access,
with some lying in freeway medians. This raises the possibility that some households
opting to reside near rail stops are also attracted by the close proximity to freeways. Also
of note is the fact that the best predicting job-accessibility isochrone was longer for
highways (45 minutes) than transit (30 minutes). This could reflect the willingness of
commuters to endure more time in the privacy and convenience of their cars than the
often crowded conditions of mass transit during commute hours.
In terms of household attributes, the model suggests that lower-income
households (making less than $40,000 annually) tended to be drawn to rail station areas,
all things being equal. This could be due to public policies that promote below market-
rate housing near rail stations, especially in the redevelopment districts that surround
many Bay Area rail stops. Under California law, at least 15 percent of housing produced
in redevelopment districts must leased or sold below market rates. On the other hand,
being a traditional household – defined as two adults between the ages of 25 and 54 years
with at least one dependent (normally a child) – discouraged transit-based residency.
Traditional households presumably value other factors, such as lower density living and
school quality, than proximity to transit when making residential choices.

15
Table 1. Nested Logit Model Results for Upper Nest (Rail Location Choice) and
Lower Nest (Rail Commute Choice). Note: Revised from original working paper
Upper Nest Lower Nest: Rail Commute
Location Choice:
Live Near Transit Live Near Transit Live Away from
Transit
Coef. T-Stat. Coef. T-Stat. Coef. T-Stat.
Location Factors
Workplace within ¼ mi. of rail station
(0-1) -- -- 0.703 2.92*** 1.149 10.87***
Workplace ¼ - ½ mi. of rail
Station (0-1) -- -- 0.477 1.82* 0.670 5.85***
Workplace within 1 mi. of
rail station (0-1) 0. 345 4.41*** -- -- -- --
Job accessibility index, highway
network, jobs (in 100,000s) within 45
minute isochrone of residence
0.013 2.10** -- -- -- --
Job accessibility index, transit network,
jobs (in 100,000s) within 30 minute
isochrone of residence
0.105 1.50 -- -- -- --
Transportation Attribute
Travel time ratio (transit
network/highway network, centroid to
centroid) -- -- -1.422 10.20*** -1.806 26.33***
Household/Neighborhood Attributes
0 cars in household (0-1) 1.931 7.16*** 3.468 6.20*** 3.394 9.48***
1 car in household (0-1) 0.859 6.95*** 1.537 4.24*** 0.709 5.88***
2 cars in household (0-1) 0.302 3.10*** 0.673 1.82* 0.400 3.72***
Lower-income household,
annual household income
< $40000 (0-1)
0.129 1.162
Traditional household (2 adults, 1+
dependents; mid-stage of lifecycle, adults
25-54 years of age) (0-1)
-0.206 2.55*** -- -- -- --
Neighborhood density (no. dwelling
units, in 10000s, within 1 mi. radius of
residence)
-- -- 0.287 1.48 0.219 2.81***
Personal Attributes
Driver’s License (0-1) -- -- -1.235 2.75*** -1.564 5.93***
Age 55+ years (0-1) -0.620 5.35*** -- -- -0.606 1.91*
Asian-American (0-1) 0.304 2.67*** -- -- 0.264 1.85*
Hispanic (0-1) 0.225 1.57 -- -- -- --
Sales-Labor Profession (0-1) -0.177 2.39** -- -- -- --
Theta (Live Near) 0.784 2.69***
-- -- --
Theta (Live Away) 0.620 2.03**
Constant -3.10 23.89*** 1.347 2.01** 1.985 5.33***
Summary statistics
No. of cases
Χ2 (prob.)
Rho-square (Nagelkerke)
10 968
368.2 (.000)
0.074
1,031
435.1 (.000)
0.521
10,338
2,864.9 (.000)
0.503
*Significant at 0.10 level **Significant at 0.05 level ***Significant at 0.01 level

16
Table 1 also shows that lower levels of car ownership (relative to the suppressed
category of 3+ cars per household) increased the chance of rail-based residency. We note
that car ownership likely influenced the decision to live near rail, however the opposite
likely also holds – living near rail reduced car ownership. The endogeneity of this
relationship is difficult to untangle with cross-sectional data, however we acknowledge
the possibility of endogeneity bias in our analysis.
From Table 1, also positively associated with the decision to reside near rail
stations were racial-ethnic, age, and occupational attributes of adult household members.
Asian-Americans and Hispanics tended to be more attracted to station areas than whites.
This could reflect a cultural dimension, especially in the Bay Area where many residents
are recent immigrants from Latin America and Asia, bringing with them a heritage of
transit-oriented living (Cervero, 1996). In contrast, older individuals and those working
in sales and as laborers tended to shy away from rail locations. This latter negative
association could reflect the car dependence of persons engaged in door-to-door sales and
among laborers (e.g., construction workers) whose job sites regularly change.
An indicator that nesting is appropriate is compliance with the McFadden
condition that holds the theta parameter on the inclusiveness term should lie within a
│0-1│ interval (McFadden, 1974). Both theta values meet this criterion and are
statistically significant at .05 probability level or better. Based on the signs of
coefficients, there appears to be unobserved similarities between rail commuting and
transit-based residency, contrasted by unobserved dissimilarities between rail commuting
and living beyond a half mile of a station. We infer that the nested logit structure
appropriately characterizes residential location and commuting for the Bay Area in year-
2000.
Car Ownership Model
While not estimated as part of the nested model structure, the multinomial logit
results shown in Table 2 indicate that both residential and workplace locations had strong
bearings on car ownership levels. Coefficient estimates reveal differences relative to the
suppressed category, zero-car households. Living within ½ mile of stations significantly

17
Table 2. Multinomial Logit Results of Household Car Ownership (1 Car, 2+ Cars; 0
Car Category Suppressed)
1 car in household 2+ cars in household
Coeff. T-Statistic Coeff. T-Statistic
Location Attributes
Reside within ½ mi. of rail station (0-1) -0.943 35.14*** -1.717 102.08***
Work within ½ mi. of rail station (0-1) -0.429 8.193*** -0.890 33.22***
Job accessibility index, auto network,
isochrone of residence 0.031 1.98 0.032 2.02
Job accessibility index, transit network,
isochrone of residence -0.191 1.70 -0.250 2.73*
Household Attributes
Household size, no. persons 0.114 1.94 1.071 170.02***
Lower-income household: <$40,000
annual income (0-1) -2.031 56.16*** -3.961 208.08***
Middle-income household: $40,000 to
$75,000 annual income (0-1) -0.871 9.92*** -1.952 50.02***
Own residence (0-1) 0.881 22.47*** 2.005 114.58***
African-American householder (0-1) -0.376 2.59* -1.183 22.40***
Constant 4.004 137.31*** 2.796 66.22***
Summary Statistics
No. of cases = 2,760 1-car households &
9,696 2+ car households
Chi-Square (prob.) = 5,243.0 (.000)
Rho-Square: 1 - L (1)/L (0) = .341
*** significant at .01 level
** significant at .05 level
* significant at .10 level
lowered the likelihood of having one car, and lowered them even more for the two-or-
more car option. These findings lend empirical support to the Location Efficient
Mortgage (LEM) concept as well as zoning codes that lower parking standards for
housing projects near rail stops, such as introduced over the past decade in Portland,
Oregon and Montgomery County, Maryland. Working near rail also lowered the odds of
owning two or more cars, though more weakly than in the case of rail-based living.
Predictably, job accessibility by highway positively influenced car ownership whereas
job accessibility by transit was negatively associated, all else being equal. Among
household attributes, car ownership tended to increase with household size and home

18
ownership and was generally lower among African Americans and for low and middle
income households.
Commute Mode Choice Model
The right-hand side of the nested logit model from Table 1 presents the commute-
mode choice results, stratified by those who live within ½ mile of a station and those who
do not. Even controlling for residential location, working in close proximity to transit
significantly affected the odds of rail commuting. As noted previously, these dummy
variables help to augment the coarser measure of comparative zone-to-zone travel times
by providing a finer-grained measure of a destination’s proximity to transit. Coefficients
suggest a gradient effect, with the likelihood of rail-commuting greatest for workplaces
within ¼ mile of a rail stop and higher for the ¼ to ½ mile ring than the suppressed
category of ½ mile and beyond. Consistent with mode-choice theory, the travel-time
ratio was by far the strongest single predictor of whether one commuted by rail transit.3
While car ownership was not imbedded into the nested logit structure, it clearly
exerted a strong influence on rail commuting as a direct predictor variable. Living in a
zero-car household significantly increased the odds of rail commuting, both for those
living near and away from stations. Having one and two cars also increased the odds
(relative to the suppressed category of 3 or more cars), although not as strongly as being
in a carless household. Together, the findings that transit-oriented living reduces car
ownership and that fewer cars are associated with transit commuting lends empirical
support for reduced, or at least flexible, TOD parking standards.
Lastly, Table 1 shows that personal attributes also influenced mode choice. Most
important was the presence of a driver’s license, which tended to deter rail commuting,
even after controlling for car ownership levels. Among those living away from transit,
the likelihood of rail commuting tended to be lower for workers above 55 years of age
and higher for Asian-Americans.
4. PROBABILITY ESTIMATION AND SENSITIVITY TESTING
The nested logit results allowed conditional probabilities to be estimated, which
were used to further probe the self-selection process and to conduct sensitivity tests. This
section presents these supplemental analyses.

19
4.1 Probabilities and Self Selection
The probability of commuting by rail (R) can be expressed as the sum of the joint
probabilities of taking rail and living near transit, p(R & NT), and of taking rail and living
away from transit, p(R & AT). These joint probabilities, in turn, can be derived from the
conditional probabilities generated from the nested logit output:
p(R) = [p(R & NT) + p(R & AT)] =
{[p(NT)* p(R │NT)] + [p(AT)* p(R │AT)]}. (5)
Using equation 5, probabilities of rail commuting were computed for the 11,533
sample cases used in estimating the nested logit models. Figure 2 plots probabilities of
rail commuting by places of residence (i.e., according to longitudinal-latitudinal
coordinates) in relation to BART, CalTrain, and VTA light rail transit services. Figure 3
zooms in on plotted probabilities along BART corridors in the East Bay (Alameda and
Contra Costa Counties).5
(Note that the City of San Francisco is omitted from the maps
since it was excluded from the analysis.) The figures reveal that the spatial relationship
between ridership and proximity to rail stops is fairly strong in the urbanized portions of
the East Bay (particularly for the bay-shore cities of Oakland and Berkeley) and weaker
as one moves outward from urban centers. Along the CalTrain corridor in San Mateo
County and in much of Santa Clara County, no discernable spatial relationship appears to
exist. The absence of distinct patterns in these lower density, more outlying settings is
likely attributable to the reliance upon park-and-ride as a means of accessing suburban
rail stops. Park-and-ride diminishes the value of living within walking distance of
stations.
From the 11,533 sample cases, the following probability averages were computed
for the upper level and lower levels of the nested logit model:
p(NT) = .0880
p(AT) = .9120
p(R │NT) = .1547
p(R │AT) = .1144

20
Figure 2. Probability Plot of Rail Commuting Among Sampled Residents of Four
Rail-Served Counties in the San Francisco Bay Areas (Excluding San Francisco):
Alameda, Contra Costa, San Mateo, and Santa Clara Counties

21
Figure 3. Probability Plot of Rail Commuting Among Sampled Residents of
Alameda and Contra Costa Counties in the East Bay

22
where NT = “live near transit”, AT = “live away from transit”, R │NT = ”rail commute
given live near transit”, and R │AT = “rail commute give live away from transit”. From
these results the following joint probabilities were computed:
p(R & NT) = [p(NT)* p(R │NT)] = (.0880)(.1547) = .0136
p(R & AT) = [p(AT)* p(R │AT)] = (.9120)(.1144) = .1043
Inputting these values into equation 5 produced the following average probability of rail
commuting:
p(R) = .0136 + .1043 = .1169
In words, the model predicts that well over 90 percent of Bay Area households reside
beyond ½ mile of a rail stop, comparable to the sample proportion. All else being equal,
if a Bay Area worker lived near transit, the odds of them rail-commuting was higher than
if they lived away from transit – on average, a 15.5 percent versus 11.4 percent
likelihood. Still, most workers living near stations were not likely to rail-commute: the
average probability of not rail-commuting, 84.5 percent, was also in line with the sample
proportion. The overall likelihood of rail commuting, regardless of place of residence,
was 11.7 percent. The joint probability estimates reveal that a large majority of Bay Area
rail commuters live away from transit, underscoring the importance of providing ample
park-and-ride facilities and good bus feeder connections in serving this market.
The influence of self-selection on transit ridership can be inferred by comparing
odds ratios based on mean conditional probabilities of rail commuters living near
[p(R │NT)] versus away from [p(R │AT)] stations. For those living near stations, the
average odds ratio of rail commuting is .1830 (.1547/.8453). Among those living beyond
½ mile of stations, the average ratio is .1292 (.1144/.8856). And among the entire
sample, the mean odds ratio is .1324 (.1169/.8831). Thus, the odds of rail commuting are
41.6 percent [(.1830/.1292)*100] greater if one lives near versus away from transit, all
else being equal. Compared to the typical Bay Area rail commuter, the odds of taking a
train to work are 38.2 percent [(.1830/.1324)*100] higher for those residing near stations.
By inference, the approximately 40 percent greater odds of rail commuting among those
living near stations is due to proximity since the logit models directly controlled for the
influences of other factors like comparative travel times, places of work, and socio-
demographic characteristics of travelers and their households. One could interpret this to

23
mean that around 40 percent of the higher rail-commuting shares among Bay Area
workers living near transit are explained by self-selection. This inference equates
proximity to stations with residential self-selection, once other factors are statistically
controlled. Given the above-calculated differences in odds ratios and the fact that many
other mode-choice factors were imbedded in the utility expressions of the nested logit
models, we feel this reasonably reflects the degree to which self selection explains higher
ridership among those residing near rail transit.
4.2 Sensitivity Testing
The affects of several policy variables on the likelihood of rail commuting were
probed by conducting sensitivity tests. This was done by inputting average values of
control variables in the utility expressions of the lower-level mode-choice models.4
Values of policy variables, like car ownership levels and travel-time ratios, were then
systematically varied to gauge likely changes in the probability of rail commuting for the
typical Bay Area worker.
One sensitivity test recorded how probabilities varied by travel time ratios among
those living within ½ mile of a Bay Area rail station versus those living beyond ½ mile.
Consistent with the mode-choice results, Figure 4 shows probabilities varied sharply with
travel-time ratios, both for those living near and away from transit. If transit travel is
twice as fast as by car, the models predict that more than half of both sets of commuters
will get to work by train. For the median case in the sample wherein it takes 2.25 as
much time to get to work via transit as automobile, there is around an 7 percent
differential in the probability of rail commuting for those living near versus away from a
station – i.e., 0.12 versus 0.05 probability. The largest probability differential, 10
percent, is for a travel-time ratio of 1.50.
A second set of sensitivity tests examined how probabilities varied as a function
of three policy variables: residential location (within ½ mile of a station or beyond);
workplace location (within ¼ mile of a station or beyond); and household car-ownership
levels (0, 1, 2, 3+). The resulting sensitivity plot, Figure 5, shows probabilities of rail
commuting are very high among all groups when the worker lives in a zero-car
household. Adding one car results in probabilities plummeting for all groups; they fall
most precipitously for those residing and working away from stations. For residents of

24
0
0.1
0.2
0.3
0.4
0.5
0.6
0
.
5
0
0
.
7
5
1
.
0
0
1
.
2
5
1
.
5
0
1
.
7
5
2
.
0
0
2
.
2
5
2
.
5
0
2
.
7
5
3
.
0
0
3
.
2
5
3
.
5
0
3
.
7
5
4
.
0
0
Travel Time Ratio (Transit/Highway)
Probability
Commute
by
Rail
Live within ½ mile of station
Live beyond ½
mile of station
Figure 4. Sensitivity Plots of Rail-Commute Probabilities by Travel Time
Ratios for Those Living Near and Away from Stations
transit-based housing, probabilities fall more gradually with car-ownership levels. For
those living away from transit, the likelihood of rail-commuting is not much different
between two-car and three-or-more-car households. And for those living and
working away from a rail stop, the odds of commuting by rail is about the same for a one
and 3+ car household – less than 1 to 10.
Figure 5 also reveals that working near transit interacts with car-ownership levels
to produce different probabilities among station-area dwellers and their counterparts.
Working near transit and having no cars means there is a very high likelihood, well over
80 percent, of rail-commuting for both groups. Adding a car to the household results in

25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 1 2 3+
Number of Cars in Household
Probability
Commute
by
Rail Reside Near/Work Near Rail
Reside Away/
Work Away from
Rail
Reside Near/
Work Away from
Rail
Reside Away/
Work Near Rail
Figure 5. Sensitivity Plots of Rail-Commute Probabilities by Number of Cars in
Household for Those Living and Working Near and Away from Stations. Reside
Near = ½ mile or less; Work Near = ½ mile or less.
the probability dropping far more sharply for non-station-area residents, however –
notably, to below the probability (0.28) for station-area residents who work beyond ¼
mile of a station. This suggests that an appreciable share of station-area dwellers who
rail-commute do so out of choice rather than necessity, further hinting that self-selection
has taken place. Adding a second car to a station-area household, however, reduces the
probability of rail-commuting sharply, below that of a non-station-area worker from a
two-car household whose job site is near a rail stop. This indicates that the transit-
ridership benefits of transit-based housing come from those with relatively few – i.e.,
under two – cars in the household. This lends further credence to the view that below-
code parking standards are appropriate for housing projects near rail stations.

26
5. SELF-SELECTION AND TRANSIT-BASED HOUSING POLICIES
Our nested logit results suggest interdependence between transit-oriented tenancy
and rail commuting, lending empirical support to the argument that self-selection
significantly accounts for the ridership bonus of TODs. These results are consistent with
other research showing that compact, mixed-use neighborhoods reduce car travel, partly
because those who dislike driving consciously choose to live in such settings (Boarnet
and Sarniento, 1998; Boarnet and Crane, 2001). A chief difference, however, is that
studies on the influences of urban designs on trip generation rates have employed
multiple regression and instrumental variable estimation to account for the inter-
relatedness of residential location and travel; for purposes of studying discrete choices,
however, we adopted a nested logit structure to gain similar insights.
The presence of residential self selection does not in any way diminish the value
or importance of targeting housing development to transit station areas. If anything, it
underscores the importance of removing barriers to residential mobility so that
households are able to sort themselves, via the marketplace, to locations well-served by
transit. Public policies should focus less on designing TODs in response to, say, political
smart-growth agendas and more on expanding market opportunities that allow those who
wish to live near transit to act on their preferences. In particular, more flexible, market-
responsive zoning should be introduced in and around rail stations that are poised for
residential development. Some U.S. rail cities, notably San Diego and Mountain View,
California, Portland, Oregon, Bethesda, Maryland, and Arlington, Virginia, have been
pro-active in this regard (Cervero, et al., 2002). Most, however, have focused on zoning
for commercial development in hopes of producing higher property tax receipts than
normally yielded by housing projects. In a review of land uses near more than 200
existing and proposed rail stations in Southern California, Boarnet and Crane (1998)
found little evidence of zoning for residential TODs in local zoning ordinances. They
inferred that, in Southern California at least, zoning for housing is viewed as less fiscally
remunerative, thus conflicting with large economic development goals.
Besides supportive zoning, a number of other recent public policy initiatives have
been introduced in recent years that could spur the production of transit-based housing.
One already discussed is Location Efficient Mortgages (LEMs), underwritten by Fannie

27
Mae and several private banks, that makes it easier to qualify for a loan to purchase a
home situated near transit under the premise that lower transportation costs free up
earnings for housing consumption. Another noteworthy federal action is the Federal
Transit Administration’s new joint development rulings that allow transit agencies to sell
land, such as parking lots, to private interests without returning the proceeds to the
federal treasury as long as the resulting development is “transit-supportive” in its design
and tied to a specific plan aimed at station-area redevelopment. To date, transit
properties in Washington, D.C., Atlanta, Portland, Southern California, and the San
Francisco Bay Area have exploited this new ruling to leverage affordable housing
projects on former parking lots. In the San Francisco Bay Area, several public agencies
have been particularly pro-active in promoting transit-based housing. The Metropolitan
Transportation Commission has set aside $9 million under a Housing Incentive Program
(HIP) as grant funds for local jurisdictions that locate compact housing near transit. To
qualify for funds, a housing project must be within a one-third mile walk of a rail station,
ferry dock, or bus route and provide at least 25 units per acre. Grants of $2,000 per unit
are being provided for projects built at 60 units to the acre. In fiscal year 2000-2001, HIP
funding helped to create 5,323 units of new housing and 2,060 affordable bedrooms
within one-third mile of a Bay Area rail or bus line. Even sub-regional governments have
introduced incentive programs. The San Mateo City-County Association of
Governments (C/CAG) authorizes $2,000 in State Transportation Improvement Program
(STIP) funds for each bedroom built within one-third of a mile of a rail station and at a
density of 40 units per net acre or more. In fiscal year 2000-2001, more than $2.2 million
of STIP funds were transferred to local governments as a reward for adding more than
1,200 bedrooms in high-density housing near rail stops.
In close, residential self-selection underscores the importance of zoning for
adequate housing production near rail stations as well as breaking down barriers to
residential mobility to enable the demand for station-area living to be met. Programs like
Location Efficiency Mortgages and Housing Incentive Programs that promote station-
area living hold promise not only for redressing affordable housing problems in pricey
real estate markets like the San Francisco Bay Area but also in enhancing urban mobility
by expanding commute choices. Public policies that recognize transit commuting and

28
residential location are jointly related can meaningfully contribute to the attainment of
such important societal goals.
Notes
1. Since each one-way commute record was for a single person, location choice models
were estimated for each person (given their residential longitudinal-latitudinal
coordinates) using the same data base. Similarly, household information for each
surveyed person was used to estimate household car ownership levels.
2. The definition of “cars” included vans, minivans, panel trucks, and sports utility
vehicles, but excluded motorcycles, recreation vehicles, and commercial trucks kept at
one’s residence.
3. Various forms of travel time were attempted as part of the nested logit modeling,
including absolute differences as well as absolute values of zone-to-zone travel times via
transit networks and highway networks. In all instances, the travel-time ratios provided
the best statistical fits.
4. For ratio-scale variables except travel-time ratios, statistical means were inputted. For
the travel-time ratio variable, median values were used instead since the sample
distribution was skewed toward high values (due to some suburban areas having virtually
no transit services, producing very high ratios). For nominal-scale (0-1) variables, the
most frequently occurring (i.e., modal) categories were used in the sensitivity tests. The
mean values of the ratio-scale variable neighborhood density were 7,100 and 6,300 units
per mile radius for those living near and away from transit, respectively. The median
values for travel-time ratios were 2.25 and 2.50 for those living near and away transit,
respectively. The most frequently occurring categories for nominal-scale (0-1) variables
(for both those living near and away from transit) were: workplace with ¼ mile of station
(0); workplace ¼ to ½ mile form station (0); zero-car households (0); one-car households
(0); two-car households (1); driver’s license (1); age 55+ years (0); and Asian-American
(0).
5. The IDW (inverse distance weighting) procedure was applied in creating the plotted
probability surfaces using the Spatial Analyst tools of Arcview, produced by
Environmental Systems Research Institute, Inc. (ESRI).

29
Acknowledgement
Alfred Round helped in compiling records from the 2000 BATS data base used to support
this analysis.
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