Post on 07-Feb-2023
Article
Locational Choices: Modeling ConsumerPreferences for Proximity to Othersin Reserved Seating Venues
Simon J. Blanchard, Tatiana L. Dyachenko, and Keri L. Kettle
AbstractThis article proposes a measurement approach to determine how consumers prefer to locate themselves in proximity toothers during consumption experiences, such as when they purchase reserved seating tickets to a performance. Applied to datafrom locational choice experiments that simulate reserved seating assortments, administered to more than 2,000 participants,this approach reveals the importance of modeling proximity to others when studying locational choices. It also emphasizes thedegree to which consumers are heterogeneous in their preferences for proximity to both focal elements (e.g., stage, screen,aisles) and other consumers. Therefore, event operators should collect data beyond purchase ticket logs and also includeconsumers who did not purchase. Furthermore, this study illustrates how managers can use fitted, individual-level parametersand an optimization model to make more effective seat-level availability decisions. In addition to these recommendations formanagers of reserved seating venues, this article offers novel contributions to research related to advance selling, spatialmodels, and personal space.
Keywordsadvance selling, concert halls, locational choices, personal space, movie theaters, spatial models
Online supplement: https://doi.org/10.1177/0022243720941525
When consumers visit a theater or book a flight, they agree to
locate themselves near strangers, a situation that demands a
locational choice. Such choices represent common but also
challenging human experiences, with considerable implica-
tions for the ultimate consumption experience. For activities
such as sporting events and concerts, consumers might derive
utility from sharing a communal consumption experience (Holt
1995) and enjoying their shared reactions (Gainer 1995). Yet
close proximity to strangers also can create discomfort, which
consumers aim to minimize (Argo, Dahl, and Manchanda
2005; Maeng, Tanner, and Soman 2013; Szpak et al. 2015).
Given these distinct goals, people’s locational preferences vary
widely across both different environments and individuals. A
pregnant film consumer might prefer to sit near the aisle, know-
ing that she will need to leave her seat frequently during the
show; another consumer might prefer to sit near the back to
avoid having anyone behind her who might kick her seat; and
yet another may prefer sitting in the middle of the row to get the
best view of the screen.
Noting the importance of these locational preferences, many
venues try to accommodate consumer heterogeneity in a way
that benefits their firm-level outcomes. Reserved seating sys-
tems, available through in-theater kiosks or online seat maps,
allow movie theater consumers to maximize their individual
locational preferences, with likely benefits for the provider as
well. Because proximity to preferred focal elements in the
consumption space (e.g., movie screen, aisles) and to others
can influence consumers’ enjoyment and satisfaction (Pedersen
1977), these systems can (1) offer the promise of additional
revenues if firms charge a premium for the most desired loca-
tions (Xie and Shugan 2001), (2) increase the likelihood that
consumers make supplementary purchases (Gardete 2015), and
(3) enhance customer responses to marketing promotions
(Andrews et al. 2015).
To attain positive firm-level outcomes, venues first must
understand how individual-level locational preferences affect
Simon J. Blanchard is Beyer Family Associate Professor of Marketing,
Georgetown University, USA (email: simon.blanchard@georgetown.edu).
Tatiana L. Dyachenko is Assistant Professor of Marketing, University of
Georgia, USA (email: tatiana.dyachenko@uga.edu). Keri L. Kettle is Assistant
Professor of Marketing, University of Manitoba, Canada (email: keri.kettle@
umanitoba.ca).
Journal of Marketing Research2020, Vol. 57(5) 878-899
ª American Marketing Association 2020Article reuse guidelines:
sagepub.com/journals-permissionsDOI: 10.1177/0022243720941525
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occupancy (i.e., whether most seats are taken when an event
begins). Operators prefer high occupancy and use various stra-
tegies to ensure that most seats are taken most nights (Desiraju
and Shugan 1999; Kim, Natter, and Spann 2009).1 Prior to the
start of an event (when consumers still can purchase tickets), an
assortment of seats surrounded by others or in less desirable
locations may lead consumers to decide not to purchase. If they
do purchase tickets, their proximity to others in crowded spaces
may lead consumers to reduce their time spent in the venue
(Hui, Fader, and Bradlow 2009) or blame any negative expe-
rience on the firm, which may decrease their future consump-
tion (Wangenheim and Bayon 2007).
To understand which data operators typically use to exam-
ine locational preferences, in support of our research goal of
determining which data might enable them to identify drivers
of occupancy more accurately, we conducted a survey of 45
managers and operators of movie theaters and concert halls,
with the help of a panel company.2 As we expected, most of
these venues (77.7%) offer advance seat selection online or
through an on-site kiosk, and two-thirds mentioned their access
to a dashboard that provides them an aggregate view of which
seat locations have been purchased. Furthermore, the majority
(64.4%) stated that they try to collect information about what
drives consumers’ decisions not to purchase, but the informa-
tion collected tends to be limited to individual consumer names
and text comments (e.g., complaints) or relies on anonymous
surveys with multiple choice questions.
Another potential source of information is purchase logs,
which often are contained in the dashboards that depict aggre-
gated seat maps of upcoming and past events. By using these
logs, managers can determine how locations’ popularity varies
as a function of proximity to focal elements (e.g., screen, aisles,
exits). If firms construct their logs to facilitate reconstructions
of individual-level assortments, they can enhance their under-
standing and predictions of occupancy, using individual-level
models that incorporate the substantial heterogeneity in loca-
tional preferences.3 However, even if these individual-level
assortment data were combined with the best individual-level
models, such analyses would pertain only to choices that
resulted in a purchase.
With the present investigation, we argue that to influence
occupancy, reserved seating venues need to leverage
individual-level assortment data from consumers who did not
purchase as well as those who did. Therefore, we propose a
novel measurement approach that makes three key contribu-
tions. First, seat choice predictions based on aggregate data and
model results are inherently limited, because locational prefer-
ences are highly heterogeneous across contexts and individual
consumers. Therefore, we establish a practical need to collect
individual-level locational choice data and analyze them
according to individual-level preferences for proximity to focal
elements (e.g., screen, stage) and to other consumers. Second,
we argue that operators that need to predict and understand the
drivers of event occupancy should collect data that include the
assortments presented both to those who purchase seats and to
those who ultimately do not purchase. With such data, opera-
tors can make more effective seat availability decisions at the
seat level. Third, we propose a specific, novel mechanism (i.e.,
seat-level availability based on locational preferences), whose
effectiveness can be further investigated as a driver of
occupancy.
Drawing on psychology literature pertaining to perceptions
of personal space, we present a measurement model to capture
the decision-making process for locational choices in the next
section. This utility specification captures heterogeneous pre-
ferences for proximity to both focal elements and other con-
sumers and can be readily estimated using hierarchical Bayes
analyses. In four experiments involving 2,119 participants, we
present two analyses of common locational choice experiences
with reserved seating (attending a concert or a movie), while
varying the number of locations to be chosen (single vs. a pair
of seats). We show that consumers are heterogeneous with
respect to their locational preferences, depending on both the
event type (concerts vs. movies) and whether they are attending
with someone else. We provide evidence that our measurement
and estimation approach provide excellent prediction accuracy.
In turn, we illustrate how operators can use our parameter
estimates to improve expected occupancy by altering seat
availability. For this illustration, we first describe a seat-level
availability optimization model that maximizes occupancy
based on trained parameter estimates. Then, using observa-
tional data obtained from local ticket sales, we apply the pro-
posed optimization model to identify which additional
locations should be marked as unavailable. We also provide
preliminary experimental evidence that seat-level availability
based on estimated locational preferences can be leveraged to
improve expected occupancy rates.
1 A focus on occupancy as a metric is common, because gross revenue mainly
comes from ticket sales, even if reserved seating venues also enjoy higher
profit margins from food and beverage sales. For example, AMC Theatres
reports a gross profit margin of 49.2% but a profit margin of 83.6%
specifically for food and beverage sales. Still, the importance of occupancy
in driving profitability is evident in earnings announcements, which primarily
focus on “attendance per screen” (AMC 2019)2 The average age of these respondents was 36.70 years (min ¼ 21 years, max
¼ 72 years), 60% were women, and they noted average managerial experience
of 7.73 years (min¼ 1, max¼ 30), involving 26–50 employees and an average
of 10 screens or stages (min ¼ 1, max ¼ 60). Twelve informants were concert
theater/hall operators, and 33 were movie theater operators. We paid $18 per
participant.3 Time-stamped lists of seat choices might not accurately reconstruct the
precise choice set for each consumer. In our discussions with operators, they
offered various reasons for the lack of detailed choice data. For example,
front-end sales systems often restrict seat offerings to facilitate consumers’
choices, but those restrictions are not recorded. Seat changes also may be
collected separately from purchases, and they often reflect specific price
tiers. Finally, locations may be released sequentially or depend on fare
restrictions or shopper status (Williams 2018), such that some consumers
have options that other consumers do not. In most data we have seen,
purchase logs need to be augmented with availability data to recreate
accurate individual-level assortments.
Blanchard et al. 879
Consumer-Level Locational Choice UtilitySpecification
We begin by assuming that consumers aim to maximize the
realized utility of a selected location, given the options avail-
able to them. The locational choice element we consider is a
grid, in which each potential location can be assigned a set of
Cartesian coordinates from the set of all possible coordinates,
St. The probability that consumer h in task t chooses a location
assigned to row i and column j is thus (we omit h throughout
the text, for expositional clarity):
Pr�
yt ¼ ði; jÞj ��¼ Prðut;ij ¼ maxfutgÞ; ð1Þ
where ut is the set of realized utilities for available locations,
and the utility for location fi; jg is
ut;ij ¼ Vt;ij þ et;ij 8fi; jg 2 SAt : ð2Þ
Here, Vt;ij is the deterministic component of the utility func-
tion, and SAt � St is the subset of coordinates that captures
all available locations for a specific task t. Assuming that
the error Et;ij in Equation 2 comes from an extreme value
Type I distribution with a location parameter 0 and scale
parameter 1, the probability of selecting location fi; jg in
task t is
Pr�
yt ¼ ði; jÞj ��¼ expðVt;ijÞXfk2SA
t gexpðVt;kÞ
: ð3Þ
In the sections that follow, we detail the two main com-
ponents of our consumer-level utility function Vt;ij: (1)
proximity to focal elements in the space and (2) proximity
to others.
Utility from Proximity to Focal Elements
In a locational choice, many aspects of the environment are
directly relevant to the consumption experience. For example,
concertgoers attend to the position of seats relative to the stage,
and moviegoers evaluate the position of seats relative to the
screen. However, within a venue, other physical elements of
the space could be important. For example, being on one edge
of a space can be important for some consumers (e.g., being
next to an aisle enables the consumer to leave more easily);
physical and psychological factors also could lead consumers
to focus more on specific aspects of the environment, such as
reference points established through experience or expecta-
tions. For example, when choosing a seat at a movie theater,
consumers may prefer a central location because they believe
the center of the room provides the best viewing angle and
sound quality. Thus, the desired level of proximity to focal
elements likely varies across individual consumers (e.g., some
people insist on aisle seats) and context (e.g., a consumer might
prefer to be close to the stage for a rock concert but in the
middle for a movie).
To define the attributes of single-person locational choice
options formally (i.e., available seats4), we denote XL;t as a
design matrix for a layout t with two dimensions: xrtas a vector
of row assignments (front-to-back) and xctas a vector of col-
umn assignments (left-to-right), within the Cartesian coordi-
nate system:
XL;t ¼ ½xr;t xc;t�: ð4Þ
We transform the elements in XL;t to restrict them between 0
and 1, reflecting the bounded nature of the environment and the
characteristics of each location, relative to the focal elements.
We use indexes for the rows to identify the front (i.e., where the
person faces) and back. For each location, a value of xr;t close
to 0 indicates a seat closest to the focal element (front), whereas
1 signals a location that is farthest from this focal element
(back). The indexes for columns instead refer to the lateral
dimension, corresponding to the edges of the environment as
reference points. A value of xc;t close to 0 on the lateral dimen-
sion refers to a location that is the farthest left possible in the
environment (left to right), and xc;t close to 1 is the rightmost
location. Location fxr;t xc;tg ¼ f:5 :5g thus represents the
center of the room.
The attribute space denoted by Equation 4 assumes that only
one seat is chosen. However, it is fairly safe to assume that a
consumer choosing a pair of seats for an event would consider
the two locations jointly and not independently. One way to
handle this dependence, as we observe in all our data and as
intuition would suggest, is to assume that most consumers
looking for two seats only consider two seats side-by-side in
the same row. If we assume two seats are selected and that they
must be contiguous in the same row, the design matrix in
Equation 4 can be adapted for pairs of seats to
xc;t ¼ :5ðxc1;t þ xc2;tÞ, where c1 and c2 are the column coordi-
nates of two available and contiguous seats (i.e., assumed
choice for pairs of seats). For the choice of a pair, xr;t does not
change, but xc;t is the midpoint between the two seats.
The design matrix XL;t thus provides a way to describe
available locations in the environment, but preferences for each
location also depend on the utility for the individual consumer,
as detailed in Equation 2. To accommodate the various ways in
which a location’s position affects consumers’ choices, as a
result of its proximity to focal elements, we specify this com-
ponent of the deterministic part of the utility function as a
bivariate quadratic function (we omit the subscript t for exposi-
tional clarity):
VL ¼ br;1x2r þ bc;1x2
c þ br;2xr þ bc;2xc þ br;cxrxc: ð5Þ
There is no intercept, and the preference parameters’ bs are
estimated relative to preferences for a seat with xr ¼ 0 and
xc ¼ 0, for identification purposes. Equation 5 is a flexible
4 Options within a locational choice (locations) may or may not be actual seats.
A movie theater may offer wheelchair-accessible locations, for example. We
still refer to them as seats.
880 Journal of Marketing Research 57(5)
specification that allows for heterogeneous effects of proximity
to focal elements. For example, considering their preferences in
the lateral dimension (left to right), consumers attending a
movie likely prefer to be located near the center of the room,
so the closer xL;th ¼ ði jÞ is to ð:5 :5Þ, the greater their
utility for a central location. However, some might prefer to
sit all the way to the left or right so that they can position
themselves near an edge in the space. Furthermore, the prox-
imal and lateral dimensions might interact; consumers attend-
ing a concert might be willing to forgo the best viewing angle if
they can get very close to the stage, for example.
The specification in Equation 5 provides several advantages
in terms of our effort to reflect heterogeneous preferences
regarding the ideal proximity to focal elements. The function
may have a vertex that represents either a utility maximum or a
minimum. For example, a person who wants a seat exactly in
the middle of the theater would produce a concave function on
both dimensions, with maximum utility at the center. However,
a person who wants to avoid the center and sit close to an aisle
instead produces a convex function across columns, with
higher utility at the edges. The location of the vertex also might
shift with changes in layouts and venues, in which the focal
point is not necessarily the center of the environment. A linear
functional form without the quadratic term is a special case of
Equation 5, when br;1 ¼ 0 and bc;1 ¼ 0. The parameter br;c
captures the potential interaction—whether a trade-off or a
compensating relationship—between the front-to-back (row)
and left-to-right (column) dimensions.
(Dis)utility from Proximity to Others
Because each potential location features proximity to others,
we seek to capture the potential (dis)utility of numerous imme-
diate and less proximal others.
Capturing the effect of immediately proximal others. Immediate
proximity may be sensed in any direction, so we use Lp spaces
to specify a one-unit L1 sphere around each seat (i.e., the dis-
tance between an available location and any other is determined
by the greatest distance along any coordinate dimension).
Because each seat varies in the number of seats around it, we
capture the presence of immediate others as the proportion of
locations at the boundary of the sphere (R1) that also are occu-
pied by others.
Formally, assume that consumer h is considering an avail-
able seat ði; jÞ for choice task t, and St is a set of the coordinates
of all seats in the environment, such that ði; jÞ defines the
origin (i.e., coordinates are centered at ½i; j�). We set attribute
xi;jR1 ¼ jSB
R1j=jSR1j, where SR1 ¼ fa 2 St : jjajj1 ¼ 1g; in addi-
tion, SBR1 � SR1 refers to the subsets of seats already occupied
by others. Therefore, xi;jR1 captures the proportion of seats at
exactly one unit away (in one or more dimension) that are occu-
pied by others. Proximal locations that do not offer seats (e.g., the
aisle is to the left) thus are not immediately proximal locations.
Finally, xR1 provides the row vector of all available seats, andbR1
is the corresponding parameter. Then the equation
VR1 ¼ xR1bR1 ð6Þ
captures the component of the utility from being surrounded by
others (i.e., proportion of occupied seats at the boundary of the
L1 one-unit sphere).
Although Equation 6 may be helpful for capturing a com-
bined effect of numerous immediately proximal others, those in
immediate proximity likely are more relevant, due to the risk
that they intrude on the focal consumer’s personal space. Thus,
an important consideration in proximity studies is the recogni-
tion that personal space is a function of others’ immediate
closeness to the individual, not general density in the space
(Harrell, Hutt, and Anderson 1980). This salience of close oth-
ers is evident in colloquial descriptions of personal space as a
“bubble” (or sphere), which can be defined as an “infinitely
malleable entity that is exquisitely responsive to situational
demands” (Hayduk 1983, p. 297). The shape of this region is
generally circular but is especially sensitive to frontal invasions
(Argyle 2013). Defining immediate closeness requires consid-
erations of not just distance perceptions but also situational,
personal, and cultural factors that may influence the shape of
the sphere. In particular, models of the effect of immediately
proximate others should reflect the direction in which those
others are located. We therefore differentiate the front (i.e.,
between the consumer and the most focal element, such as a
screen or stage), back (behind the consumer), and sides (to the
left or right of the consumer) and how they relate to different
uses of the environment and expectations. If the focal element
in the environment is a screen, a proximal person in front may
block the field of vision, which would affect the experience
differently than a proximal person to the focal consumer’s side
or back. Therefore, we introduce a (directional) specification of
the effect of immediately proximal others:
VPS ¼ XPSbPS; ð7Þ
where XPS is a design matrix.
Our use of the subscript “PS” reflects a common terminol-
ogy to refer to the immediate proximity of others that impinge
on personal space. The vector bPS includes the corresponding
parameters that describe the effects of attributes on the utility
of each potential seat. Each available seat is represented by a row
vector xPS. The elements ðxleft; xright; xfront; xbackÞ represent
the number of occupied seats in these directions. For a single seat
choice, the count for all four elements of the vector is necessarily 0
(empty) or 1 (occupied). However, for pairs of contiguous seats,
xfront and xback can take values of 0, 1, or 2, so we code them as
spaces occupied. Finally, we count the number of occupied seats
in front or back corners: xcountFc and xcountBc, respectively. The
vector for the directional proximity to immediate others is
xPS ¼ ðxleft xright xfront xback xintLR xcountFc xcountBcÞ;ð8Þ
and the parameter vector is
Blanchard et al. 881
bPS ¼ ðblef t bright bf ront bback bintLR bcountFc bcountBcÞ:ð9Þ
We further note that xLRint equals 1 if seats to both the left
and right are occupied (e.g., middle seat). If a consumer derives
negative utility from the immediate proximity of others, simul-
taneous intrusions on personal space from multiple dimensions
might provide a strong deterrent, due to the superadditive prop-
erty of this (dis)utility. Public transit passengers often exhibit a
preference to stand rather than to take an empty seat between
two occupied seats (Fried and DeFazio 1974). Accordingly, the
disutility of having somebody in seats to both the immediate
left and the immediate right could be even greater than the sum
of the individual disutilities of having someone in either seat
(Hayduk 1978). In turn, the parameter bintLR would be negative,
such that conditional on neighboring seats already being occu-
pied (e.g., on the right), adding a second occupied seat (e.g., on
the left) is worse than if that occupancy occurred in conjunction
with an otherwise empty seat. A consumer who expresses such
values likely is particularly averse to invasions of personal
space on that dimension. However, if bintLR is positive, it indi-
cates a subadditive property of the utility; a person might be
averse to an invasion of personal space to the left and right, but
the effect of adding the second neighbor might not be as neg-
ative as would be implied by the original additive structure in
this case.
Capturing the effect of less proximal others. Others outside the
boundary defined by the one-unit L1 sphere could also influ-
ence the utility of a potential seat. For example, those within
two seats (in any direction) may have an effect, such that
consumers might extract information about popular areas in
the space. Expanding beyond immediately proximal locations,
but assuming that directionality becomes less important
beyond immediate proximity, we can define larger spheres of
potential effects of (less) proximal others. For any number n,
we set xi;jRn ¼ jSB
Rnj=jSRnj, where SRn ¼ fa 2 St : jjajj1 ¼ 1g.Here again, SB
Rn � SRn is the subset of locations already occu-
pied by others. Then, we can define
VRn ¼ xRnbRn; ð10Þ
where xRn is a row vector that, for each available location,
records the proportion of seats that are occupied within an n-
unit sphere (still in L1 norm), and bRn is a parameter that
captures the effects. Figure 1 summarizes how our various
measures capture proximity to others with respect to R1, PS,
R2, and R3 around the focal location ði; jÞ.
Hierarchical Model
Consumers’ choice from a set of available seats can be a func-
tion of preferences with respect to any combination of the
proximity to focal elements (VL) and the proximity to others
(VPS, VR1, VR2, and VR3) Depending on the assumptions of the
data-generating mechanism, we can consider different model
specifications. For example, the model
Vt;ij ¼ VLt;ijþ VPSt;ij
þ VR2t;ijþ VR3t;ij
ð11Þ
combines proximity to focal elements (VL), immediate prox-
imity of others according to a directional one-unit sphere (VPS),
and effects of nonproximal others (VR2 and VR3) to describe
the deterministic component of the model in Equation 2, using
Figure 1. Visual depictions of how proximity to (immediate) others is captured.Notes: In the left panel, xR1 ¼ :5, xR2 ¼ :38, and xR3 ¼ :42. With respect to XPS, xleft ¼ 0; xright ¼ 1; xfront ¼ 1, xback ¼ 1; xintLR ¼ 0; xcountFc ¼ 1 and xcountBc ¼ 0.In the right panel, xR1 ¼ :5, xR2 ¼ :38 and xR3 ¼ :42. With respect to XPS, xleft ¼ 0;xright ¼ 1; xfront ¼ 2, xback ¼ 1; xintLR ¼ 1; xcountFc ¼ 0 and xcountBc ¼ 0.
882 Journal of Marketing Research 57(5)
the specification in Equations 5, 7, and 10. It assumes that no
outside option is available; the consumer must choose. But in
most cases, consumers have the outside option, because they
are not forced to choose seats. Exercising this outside option
takes many forms in the real world (e.g., buying seats for
another event), but we assume that it entails skipping the par-
ticular event for which the assortment is being presented. Con-
sistent with prior literature, we refer to it as the “no-choice”
option. To estimate bno-choice, which describes a preference for
the no-choice option, we modify the design matrix for each
choice by adding a row for the no-choice alternative in each
choice’s design matrix, as well as a column of zeroes to all
except the row representing the no-choice option (see Haaijer,
Kamakura, and Wedel 2001).
The probability of selecting a location ði; jÞ is given by
Prðyt ¼ mj�Þ ¼ expðVt;mÞXfk2fSA
t ;no-choiceggexpðVt;kÞ
; ð12Þ
where m is either a seat or an outside option. In this example,
the likelihood for all respondents h ¼ f1; :::;Hg in all tasks
t ¼ f1; :::;Tg is
‘ ¼YHh¼1
YT
t¼1
Prðyh;tjXLh;t;XPSh;t
;XR2h;t;XR3h;t
; bLh; bPSh
; bR2h; bR3h
; bno-choicehÞ:
ð13Þ
In the hierarchical model specification for heterogeneous
preferences among consumers, the parameter vectors
bh ¼ fbLh; bPSh
; bR2h; bR3h
; bno-choice;hg are specific to each
individual and assumed to reflect a normal distribution with
parameters:
bh*NðD0zh;DbÞ; ð14Þ
where zh is a vector of respondent-specific or environment-
specific covariates. If no individual-level or context-level cov-
ariates are used, zh is a vector of 1s.
We investigate all models that vary in terms of whether (and
how) the proximity of others is considered. We estimate our
models within a Bayesian framework, which provides multiple
well-established benefits for researchers, and especially for
estimating hierarchical models to accommodate heterogeneous
consumer preferences or making probabilistic statements about
the parameters. The details of the estimation are in Web
Appendix A, and a simulation study (for parameter recovery
and convergence) is in Web Appendix B.
Prediction Benchmarks
To provide managers with insights into how consumers make
locational choices and to enable individual-level predictions,
we introduce both a way to codify individual-level locational
data and an individual-level utility function with a significant
amount of structure. If the focus is not necessarily on under-
standing the precise nature of the heterogeneous patterns, such
that the operator solely wishes to make predictions about which
available seat(s) are likely to be chosen, it could resort to the
many available supervised learning methods that can be trained
to recover the latent structure (e.g., Equation 11) or learn it
from data. Convolutional neural networks (CNNs) are particu-
larly useful for inferring structures from marketing data auto-
matically (e.g., Xia, Chatterjee, and May 2019; Timoshenko
and Hauser 2019). With sufficient data and an appropriate
specification, such models should be able to recover the utility
specification that we propose. However, their ability to do so
depends on the amount of data provided per consumer and
whether there is substantial individual heterogeneity to accom-
modate. These networks benefit from pooling operations, so
substantive individual heterogeneity would make the predic-
tion problem more difficult for them.
To illustrate the difficulty of this prediction exercise and
provide guidance for users interested solely in prediction,
we implement a CNN. For layouts with sizes of up to 20
locations per dimension, we create an input vector of size
400, where 0 indicates that the location is unavailable and 1
implies it is available. Locations that pad the space (i.e.,
that are not seats) are marked by 0. Then, we use PyTorch
(Paszke et al. 2017) to devise a model with one convolu-
tional layer, one channel, a kernel size of three, a stride of
one, and a linear layer of 400 � 400. In the linear layer, all
the neurons (i.e., locations) are connected, so we can define
spatial preferences within the room. With the 3 � 3 con-
volutional layer, we capture effects that are spatially invar-
iant.5 The convolutional layer thus should capture
immediate proximity to others, whereas the fully connected
layer captures the preference for locations within the phys-
ical space. We trained the model with Adam (Kingma and
Ba 2014), to minimize networks’ cross-entropy losses,
which is equivalent to minimizing the negative log-
likelihood of the data. Throughout this manuscript, we
report the in-sample and holdout prediction using this
benchmark predictive model. We reserve our interpretation
of the benchmark model’s results for the “General Dis-
cussion” section.
Experimental Insights
We gathered experimental data about two locational choices
that are common consumer experiences: reserved seating at
movie theaters and concert halls. In both cases, we expect
heterogeneous location preferences, thus substantiating the
need to use individual-level locational data when studying
occupancy. Before we turn to our analyses, we offer three key
points.
First, our data were collected entirely through experiments
involving a locational choice platform, seatmaplab.com. As we
5 Across our experiments, we find little evidence that additional convolutional
layers would be helpful. A multilayer perceptron instead performs nearly as
well as the final CNN.
Blanchard et al. 883
noted previously, ticket purchase logs do not capture the
individual-level choice set of those who choose not to pur-
chase, rendering individual-level analyses of the drivers of
occupancy questionable at best.
Second, we report only two analyses based on subsets of
data from four large experiments collected as part of this
project. Our four experiments varied the context (movie/con-
certs) and the number of tickets (pairs/single). However, we
conducted these experiments in hopes of providing expansive
coverage of many other factors that may be relevant to loca-
tional preference, such as existing occupancy (i.e., proportion
of seats already purchased in the map shown to a participant),
whether a no-choice option is offered, the timing of the event
(e.g., soon or a few months away), and the room layout (e.g.,
portrait vs. landscape). To maintain clarity, we only discuss
subsets of these data. We encourage readers who are inter-
ested in understanding how we could (and did) incorporate
important covariates, such as occupancy (e.g., popularity of
the event), to refer to Appendix A, which details each
experiment.
The analyses herein are organized into two sections. In the
first, we illustrate descriptively how aggregate analyses threa-
ten to mask substantial heterogeneity in individual-level pre-
ferences and systematic differences based on the number of
locations chosen (a pair vs. a single seat). In the second section,
we provide further evidence of the need to analyze individual-
level locational choice data in a different context, namely, pairs
of seats for a concert. Relative to the movie theater analysis,
these locational preferences are drastically different, yet still
heterogeneous at the individual level. Finally, we use a concert
context to provide an example of a usage scenario for the
model’s parameter estimates, designed to identify optimal
seat-level availability.
One or Two Seats for the Movies
We present an analysis of seat selections in a high occupancy
(75%) showing (i.e., only 25% of seats were left), such that
participants choose tickets for either one or two seats, or else
the outside option not to attend the movie. This analysis is
based on two subsets of our experimental data.
First, we asked participants to pick two seats for a movie.
Specifically, we asked participants from Amazon Mechanical
Turk (MTurk) to complete a ten-minute study about going to
the movies with a friend. When they started the study, partici-
pants had to imagine the following scenario:
You and a friend have a few hours to kill, and you walk to the
movie theater to see a movie you’ve wanted to see. You stop by
one of the ticket machines and look at the seat map. The movie
starts in a few minutes. Which seats would you choose? If you
don’t like the options available, you may decide to walk away and
go do something else.
After reviewing the instructions, participants received the loca-
tional choice interface (see Figure 2), which was a seating chart
similar to ones found on real-world seat booking websites. On a
left panel, we reminded participants that they needed to choose
two seats and that they would see different assortments in a
12� 12 theater. A counter of their progress appeared on the
screen. A color-coded legend indicated which seats were (un)a-
vailable,6 and a clickable text button below the seating chart
represented the no-choice option. After participants indicated
their choice, the software platform recorded the chosen pair of
locations, the seating layout characteristics, and the random
Figure 2. Movie analysis: Sample locational choice experimentinterface.Notes: This participant has selected the first of a pair of seats. The seats markedas occupied cannot be selected.
6 Choosing seats for the movies (or for a concert) is such a common experience
that we expected participants to have well-defined preferences. As such, we
expected that the specific way we chose to randomize would have little impact
on the coefficients extracted over repeated choices. In this experiment, we
proceeded with the simplest approach. For each participant’s load of a seat
map layout, based on occupancy (e.g., 75% occupied), a seat would be drawn
from two univariate uniforms. If the seat was available, it was then marked as
occupied. The process was repeated until the desired occupancy was reached.
We appreciate that such a randomization may not perfectly recreate the way
halls naturally fill. As such, we also experimented alternative randomization
processes (e.g., adding people by groups or based on an expected distribution).
We did not find meaningful differences with respect to model estimates or
accuracy.
884 Journal of Marketing Research 57(5)
seat availability that they saw. The analyses rely on data from
233 participants who completed at least 15 of 16 such choices.
The data and file details (E1-Movie-Pairs.NC:75) are in
Appendix A.
Second, in another experiment, we asked participants to
pick one seat for a movie. Specifically, we used data from
300 participants who first completed 12 tasks for which
occupancy was 75% in a similar 12� 12 theater, with a
no-choice option. Here, 18.7% (or 56) of participants pre-
ferred to skip the movie at least once, and the no-choice
option represented 4.4% of all choices. The data and file
details (E2-Movie-Singles.NC/FC: NC) are in Appendix A,
and we provide detailed estimations results for both these
analyses in Web Appendix C.
Model-free evidence. Figure 3 displays the frequencies of seat
choices separately for those who chose a pair of seats and those
who chose a single seat. When participants chose pairs of seats,
58% (or 136) of them opted for the no-choice option at least
once. Even though some participants always chose seats,
26.5% of all seat choices offered resulted in the participant
choosing to skip the movie and that number was not driven
by a few unmotivated participants.
Across both data sets, we find that the most popular seats
are the two in the middle center (row 7, columns 6 and 7);
we also note some preference for the middle aisles and back
center. However, participants selecting a pair of seats are
more likely to prefer being in the center and slightly to the
back relative to other popular locations. The choice fre-
quency also appears more dispersed than that among parti-
cipants who choose a single seat. For example, we find a
relatively stronger preference for the aisles in single seat
choice contexts. Unfortunately, this evidence does not allow
us to make statements about whether individual preferences
are dispersed similarly for all respondents or if the various
preferred locations might be preferred by different individ-
ual consumers.
Model fit. Table 1 presents the model fit statistics for both pairs
and single seat selections. First, we report the Newton and
Raftery estimator (Newton and Raftery 1994) of log-marginal
density (LMD NR).7 Second, we report the average choice
probability of the selected seats, as predicted by the model.
Third, we present the hit rate, obtained by selecting the option
with the highest choice probability. We break down the mean
choice probabilities and hit rate by in-sample and holdout sets.
The in-sample fit reflects data used to estimate the model;
holdout fit instead refers to the predictive fit of three choices
randomly removed from the sample. For these measures,
higher numbers indicate the model offers better fit and predic-
tive ability.
The results in Table 1 suggest that proximity to others is an
important determinant, regardless of whether one is choosing
one or two seats. Fit improves when we incorporate the para-
meters related to the proximity of others; this result is not
merely due to an increase in the number of parameters esti-
mated in the models. When looking for pairs, including the
directional effects of immediately proximate others (i.e., VPS)
improves both in-sample and holdout fit more than including
the three nondirected spheres of proximate others (i.e.,
VR1;VR2, and VR3). That is, adding the directional effects
of immediately proximate others increases the mean probabil-
ity and hit rate by 7%–10%, for both in-sample and holdout
choices. The importance of breaking down the directionality
of personal space is less important when buying a single seat;
it offers no improvement in holdout samples. In both cases,
Figure 3. Movie context: Observed choice probability by seat loca-tion and number of seats to be chosen (pairs vs. single).Notes: The movie screen was indicated to be ahead of row 1 (at the top). Thecolor bar values indicate the percentage of choices that were in that location(e.g., 2.5 is 2.5%). Uniform preference over all locations would lead to .7% inthe movie-pair condition, and 2.7% in the movie-single condition.
7 Details of the estimation and convergence diagnostics are in Web
Appendix C.
Blanchard et al. 885
proximity to others is particularly important, and it is largely
limited to immediate proximity; the improvements between L
þ PS and L þ PS þ R1R2 are smaller than the change
between L þ R1R2R3 and L þ PS þ R1R2. All these models
substantially outperform chance, which is approximately 7%,
and our benchmark model. Taken together, these fit results
suggest that our individual-level measurement model is an
excellent approximation of the individual process involved
in choosing either one or two seats and that the inclusion of
proximity to not only focal elements but also others is
necessary.
Interpretation of parameters. Table 2 contains the posterior
means and 95% credible intervals (CI) of the upper-level para-
meter estimates, based on the best fitting model for single and
pairs of seat choices. Figure 4 displays a predictive “heat map”
for proximity to focal elements (i.e., excluding proximity to
others).
We note several similarities between the decision to buy a
pair of seats and the decision to buy a single seat. In terms of
locational preferences, in neither case do we find any evidence
that the rows and columns interact (i.e., the CI of brc includes
0).8 As we can show with Figure 4, participants exhibit a pre-
ference to sit in the middle of the theater, as well as a desire to
avoid less proximal others, such that both bR2and bR3
are
negative.
Yet we also can specify some pertinent differences.
When choosing a pair of seats, the potential lateral inva-
sions of personal space (i.e., someone to the left or right of
the pair) have a greater (negative) impact than do people to
the front or back. The presence of one person on either side
makes the addition of a second person on the other side
seemingly minimal. However, consumers choosing only one
seat are more likely to insist on being in the middle of the
theater (front to back), at the expense of both personal space
(i.e., fewer significant parameters with VPS) and a centered
view (left to right).
Table 1. Movie Seat Analysis: Model Fit and Predictive Ability.
Model LMD NR
Mean Probability Hit Ratea CNN Benchmark
In-Sample Holdout In-Sample Holdout In-Sample Holdout
Pair of SeatsL �2,942 .3783 .3850 50.95% 49.93%L þ R1R2R3 �2,833 .5838 .5407 71.20% 64.52%L þ PS �2,310 .6927 .5853 81.92% 64.95%L þ PS þ R2R3a �2,270 .7009 .5879 82.22% 64.80% 41.78% 25.55%Single SeatL �6,972 .2116 .1836 33.40% 26.17%L þ R1R2R3 �6,896 .2193 .1861 35.27% 26.50%L þ PS �6,721 .2535 .1876 42.93% 26.17%L þ PS þ R2R3 �6,682 .2598 .1898 44.03% 26.33% 14.52% 7.02%
aIn the single-seat data, chance was 2.7%. In the pair-of-seats data, chance was 6.9%, because there are fewer options (contiguous pairs of seats) available.Notes: Boldface indicates the best model within each column.
Table 2. Movie Analysis: Posterior Means and 95% Credible Intervals(L þ PS þ R2R3: 75% Occupancy).
Parameter
Sample
Pairs Single
Mean 95% CI Mean 95% CI
br1 �49.3 (�56.4, �42.4) �42.5 (�78.8, �37.8)br2 56.7 (49.1, 64.1) 46.2 (40.8, 52.2)bc1 �38.6 (�47, �31.1) �29.6 (�36.6, �22.7)bc2 39.8 (32.2, 48.6) 31.0 (24.3, 37.8)brc �.4 (�3, 1.9) 1.0 (�2.8, 1.2)
bleft �1.25 (�1.88, �.6) �.08 (�.23, .08)bright �1.07 (�1.63, �.43) �.19 (�.38, �.05)
bLR .47 (�.15, .99) �.01 (�.23, .22)bfront �.19 (�.38, �.01) �.06 (�.17, .07)bback .05 (�.13, .23) .06 (�.07, .17)bcornersF �.08 (�.24, .12) �.08 (�.16, .01)bcornersB �.01 (�.17, .19) �.13 (�.23, �.03)
bR2 �.32 (�1.23, .65) �.67 (�1.08, �.25)bR3 �1.03 (�1.99, .12) �.48 (�.99, 0)bno-choice 20.71 (17.62, 24.07) 16.28 (13.66, 19.03)
Notes: Boldfaced values represent the means for which the 95% CI does notinclude 0. Recall that for locational parameters, (0, 0) is at the front left of thetheater.
8 In the presence of two quadratic terms and an interaction term (bRC), we must
be careful to interpret the locational parameters. Recall that the design matrix X
is coded such that (0,0) represents the front-left of the room, and bRC captures
the interaction between the two locational dimensions. To use the parameters in
Table 2 to obtain marginal effects, we must set a value of X between (0,0) and
(1,1) to serve as reference point. For example, selecting a pair of seats at ð:5; :5Þ(middle of the room) offers locational utility of 26.13. Moving from this seat to
midway between the aisle and middle ð:5; :75Þ reduces utility by 7.08, or nearly
as much as moving completely to the aisle, which implies a 9.30 reduction
ð:5; 1Þ.
886 Journal of Marketing Research 57(5)
Preference heterogeneity. Model-free analyses (Figure 3) and
investigations of upper-level level parameters (Table 2) are
informative regarding what drives locational preferences and
occupancy in the aggregate. However, they do not clearly illus-
trate the extent to which consumers are heterogeneous. In
Table 3, we present some common, individual-level locational
preferences that can be represented by coding patterns across
locational parameters in VL and visual inspection. In Figure 5,
we depict three respondents, representing the three most com-
mon patterns from Table 3 (pairs): middle and center, aisles
near the middle, and rear center.
Table 3 reveals some important complexities that reflect
substantial heterogeneity; it would be masked if we relied
solely on upper-level parameters. First, consumers selecting
one seat are significantly more likely to pick aisle seats and
front center seats. Second, from individual-level preferences,
we can identify the preferences of those who allocate more
importance to their proximity to focal elements (#99 and
#104) as well as distinguish those who are most likely to skip
events if they cannot find seats they like (#104), from Figure 5.
These individual-level analyses reveal how consumers differ in
the relative importance they assign to different components and
what constitutes an ideal location for them (#99: somewhere
near the middle, #104: centered, back row if possible, #55: aisle
seat, with no one on at least one side). We also cite some
representative quotes from the participants, describing how
they made their locational choices, which vary in whether they
predominantly focused on proximity to focal elements (e.g.,
screen, exits) or proximal others (e.g., maintaining personal
space).
Discussion
From this first analysis, we make several observations. First,
to understand how consumers make locational choices, it is
critical to consider proximity to focal elements but also prox-
imity to others. With three components in the best-performing
model and with data about assortments that lead to the selec-
tion of the no-choice option, we accurately predict more than
50% of the holdout choices for a pair of tickets (recall that
chance is approximately 7%). Our ability to predict choices
persists even in the more difficult single-ticket choice setting
(chance is approximately 2.7%), for which we find not only
that proximity to others matters but also that the directionality
of potential invasions matters less. Moreover, we provide
evidence from the individual-level estimates that consumers
differ in the kind of proximity that they prioritize, and this
considerable source of heterogeneity is masked by model-free
analyses that aggregate across contexts (e.g., number of seats
chosen) and individuals. In other words, the descriptive anal-
yses suggest that our measurement model and estimation pro-
cedure are particularly effective at making predictions about
locational choices. Finally, our investigation into the nature of
the individual heterogeneity suggests that even with
individual-level data, aggregate interpretations mask the
Figure 4. Movie analysis: Estimated aggregate probability of choice.Notes: In both conditions, colors closer to yellow (lighter) indicate a moredesired location.
Table 3. Movies Analysis: Summary of Locational PreferenceHeterogeneity Across Respondents by Number of Seats.
Row Dimension
Column Dimension
Row TotalCenter Aisles Any Column
Movies: Pair of SeatsFront 2% 1% 0% 3%Middle 74% 15% 0% 89%Back 0% 3% 4% 7%Any row 0% 0% 0% 0%Column total 76% 20% 4% 100%Movies: Single SeatFront 3% 0% 1% 4%Middle 65% 20% 0% 85%Back 2% 4% 4% 10%Any row 1% 1% 0% 1%Column total 70% 25% 5% 100%
Blanchard et al. 887
extent to which consumers fail to attain utility from locations
that may be liked by many others. In the next subsection, we
further illustrate how vastly different locational preferences
are among individuals and across contexts (concerts vs.
movies). We also investigate how operators might use our
model output to influence occupancy; they must first gather
data that include seat assortments presented to consumers who
ultimately do not choose any seat.
Figure 5. Movies, pair of seats: Preference heterogeneity.
888 Journal of Marketing Research 57(5)
One or Two Seats at a Concert Hall and Seat-LevelAvailability to Influence Expected Occupancy
An important implication of collecting individual-level loca-
tional choice data, including those derived from assortments
from which consumers choose to not make a purchase, is that
we can make recommendations about which seats in an assort-
ment will be preferred as well as whether a consumer is likely to
choose any seat from each assortment. Across many individual
consumers, such individual-level estimates of the no-choice
probability can be used as a proxy for expected occupancy. That
is, our parameter estimates provide information about seat-level
availability decisions. Notably, offering early (premium) access
or last-minute discount seats, as well as withholding (and releas-
ing) seats, are common tactics for many venues; they might hold
seats for the press, members of the staff, or other stakeholders,
for example (e.g., Sutterman 2015). With this analysis, we can
also explore how seat-level availability decisions can be made to
influence event-level occupancy rates.
First, we collect experimental data about the choice to attend
a concert with a friend and which seats are chosen. We report
the model fit and describe the magnitude of individual hetero-
geneity in locational choices that would be masked by aggre-
gated seat location “heat maps.” This part is similar to the
analysis of movie seat preferences but focuses solely on
choices of pairs of seats, as a common consumption experience.
Second, we propose an optimization model that uses the fitted
parameters as input to identify which seats should be marked as
unavailable (i.e., seat-level availability). Third, we provide pre-
liminary evidence that the use of the layout as suggested by the
optimization model can improve intentions to attend.
Locational Preferences for a Concert
For the locational choice experiment data, we recruited partici-
pants from MTurk for a study about attending concerts. The
scenario explained that they were thinking about going to a
concert with a friend. After reviewing the instructions, partici-
pants considered the same locational choice interface: a panel, a
reminder that they needed to choose two seats and that they
would do so for multiple assortments, a counter of their progress,
a color-coded legend indicating which seats were (un)available,
and a clickable text button located below the seating chart as the
no-choice option. After participants indicated their choice, by
clicking on two available seats or skipping the concert, the soft-
ware platform recorded the chosen pair of locations, the seating
layout characteristics, and the seat availability they saw. The
analyses rely on data from 383 participants who chose 30 pairs
of seats for a concert at least a few days in advance, with varying
occupancy levels (40%, 60%, and 80%), in a layout that was
either 12� 20 or 20� 12. The data and file details (E3-Concert-
Pairs.FC/NC: NC) are in Appendix A.
Model-free evidence. In Figure 6, we present the aggregate
(rescaled) frequency heat map of the most often chosen loca-
tions (i.e., seats). Aggregate locational choices noticeably
differ from what we observed in the movie analysis. For con-
certs, the most chosen locations are in the front-center, and any
departures away from those locations strongly influence the
odds of a seat being selected. However, at a certain level, being
in the middle-center is preferred over being slightly closer to
the stage.9 What is unclear from these observational data, how-
ever, is whether such a pattern reflects individual-level loca-
tional preferences or substantial individual-level heterogeneity
among consumers with very different locational preferences.
Model fit. Table 4 includes the in-sample and holdout fit sta-
tistics. Four choices were used as the holdout sample for each
participant. The results show that proximity to others is an
important determinant of participants’ choices, further
emphasizing the need to gather locational choices with
individual-level assortment data. Specifically, the model that
incorporates both proximities to focal elements and to others
fits the data best. Similar to our results from the movie illus-
tration, including the directional effects of immediately prox-
imate others (i.e., VPS) improves fit more than including all
three nondirected spheres for proximate others (i.e., VR1;VR2,
and VR3). We also find a significant (but small) improvement
achieved by including less proximal others. However, we do
not find strong evidence that improvement due to the addition
Figure 6. Concert analysis: Observed choice probabilities.Notes: The concert hall’s stage was on top of row 1 (top). The color bar valuesindicate the percentage of choices in that location (e.g., 2.5 is 2.5%). We scaledfrequencies to a 13 � 13 space for the chart, because the layouts varied theorientation of the layout.
9 One way to compare the two-dimensional distributions is to use the Earth
mover’s distance (EMD) (Rubner, Tomasi, and Guibas 2000) to compare the
two-dimensional empirical distributions from the movie and concert (pairs)
selection studies. The EMD is zero when there are differences between the
distributions. Considered in a bivariate form, EMD ¼ 4.26 indicates a
significant difference between the (normalized) distributions. Univariate
comparisons (row and columns separately) suggest that the contexts mostly
differ from the row dimension ( EMD R ¼ 4:22 vs : EMD C ¼ :47).
Blanchard et al. 889
of parameters to capture the proximity to others holds in terms
of holdout prediction.
Interpretation of parameters. Table 5 reports the posterior
means and 95% CIs of the upper-level parameter estimates.
Figure 7 depicts the aggregate preferences, based on the full
model.
With regard to proximity to focal elements, in sharp contrast
with the movie analysis but in line with the model-free evi-
dence, we find an interaction between proximity to the stage
(front to back) and consumers’ willingness to sacrifice their
viewing angle (brc<0). We also find little evidence that con-
sumers actively try to avoid proximate others. Instead, the pos-
itive upper-level parameters of immediate directional
proximity (PS) indicate that when attending a concert with a
friend, consumers prefer locations that are in proximity to oth-
ers. Those who are more than two seats away (i.e., R3) have
little impact. Whereas these upper-level parameters imply that
most concert-goers would be pleased with a seat that is front
and center and surrounded by others, it may be that substantial
heterogeneity exists and needs to be considered.
Preference heterogeneity. Therefore, we turn from the upper-level
parameters to consumer-level heterogeneity. Although we obtain
strong evidence of consumers’ tendency to prefer seats close to
the stage, especially in the center, intuitively we anticipate that
concertgoers might vary more in what they consider an ideal
location, particularly when the ideal seats are not available.
Recall from Figure 6 that we saw some preference for the front
and center, some for the front aisles, and some for the center. In
Table 6, we summarize how we can capture individual hetero-
geneity. In Figure 8, we take three participants, representative of
the most common preference categories: front and center, front
aisles, and middle and center.
The first consumer (#10) represents the aggregate pattern
fairly well. He chose his seats based on proximity to the front and
center, with little regard for much else. However, the second
consumer (#161) strongly prefers aisles, due to her desire to avoid
others; she would not consider the popular front and center seats
Table 4. Concerts Analysis: Model Fit and Predictive Ability.
Mean Probability Hit Ratea CNN Benchmark
Model LMD NR In-Sample Holdout In-Sample Holdout In-Sample Holdout
L �13,134 .4580 .4316 60.79% 56.85%L þ R1 þ R2 þ R3 �12,733 .4737 .4427 62.42% 56.85%L þ PS �12,199 .5050 .4548 64.75% 56.33%L þ PS þ R2 þ R3 �12,038 .5129 .4592 65.57% 56.66% 45.91% 35.93%
aChance is approximately 5%.
Table 5. Concert Analysis: Posterior Means and 95% CIs.
Parameter Mean 95% CI
br1 .0 (�3.2, 3.2)br2 �15.1 (�18.5, �11.8)bc1 �50.1 (�54.9, �45)bc2 50.7 (45.4, 55.5)brc �2.0 (�3.4, �.1)bleft .48 (.30, .67)bright .57 (.38, .74)
bLR �.5 (�.24, .13)bfront .17 (.10, .25)bback �.02 (�.08, .04)bcornersF .14 (.07, .21)bcornersB �.04 (�.10, .03)bR2 .49 (.16, .87)bR3 .23 (�.14, .61)bno-choice 6.60 (5.07, 8.08)
Notes: Boldfaced values represent means for which the 95% CI does notinclude 0.
Figure 7. Concert analysis: Estimated locational preferences.
Table 6. Concert Analysis: Individual-Level Locational Heterogeneity.
Column Dimension
Row Dimension Center Aisles Any Column Rows Total
Front 53% 4% 11% 68%Middle 24% 4% 1% 29%Back 1% 1% 0% 1%Any row 1% 0% 0% 2%Column total 79% 9% 12% 100%
890 Journal of Marketing Research 57(5)
or anything in the front. The third respondent (#132) expresses a
preference for anywhere in the back row, which she attributes (in
her words) to being noise sensitive. Another preference (though
she did not state it directly) becomes evident when we note that
despite her claim that she must be in the back row, she trades off
sides (left or right) to avoid having others right next to her.
We thus continue to find substantive evidence of the impor-
tance of collecting individual-level data and applying models
that allow for substantial individual-level heterogeneity in
locational choice data. Looking only at heat maps or upper-
level parameters prevents insights into whether most concert-
goers are likely to choose a seat in front and center. It is clearly
a high-utility location for many consumers, yet approximately
half of our participants cite equivalent or even greater utility
with different locations, such as the center or anywhere in the
front row.
Figure 8. Concert analysis: Locational heterogeneity across respondents.
Blanchard et al. 891
Optimal Seat-Level Availability Based on LocationalPreferences
Our specification acknowledges that consumers express their tol-
erance for immediately proximate others but also evaluate the
presence of less proximate others (e.g., people two or more seats
away). In the analysis of concertgoers looking for two tickets, we
find that most decision makers are tolerantof potential invasions to
their personal space (i.e., nonnegative coefficients for counts
within the one-unit L1 sphere) and even exhibit positive utility
for seats in areas where many others are present (i.e., positive
coefficients for the count on the two- and three-unit L1 spheres).
Therefore, it should be possible to identify which individual seats
should be marked as unavailable, in an effort to increase the aver-
age expected utility of the assortment, relative to the utility of a no-
choice option. That is, it should be possible to use individual-level
locational preferences to inform seat-level availability decisions
associated with any given assortment and thereby reduce the odds
that a consumer selects the no-choice option.
To begin, we assume that all model coefficients (i.e.,
individual-specific posterior means) have been estimated using
a training sample. Thus, �bh
are known for each participant h in
the sample, and the set of available seats SA can be further
reduced to SA0¼ SA � SB, where SB includes a subset of sets
that could be marked as unavailable, such that
SA0¼ arg min
SB
XH
h¼1
expðVhno-choiceÞ
expðVhno-choiceÞ þ
Xk2ðSA�SBÞ
expðVhkÞ
8>><>>:
9>>=>>;:
ð15Þ
In this instance, there are 2jSAj possible SB sets of unavail-
able seats, so solving the seat-level availability problem in
Equation 15 would create exponentially great time complexity
demands. Therefore, we devise a greedy heuristic for this com-
binatorial problem in Algorithm 1.
The heuristic begins with the entire set of seats S, those that
are currently available SA, and empty set SB. Through each
major loop, it marks as unavailable the seat that provides the
greatest reduction in the average no-choice probability across
all individuals. The algorithm stops when marking a seat as
unavailable no longer reduces the expected probability of a
no-choice option selection. The heuristic rapidly converges to
a critical point, though there is no guarantee that it will be to a
global (or even a local) minimum. In the “General Discussion”
section, we discuss metaheuristic frameworks that can be used
to improve this local search procedure.
Illustrative Usage Scenario for a Concert at the John F.Kennedy Center
On September 4, 2019, the National Symphony Orchestra and
Jim James (frontman of the indie-rock band My Morning
Jacket) held a concert at the John F. Kennedy Center in
Washington, D.C. On September 1, three days before the event,
the middle section of the opera-level rows had 196 seats (14 �14) that were initially made available, and 84 seats remained.
The seat map in Figure 9, Panel A, is what would have been
visible to a visitor considering seats in this section. The layout
and occupancy pattern in this section is similar to what we have
observed experimentally. Specifically, we note consumers’
strong preference to sit near the front of the section, though
some choose aisles over closer seats, and a few prefer locations
near the back.
Figure 9, Panel B, presents the aggregate predicted probabil-
ities for someone looking for a pair of tickets, based on the
individual-level parameter estimates. In this rescaled locational
choice map, gray indicates unavailable, contiguous pairs of seats.
Thus, row 6, column 3, is available (shaded) in Figure 9, Panel A,
but the seat to the right (column 4) is not, so the pair beginning in
row 6, column 3, is marked as unavailable. We expect most con-
certgoers to pick a pair of seats in front when the concert hall is
completely empty (.066% no-choice probability), yet the average
individual-level no-choice probability in response to this assort-
ment actually is much higher. The most preferred seats become
those in the middle-center instead of front-center. When we apply
Algorithm 1 to the layout in Figure 9, Panel B, it shows that
marking an additional 24 seats unavailable could reduce the aver-
age no-choice probability by 12.5% (from 48% to 42%). Figure 9,
Panel C, displays the various choice probabilities for a pair of
seats in this treatment layout.
We illustrate some individual-specific changes in no-
choice probability in Figure 10. The second column contains
the predicted probabilities for three individual consumers,
identified from the concert data set. Individual 5 indicates a
strong preference for the front-center of the theater, likely
moving back to the middle if the first seven rows are unavail-
able. Individual 166 weakly prefers the middle-right, and
individual 247 wants to be in one of the front aisles. That
is, two of these three consumers likely have smaller odds of
selecting the no-choice option when the seat map shows
higher occupancy (individuals 166 and 247). For individual
Algorithm 1. Greedy Heuristic for Seat-Level Availability DecisionsBased on Locational Preferences SB
Require: S (layout coordinates), SA (available seats), βh (fitted parameters)1: Initialize SB = {},2: repeat3: SA′
= SA − SB
4: Pr′ =∑H
h=1
{Prh
no−choice |SA′, βh
}
5: for each (i) ∈ SA′do
6: SA′′= SA′ − (i)
7: Pr′′[i] =∑H
h=1
{Prh
no−choice |SA′′, βh
}
8: end for9: i∗ ← arg mini (Pr′′[i])
10: Δ = Pr′ −Pr′′ [i∗]11: if Δ ≥ 0 then SB = SB + (i∗)12: until Δ < 013: return SB
892 Journal of Marketing Research 57(5)
5, this probability instead would increase. The layout in Fig-
ure 9, Panel C, thus would decrease the probability of select-
ing the no-choice option for 54.8% (210 of 383) of
participants.
Using these data, we can investigate seat-level availability
decisions, using locational preference data and our optimization
model, in an attempt to reduce the chances that people select the
no-choice option. We therefore conduct an experiment that fea-
tures two layouts: the one visible on the Kennedy Center’s web-
site (control), as well as one marked with additional unavailable
seats, in accordance with our optimization model (treatment).
For this experiment, we asked 523 MTurk participants to imag-
ine they had been contacted by a friend who was interested in
seeing a concert, happening in three days. The friend had recom-
mended buying tickets in a section for which the ticket price was
$29.99 but has asked the participant to decide if they should go
and, if so, which seats to pick. The respondents then were ran-
domly assigned (between-subjects) to either the control or treat-
ment condition. After they made their choice, we asked these
participants to describe how they chose or why they did not make
a seat choice. After eliminating 35 participants who selected the
no-choice option or noted that they randomly picked seats because
they would never consider going to such a concert (17 in the
control, 18 in the treatment condition), we were left with 488
participants for our analyses for whom the task is relevant. Parti-
cipants presented with the treatment layout were marginally less
likely (5.3%) to select the no-choice option than those in the con-
trol condition (9.4%, relative risk: .57;w2ð487Þ ¼ 2:91; p ¼ :09).
General Discussion
We propose a novel measurement approach to study the drivers
of locational choices and occupancy. Drawing on psychology
literature pertaining to personal space, our approach begins
with the specification of a utility function to describe the
data-generating mechanism behind locational choices, which
could vary based on proximity to focal elements and proximity
to others. Across multiple experimental investigations, using
our developed locational choice experimental platform, we
show both that the proposed specification predicts locational
choices effectively, by using proximity to others, and that it can
accommodate heterogeneity in individual preferences and con-
texts (e.g., number of tickets, concert vs. movie). Moreover, we
illustrate that it is possible to use individual-level outputs from
a trained locational choice model to influence occupancy, by
selectively marking certain seats as unavailable (i.e., seat-level
availability).
Substantive Implications and Recommendations
We offer three recommendations for marketing scientists work-
ing for venue operators. First, they should use dashboards and
recommendation agents that model individual-level locational
choice data over multiple assortment decisions. Second, opera-
tors should augment their purchase log data to include consu-
mers who do not purchase alongside the assortment data
pertaining to those who do. Third, we encourage reserved seat-
ing venue operators to take advantage of experimental plat-
forms to explore how changes to seating charts could affect
occupancy.
Gather and analyze locational choice data at the individual level overmultiple purchase occasions. Our exploratory survey of operators
Figure 9. Counterfactual illustration: Choice set for “The NSOPresents Jim James.”Notes: Column dimensionality reduces to 14 � 13 in the charts in Panels B andC, which reflects the choice pair beginning in the leftmost seat.
Blanchard et al. 893
and review of prior research show that operators are con-
cerned with occupancy, yet the data collected to understand
its drivers are limited mainly to survey measures or logs of
purchased seats. To make more strategic decisions, manag-
ers should augment their data and capture individual-level
choice-set data. As we show, aggregate analyses mask
significant latent heterogeneity; aggregate representations
of the concert seats preference data suggest a higher fre-
quency of choice in the first row center, which diminishes
as we move to the sides or toward the back. We also find a
slightly higher choice frequency in the middle of the room.
The aggregated analysis may suggest that everyone prefers
the front- or middle-center, but we show that a more com-
mon pattern of individual preferences involves preferences
for the front aisles. Roughly one-fourth of the sample would
prefer to be in the middle, from front to back. Simply
put, locational data contain so much heterogeneity that
aggregate analyses can indicate false individual preference
patterns that do not exist (Hutchinson, Kamakura, and
Lynch 2000).
Figure 10. Concert hall illustration: Preference heterogeneity.
894 Journal of Marketing Research 57(5)
Train models and recommendation agents on locational choiceassortments that do not result in purchases. Even if operators can
reconstruct individual-level assortment data for visits that lead
to purchases, such insights ignore data associated with assort-
ments that do not prompt a purchase. Purchase logs only note
choices made; at best, they record the locations of those who
made a selection, not those who reviewed the available options
and decided to pass. Failing to train models with data from
consumers who opt for the no-choice option can affect
model performance. In Appendix B, we report on a second
set of choices that participants make when they lack a no-
choice option. Specifically, training a model on forced-
choice data affects its predictions, which may be inaccurate
when the real choice process includes a no-choice option
(and vice versa). We find that a model trained only on
forced-choice data, then applied to a context with a no-
choice option, is approximately 24% less accurate. When
training locational choice models, scientists thus should
train their models using data from locational choice assort-
ments that do not result in a purchase.
Conduct locational choice experiments to test seat-level(un)availability or seat map designs. If an operator has access to
individual-level locational choice data that also capture oppor-
tunities that lead to no-choice, it can use the output of our
parametric model to decide which seats to mark (temporarily)
as unavailable to improve occupancy rates. Our optimization
model for seat-level availability decisions that are not based on
price also can be used and updated nearly in real-time for
dynamic seat presentations to consumers. We provide an illus-
trative example of how an operator could use an experimental
environment, similar to a conjoint analysis, to compare occu-
pancy expectations among alternative layouts. Even if they
suffer from reduced external validity, seating chart experiments
such as ours can provide experimentally controlled assessments
of which of several layouts is likely to lead to greater occu-
pancy or, perhaps, willingness to pay. Like conjoint analysis
experiment, locational choice experiments offer an alternative
to using secondary data to approximate relative shares of pre-
ferences among seat assortments. Moreover, such experiments
can be adapted to include various types of location-specific
characteristics (e.g., prices, reclining, accessibility, VIP
access), which can be used with ticket purchases. It is important
to adapt the experimental paradigm to make it as externally
valid as possible. One should give participants a full picture of
the event’s popularity, timing, and expectations, and develop-
ing an incentive-aligned mechanism is important if one is try-
ing to use our model’s estimates to make predictions on real
data.
Theoretical and Methodological Implications
Firms can maximize revenue by adjusting their pricing accord-
ing to the (expected) occupancy as the time to an event shortens
(Desiraju and Shugan 1999; Shugan and Xie 2000). Research
on dynamic seat pricing (e.g., Williams 2018) shows that
dynamic pricing and demand affect each other in turn. The
early release of seats at a premium price appears optimal from
a revenue perspective, as long as marginal costs are small and
consumers are uncertain about whether they will miss out on an
opportunity for seats (Desiraju and Shugan 1999; Shugan and
Xie 2000). Such practices are effective when consumers are
heterogeneous in their willingness to pay. Yet venues cannot
always expect to be at capacity for every event. We therefore
suggest an alternative mechanism (i.e., individual-level prefer-
ences for proximity to focal elements and others) for defining
seat-level availability decisions (i.e., withholding or release of
seats), which may help improve occupancy at such events.
We also contribute to the marketing literature on spatial
models. Spatial models are used when consumer behaviors
depend on the actions of proximal others (e.g., Andrews
et al. 2015; Bell and Song 2007; Jank and Kannan 2005). Most
spatial models incorporate the influence of others by consider-
ing whether consumers are more likely to make the same
choice (e.g., buy the same product, choose the same store)
when distance between consumers decreases. In locational
choices, we focus on consumers’ choice of location, which
cannot be identical by incorporating the characteristics of both
surrounding others and the physical environment (i.e., Type II
spatial model; see Bradlow et al. 2005). We thus contribute
novel insights into how consumers prefer to locate themselves
when they expect to be near others (Hui, Fader, and Bradlow
2009).
We also contribute to the literature on personal space. Col-
loquially, people describe personal space as a “bubble” into
which unwanted intrusions cause discomfort. We show that
personal space is both context-dependent and spatially
oriented, as well as highly malleable. Whereas prior research
has implied that the personal space sphere is circular and inten-
sified in the front (Argyle 2013), we find that tolerance for
immediately proximate others differs depending on the loca-
tional choice context. In a movie theater, consumers avoid
immediately proximate others to their sides but are generally
indifferent to having somebody in front of them. In a concert
hall, consumers show greater overall tolerance for immediately
proximate others, and presence to their sides offers little poten-
tial discomfort, perhaps because in this context proximity to
others is expected.
We would be remiss to ignore the COVID-19 pandemic’s
impact on current and future locational choice research.
Although any pandemic probably decreases consumers’ toler-
ance for proximate others, we anticipate substantial heteroge-
neity in the willingness to risk personal space invasions and
consumer willingness to pay to reduce such risk. Whereas our
research has focused on personal space in terms of seat loca-
tions at reserved seating venues, we speculate that intolerance
for proximate others during a pandemic provides opportunity
for firms to offer (and charge for) reserved space in consump-
tion venues such as restaurants and grocery stores. As one
example, applying our approach to different venues offers the
potential for additional revenues by charging a premium for a
greater amount of personal space, or increasing the likelihood
Blanchard et al. 895
of attendance (vs. not attending due to an expected lack of
personal space).
Future Research
Dynamic optimization of seat-level availability decisions. The output
of our parametric model, with layouts including both available
and unavailable seats, establishes a new, exponential-time, bin-
ary unconstrained optimization model for seat-level availabil-
ity decisions. The optimization model in our case also is
myopic, in that it only aims to maximize expected occupancy
when all members of the sample have access to the same assort-
ment at one point in time. Such a scenario is not realistics as
consumers who purchase early (with lower occupancy) versus
late (with higher occupancy) also likely express different utility
functions (Williams 2018; e.g., business travelers are more
likely to purchase tickets at the last minute). Even without any
such modification and for modest problem sizes, solving the
problem in Equation 15 to a global optimum is difficult and we
proposed a greedy heuristic to illustrate the problem. Further
research could leverage the literature on metaheuristics to gen-
erate algorithmic approaches that in turn might produce suffi-
ciently good solutions in real time (e.g., Variable
Neighborhood Search; see Blanchard, Aloise, and DeSarbo
2017; Mladenovic and Hansen 1997).
Improved model-free classifiers. With sufficient data, the best
machine learning models should learn the data structure and
outperform our statistical model. We did not find that the
benchmark CNNs were able to learn the theoretically proposed
structure that we suggest and that we implemented using the
design matrix. Considering the potentially close links between
the locational choice task and image classification—a task for
which neural network models perform particularly well—this
outcome seemed surprising. Perhaps the disparity in perfor-
mance is due to our implementation. However, locational
choice tasks are not like typical image classification tasks in
which the researcher does not care about the precise nature of
each individual pixel in an image. Rather, we can set up a
model that relies on pooling to see the “big picture,” beyond
the more detailed-level characteristics (e.g., edge, shape). For
locational seat maps, each pixel represents a seat, and each
seat’s characteristics are important. Pooling seats therefore
results in the loss of important information, for which networks
need to compensate by obtaining more data. These data then
become compounded by the presence of substantial individual
heterogeneity (e.g., disagreements among decision makers).
Even augmenting the input vector with additional information
(e.g., individual participant indicator) did not improve the fit
significantly; as a reference, we find that even 50,000 data
points (e.g., 463 people � 115 training choices) is insufficient.
Still, considering that a neural network model can be estimated
in a matter of seconds, finding ways to apply machine learning
methods successfully to predict locational choices, perhaps
starting with the proposed attribute structure, could be fruitful.
Appendices
Appendix A: List of Experiments
In this section, we provide a full list of the experiments and
the conditions we manipulated in each of them. To refer to
the appropriate data sets, we name the analysis files as a
function of the experiment number (as indicated in the main
text), the context (movie or concert), and the number of
locations to be chosen (pairs versus singles) in Table A.1.
Each experiment may include several between- or within-
subject conditions, such as the presence of a no-choice
option or the density of the room (see Table A.2). Thus for
example, E1-Movie-Pairs.NC:75 refers to the first experi-
ment, a pair of movie tickets (E1-Movies-Pairs), and the
between-subject condition for which tasks offered a
no-choice option or not. Occupancy was manipulated
within-respondents, to be either 50% or 75%, so the data
set E1-Movie-Pairs.NC:75 refers to a subset of choices for
which occupancy was set to 75%.
Appendix B: Using Only Customers Who Chose Seats
For many events, including concerts and movies, the loca-
tional choices have an outside option. In the experiments in
the main text, we explain the outside option; it refers to a
decision not to attend the event (no-choice option at the
event level). But an outside option can take various other
forms too. For example, a customer who decides not to
attend one showing might attend another, buy tickets for a
different event (e.g., different artist, another movie), pur-
chase from a competitor, or not buy anything. Data col-
lected through movie and concert ticket sales instead tend
to omit assortment information about consumers who exer-
cise the no-choice option.
In this Appendix, we collect data from consumers who
make a choice in the presence or absence of an outside
option. We then present the parameter estimates and predic-
tions that result when we use a model trained without a no-
choice option to make predictions about choice scenarios
that actually do include this option. Detailed descriptions
of the samples are in Web Appendices C (movies) and D
(concerts). Across studies, the results support our proposi-
tion: To understand locational choices, it is critical to use
data that capture locational details when consumers do not
end up selecting any seat.
Model fit comparisons. In Table B.1, we present the results when
we find fit between the assumed process (with or without a no-
choice option) and the training and holdout prediction data.
Comparing the forced-choice and no-choice data (with the
appropriate model) seems inconclusive. On the one hand, with
movie data, the mean probabilities and hit rates are better for
no-choice than for forced choice. On the other hand, for con-
certs, fit is better for forced choice than no-choice. However,
concertgoers and moviegoers rarely would be forced to attend,
so using information obtained with forced-choice data likely
896 Journal of Marketing Research 57(5)
Tab
leA
.1.
List
and
Pro
per
ties
ofG
ener
ated
Dat
aSe
tsfr
om
the
Exper
imen
ts.
Nu
mb
er
of
Ch
oic
es
inA
naly
sis
Gen
era
ted
Files
Sam
ple
Siz
eT
ota
lIn
-Sam
ple
Ho
ldo
ut
Use
din
…
E1-M
ovi
e-Pai
rs.N
C:5
0–75
233
30–32
27–29
3W
ebA
ppen
dix
B.1
E1-M
ovi
e-Pai
rs.N
C:7
5233
15–16
12–13
3M
ovi
eA
nal
ysis
E1-M
ovi
e-Pai
rs.F
C:5
0–75
267
30–32
27–29
3W
ebA
ppen
dix
B.1
E2-M
ovi
e-Si
ngl
es.N
C/F
C:N
C300
12
10
2M
ovi
eA
nal
ysis
E2-M
ovi
e-Si
ngl
es.N
C/F
C:FC
300
12
10
2A
ppen
dix
CE2-M
ovi
e-Si
ngl
es.F
C/N
C:FC
300
12
10
2A
ppen
dix
C,W
ebA
ppen
dix
B.2
E2-M
ovi
e-Si
ngl
es.F
C/N
C:N
C300
12
10
2A
ppen
dix
C,W
ebA
ppen
dix
B.2
E3-C
once
rt-P
airs
.FC
/NC
:FC
383
22–24
18–20
4W
ebA
ppen
dix
C.1
E3-C
once
rt-P
airs
.FC
/NC
:N
C383
28–30
24–26
4C
once
rtA
nal
ysis
,A
ppen
dix
CE4-C
once
rt-S
ingl
es.F
C463
120
115
5W
ebA
ppen
dix
C.2
Not
es:FC¼
forc
edch
oic
e;N
C¼
no-c
hoic
e.
Tab
leA
.2.
Exper
imen
tD
etai
ls.
Exp
eri
men
tN
um
ber
Ven
ue
Nu
mb
er
of
Seats
Ou
tsid
eO
pti
on
Co
nd
itio
n
Data
Ch
ara
cte
rist
ics
Occu
pan
cy
(Even
lyS
plit
Wit
hin
-Su
bje
ct)
Layo
ut
an
dS
cen
ari
oC
hara
cte
rist
ics
(Wit
hin
-Su
bje
ct)
#o
fP
art
icip
an
tsT
ota
l#
of
Ch
oic
es
#o
fC
ho
ices
per
Su
bse
tV
en
ue
Siz
eT
imin
gG
en
era
ted
Files
Exper
imen
t1
Movi
e2
Gro
up
1(N
C)
300
32
Subse
t50:16
50%
12�
12
Ina
few
min
ute
sE1-M
ovi
e-Pai
rs.N
C:5
0–75
Subse
t75:16
75%
E1-M
ovi
e-Pai
rs.N
C:7
5G
roup
2(F
C)
300
32
Subse
t50:16
50%
12�
12
Ina
few
min
ute
sE1-M
ovi
e-Pai
rs.F
C:5
0–
75
Exper
imen
t2
Movi
e1
Gro
up
1(N
Cfir
st,FC
seco
nd)
319
24
Subse
tN
C:12
75%
12�
12
E2-M
ovi
e-Si
ngl
es.N
C/
FC:N
CSu
bse
tFC
:12
Ina
few
min
ute
sE2-M
ovi
e-Si
ngl
es.N
C/
FC:FC
Gro
up
2(F
Cfir
st,N
Cse
cond)
311
24
Subse
tFC
:12
E2-M
ovi
e-Si
ngl
es.F
C/
NC
:FC
Subse
tN
C:12
E2-M
ovi
e-Si
ngl
es.F
C/
NC
:N
C
Exper
imen
t3
Conce
rt2
Gro
up
1(F
C,N
C)
426
54
Subse
tFC
:24
40%
,60%
or
80%
12�
20
or
20�
12
Ina
few
day
sor
ina
few
month
s
E3-C
once
rt-P
airs
.FC
/N
C:FC
Subse
tN
C:30
E3-C
once
rt-P
airs
.FC
/N
C:N
C
Exper
imen
t4
Conce
rt1
Gro
up
1(F
C)
463
120
—225%
,50%
or
75%
10�
20,10�
10,
20�
10,o
r20�
20
Ina
few
day
sE4-C
once
rt-S
ingl
es.F
C
Not
es:FC¼
forc
edch
oic
e;option
tosk
ipth
eev
ent
was
not
avai
lable
.N
C¼
no-c
hoic
e;option
tosk
ipth
eev
ent
was
avai
lable
.
897
leads to erroneous predictions about the decision process that
consumers encounter in reality, in which they have an outside
option.
We investigate this conjecture with the concert-pairs study,
in which participants had to make both types of choices in a
within-subject design. For each consumer, we thus compare
the predictive accuracy of a model estimated with forced-
choice (no-choice) data, which we then use to forecast the
holdout choice by consumers who do (not) have an outside
option. The results are in Table B.2. We find that a model
trained on no-choice data performs similarly on both forced-
choice and no-choice holdout tasks (2.21% increase when
applied to predict forced-choice holdout tasks). However, a
model trained on forced-choice data does considerably worse
on no-choice tasks than on forced-choice tasks (approxi-
mately 24% worse; 14% hit-rate reduction), regardless of
whether we include the 11% of selections of the no-choice
option, which are obviously mispredicted by a model that
does not include this option.
Acknowledgments
The authors thank Theo Moins, Quentin Fournier, and Alexander
Dyachenko for their technical expertise. Finally, they extend their
sincere gratitude to the JMR review team for its constructive sugges-
tions throughout the revision process. All locational choice data sets
were obtained using http://www.seatmaplab.comseatmaplab.com.
Data and codes (R and Python) are stored at https://github.com/blas
imon/locationalchoicegithub.com/blasimon/locationalchoice.
Author Contributions
The first two authors contributed equally to this article.
Associate Editor
Fred Feinberg
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to
the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for
the research, authorship, and/or publication of this article: The authors
thank the Marketing Science Institute (grant 4000114) and the Penn
State Center for Sports Business Research for financial support.
References
AMC (2019), “AMC Entertainment Holdings Third Quarter 2019
Results,” https://www.businesswire.com/news/home/
20191107005322/en/AMC-Entertainment-Holdings-Announces-
Quarter-2019-Results.
Table B.1. Effect of Using a Model Trained on No-Choice/Forced-Choice Data to Predict Holdout No-Choice/Forced-Choice Data (Match).Model L þ PS þ R2R3.
Mean Probability Hit Ratea CNN Benchmark
Data Set LMD NR In-Sample Holdout In-Sample Holdout In-Sample Holdout
Movie-PairsE1-Movie-Pairs.NC:50–75 �7,341 .5410 .4845 68.60% 58.80% 26.59% 23.25%E1-Movie-Pairs.FC:50–75 �8,945 .5063 .4425 65.14% 55.06% 22.43% 17.07%Movie-Singles: First BatchE2-Movie-Singles.NC/FC: NC �6,682 .2598 .1898 44.03% 26.33% 14.52% 7.02%E2-Movie-Singles.FC/NC: FC �6,540 .2553 .1958 44.10% 28.67% 11.64% 10.53%Movie-Single: Second BatchE2-Movie-Singles.FC/NC: NC �6,355 .2892 .2164 46.27% 30.67% 12.45% 12.39%E2-Movie-Singles.NC/FC: FC �6,568 .2623 .2051 43.20% 28.33% 16.73% 7.89%Concert-PairsE3-Concert-Pairs.FC/NC: NC �12,038 .5129 .4592 65.57% 56.66% 45.91% 35.93%E3-Concert-Pairs.FC/NC: FC �8,136 .5620 .5138 69.80% 61.55% 49.43% 40.05%
Notes: FC ¼ forced choice; NC ¼ no-choice.
Table B.2. Concert-Pairs: Effect of Using a Model Trained on No-Choice/Forced-Choice Data to Predict Holdout Forced-Choice/No-Choice Data (Mismatch). Hit Rates.
Prediction Sample
HoldoutFC Tasks
Holdout NC Tasks
Estimation Model/Training Data Used
NC OptionNot Chosena
AllChoices
Vno�choice Included/NCdata
57.91% 56.66% 56.66%
Increase due to mismatch þ2.21%Vno�choice Excluded / FC
data61.55% 47.11% 46.78%
Reduction due tomismatch
�23.46% �24.00%
aIf we use a model without no-choice and predict choices when the no-choiceoption is available, the parameters cannot predict the no-choice option. Taskswith a no-choice option selected are excluded; they all would have beenmispredicted.
Notes: NC ¼ no-choice; FC ¼ forced choice.
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