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Shopping Cart Abandonment at Retail Websites –
A Multi-Stage Model of Online Shopping Behavior
Shibo Li and Patrali Chatterjee
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February 16, 2005
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Shibo Li (shibo_li@rbsmail.rutgers.edu, Tel: 732-445-5642, Fax: 732-445-3816) is an Assistant Professor of
Marketing at Rutgers Business School – Newark and New Brunswick, Rutgers University, 228 Janice Levin
Building, 94 Rockafeller Road, Piscataway, NJ 08854. Patrali Chatterjee (patrali@andromeda.rutgers.edu, Tel: 973-
353-5476, Fax: 973-353-1325) is an Assistant Professor of Marketing at Rutgers Business School – Newark and
New Brunswick, Rutgers University, 180 University Avenue, Newark, NJ 07102. This paper benefited from
comments received at the presentation. The authors thank Donna Hoffman, Sharan Jagpal, Alan Montgomery and
participants at the 2004 Marketing Science Conference, Rotterdam and NYU-Stern seminar for their valuable
comments and suggestions. The authors wish to thank comScore Networks for their generous contribution of data
without which this research would not have been possible.
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Shopping Cart Abandonment at Retail Websites –
A Multi-Stage Model of Online Shopping Behavior
Abstract
We propose a four-stage model of online shopping process to study shopping cart abandonment.
Consumer heterogeneity is accounted within a hierarchical Bayesian framework. A hidden
Markov switching process is used to capture unobserved user navigation orientation. Managerial
implications for customized web pages to reduce the attrition at each stage are discussed.
Keywords: Online Retailing, Virtual Shopping Carts, Clickstream Data, Hierarchical Bayes
Models, Hidden Markov Chain Models
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Shopping Cart Abandonment at Retail Websites –
A Multi-Stage Model of Online Shopping Behavior
INTRODUCTION
While e-commerce channels are generating millions of dollars in sales for many
businesses, the most successful e-commerce channels convert only 8% of their online visitors to
paying customers. Most firms are able to convert only 2 to 3 percent (Goldwyn 2003). Online
retailers have been able to drive down their acquisition costs by their increasing sophistication in
using both online and offline channels to drive website traffic and lower advertising rates from
an average of $38 in 1999 to $14 in 2001 per consumer (Boston Consulting Group Survey 2002).
However shopping cart abandonment is a significant problem for large and small e-tailers with
estimates ranging over $6.5B (Buerki 2003) and is significantly affecting their profitability
(Gutzman 2000). Reports in the commercial media suggest that 78% of online buyers abandon
their shopping carts (Goldwyn 2003), with 55% abandoning carts before they enter the checkout
process and 32% abandoning their carts at the point of sale e.g. when they should fill in shipping
and payment information. Commercial studies have investigated online shopping cart
abandonment at an aggregate website level, providing little guidance on when shopping carts are
abandoned and how they can be mitigated (Cotlier 2001).
A major challenge in measuring shopping cart abandonment is due to differences in
defining when a shopping cart is abandoned. We consider shopping cart abandonment to take
place only after consumers place items in their shopping cart. Hence, if the consumer leaves the
site after information search without adding items to her virtual cart, there is no shopping cart
abandoned. If the consumer adds item(s) to her shopping cart and leaves the site without a
purchase, the shopping cart is designated as being abandoned. Unfortunately, most commercial
clickstream analyzers do not distinguish between these two categories of no-purchase sessions,
nor can they identify where abandonment occurs. Reasons for shopping cart abandonment could
be categorized into two categories - challenges posed by web site design and factors influencing
consumer purchase motivation. According to research conducted by BCG (Wellner 2001) most
shopping cart abandonment is due to faulty website design and navigational issues. Reasons for
shopping cart abandonment that can be addressed by better web site design include insufficient
information on products and shipping costs (ResearchandMarkets.com 2004), limited
functionalities on webpages, confusing buttons or icons, low quality of user interface, detailed
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registration requirement before purchase (39%), unstable or unreliable interactivity at website
(31%) and multipage time-consuming checkout process (27%) (Vividence Corp. 2001).
However abandonment does not always indicate specific website design problems. In
many cases, it is driven by characteristics of how consumers shop online and their expectations
of the experience. High shipping prices (72%), desire to comparison shop or browse prior to
purchase decision (61%), changing one’s mind (56%), saving items for later purchase (51%) and
high total cost of items can deter consumers from completing the final stage of their purchase
process (Vividence Corp. 2001). The source of shopping cart abandonment seems to have
dramatically contrasting implications for the online retailer. Wellner (2001) quoting the BCG
study reports that 28% of shoppers who abandoned shopping carts due to technical and
navigational failures at the website will not buy from that site again and a smaller but still
significant 10% stopped shopping online altogether. In contrast, the Vividence study suggests
that many abandoned shopping carts are accessed and some are purchased in future visits.
Technical and operational glitches contributing to shopping cart abandonment can be
addressed by e-tailers. However e-tailers cannot mitigate shopping cart abandonment due to
customers’ purchase motivation and navigation orientation, while shopping at online stores. For
example, 61% of respondents in the Vividence study indicated that they were comparison
shopping or browsing online, and many of them ultimately prefer to conclude their transactions
at the online retailers’ brick and mortar stores. This is backed up by Shop.org’s annual survey of
retail sales (which interviewed 48,000 US shoppers in March 2002), 73% of respondents
indicated that they research some of their purchases online before coming to the store. In this
case, online stores will have high shopping cart abandonment if they excel in driving qualified
traffic to brick-and-mortar stores by offering features that facilitate the entire shopping process.
In a multi-channel operation using shopping cart abandonment rates to measure effectiveness of
an online channel can be very myopic. Hence it is important to understand where in the
consumer’s shopping process shopping cart abandonment occurs so remedial actions can be
appropriately directed.
Hence, we propose that a consumer’s shopping process at an online store can be
decomposed into four stages: (1.) the consumer views a shopping page, (2.) adds items to their
shopping carts conditional on page view a shopping page, followed by (3.) decision to start
checkout by page view the shopping cart, conditional on page view shopping page and placing
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items in shopping cart and finally (4.) decision to purchase item(s) in shopping cart. We model
consumers’ decision to continue (or abandon) the shopping process at each of these stages, as a
series of conditional binary probit models. Modeling substages in the shopping process offers us
several advantages over modeling only the purchase/abandon events at the session level. First,
we separate no cart activity sessions for information searchers, from sessions in which shopping
carts were abandoned and purchasers. Second, this allows us to investigate if the covariates differ
in their impact on the purchase/abandon behavior at each of the stages. Third, modeling sub-
stages is methodologically superior and should predict shopping cart abandonment better than
modeling only purchase/ no purchase events (Sismeiro and Bucklin 2004). Consumer
heterogeneity at consumer level is accounted for within a hierarchical Bayesian framework. Our
model incorporates a mixture process whose multiple states are governed by a hidden Markov
switching chain, to capture time varying, within user heterogeneity (due to the influence of
unobserved purchase intent on navigation orientation during the visit). Navigation orientation
varies within the session in response to promotional stimuli encountered while browsing and
determines the culmination of an online visit in terms of shopping cart purchase or abandonment.
Shopping Cart Abandonment Online vs. Offline
The key to investigating shopping cart abandonment online involves understanding the
differences between online and offline shopping activity and the role virtual shopping carts play
in online stores. Offline shopping activity involves significantly higher tangible and
psychological costs (time, transportation costs etc.) than online shopping activity (Moe and Fader
2003). Information search, alternative evaluation and decision-making precedes most offline
shopping activity since there are limited returns to multiple store trips and consumers are more
likely to seek closure to a purchase decision. Very few customers leave stores with no purchases,
except for durable, complex or high-cost purchases where consumers may make multiple store
trips while deliberating on a purchase decision (Putsis and Srinivasan 1994). The relatively
negligible costs of undertaking online shopping activity and information-rich environment at
most online stores makes information gathering an integral part of the online shopping process.
Online shopping activity even in the case of frequently purchased goods parallels the search and
deliberation activity that is typically observed for offline durable purchases. Hence, shopping
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cart abandonment online will always be higher than shopping cart abandonment in bricks and
mortar stores.
Further, the role of shopping carts at online stores differs significantly from their
counterparts at bricks-and-mortar stores. Virtual shopping carts are primarily used as external
memory aids to “bookmark” products that could be lost while browsing other pages or bought on
future visits - similar to “wishlist” feature. Research on consumer decision-making in
information-rich environments like the WWW suggests that consumers use a two-stage decision
process to simplify their product choice task (Haubl and Trifts 2000). In the first stage consumers
screen alternatives to create consideration sets of fewer items in order to reduce cognitive load
and effort (Bettman 1979). In the choice stage, consumers use more effortful compensatory
strategies to evaluate alternatives in the consideration set to make their purchase decision
(Iyengar & Lepper 2000).
Items in virtual shopping carts represent the first-stage process, i.e., consideration set or
items consumers’ are interested in considering in the choice stage, like turning down or marking
page in a catalog, but not necessarily purchase on that visit. In contrast, items are placed in
traditional shopping carts after alternatives have been considered, evaluated and a choice to
purchase has been made at the conclusion of the second stage choice process discussed in
literature. Further abandoning an online shopping cart with the click of a mouse on an external
hyperlink to jump to another website or close the browser represents the default option and is
relatively easier to do, than registering, providing financial information to complete the purchase
process. It is a lot more embarrassing to abandon a shopping cart at the checkout lane in a bricks-
and-mortar store. This might explain why drop-off rates of 2-3% at offline stores may be very
difficult to achieve at online stores.
Clearly shopping cart abandonment may not necessarily be detrimental to the retailer, it
can provide a wealth of information on consideration set formation, complementarity between
items, how consumers respond to pricing offers and items that are preferred by its consumer
base. Items in a customer’s shopping cart are measure of a consumer’s interest even if she does
not proceed with her purchase. In the following section we review the limited published research
on online shopping cart abandonment. Next, we present our conceptual framework by
discussing the role virtual shopping carts play at online stores and present a model of online
shopping behavior. Then, we discuss our empirical context and clickstream data. We develop our
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econometric model and present estimation details. We conclude with a discussion of our results
and managerial implications.
LITERATURE REVIEW
To our knowledge there has been very little research on online shopping cart
abandonment in the marketing literature. In the context of offline shopping, consumer search and
shopping as a consumption experience and the role of purchase intent and purchase motivation
on conversion has been extensively studied. However, compulsive shopping and impulse buys
(O’Guinn and Faber 1989) though related to experiential and goal-directed shopping behavior
have been largely unexplained or explicitly modeled. Researchers have demonstrated that store
atmospherics and surprise promotions have utilitarian and hedonic benefits in purchase decision-
making and change basket size and increase unplanned purchases (Chandon, Wansink and
Laurent 2000, Heilman, Nakamoto and Rao 2002). The underlying assumption in this research is
that purchase motivation and intent remains stable throughout the shopping process, since in-
process measures were largely unavailable.
In the context of online shopping behavior, Oliver and Shor (2003) investigated the role
of online promotion codes as a dissatisfier leading to shopping cart abandonment. They found
that most online shopping carts were abandoned when consumers, who did not have promotional
codes, were prompted for “enter online coupon or redemption code” in the checkout stage.
However, this does not address shopping cart abandonment at websites that do not prompt
consumers for a coupon. In another study investigating the effect of checkout process on
shopping cart abandonment, Eisenberg (2003) found no correlation between reduction of steps in
the checkout process and reduction in abandonment rate. He suggested that including a progress
indicator with numbered steps on each checkout page and allowing shoppers the opportunity to
review what they did in previous steps and a way to return to their current step will reduce the
negative impact of having a multi-page checkout process. Both of these studies investigated the
effect of retailer controllable design features of the online store on shopping cart abandonment. It
is less clear how what consumers do, what they are exposed to while browsing the retailer
website affects shopping cart abandonment.
Most existing research on online purchase behavior using clickstream data discussed
above have categorized consumer purchase intent or motivation as a stable characteristic
throughout the session. However, Mandel and Johnson (2002) find that users dynamically adapt
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their behavior to the page-by-page stimuli presented to them, even when unaware of their own
adaptive behavior. Hence content, hyperlinks, promotion and ad stimuli consumers encounter
during online navigation may cause interruptions, diversions and abandonment of their original
shopping goals. Moe and Fader (2004) develop an individual probability model to predict those
visits likely to convert to purchases. Their model allows shopping behavior to change across
visits (but not within a visit) as a function of past experiences. However, within-visit activities
such as browsing behavior and exposure to site design and content are not studied.
Montgomery, Li, Srinivasan and Liechty (2004) in their path analysis of content browsed
through a website use a hidden Markov chain to model the change in browsing behavior state
depending upon a user’s current goals or state of mind during the course of a session. However,
they do not consider the effect of site stimuli as covariates in determining the change in browsing
state, nor do they separate recreational no-purchase from abandonment.
Our conceptualization of online shopping process as comprising of four stages bears
resemblance to Sismeiro and Bucklin’s (2004) proposition of a task-completion approach to
modeling the shopping process at an online automobile website. They use sequential binary
probit models to model task completion at each stage conditional on completing task at the prior
stage. However their empirical context does not allow them to examine effects of exposure to
promotional stimuli or comparison shopping. Further they specify heterogeneity at the county
level instead of the individual level as we do in this paper. In the next section we propose a
conceptual framework to modeling shopping cart abandonment.
CONCEPTUAL FRAMEWORK
Proposed Model of Online Shopping Behavior
We propose a model of online shopping behavior based on the information processing
theory of consumer choice (Howard and Sheth 1969). We adopt a four-stage model that parallels
consumer decision-making stages. A consumer enters an online store and engages in information
search (i.e., consumer views pages with product information at the site), followed by
consideration stage (placement of items in the virtual shopping cart), an evaluation stage
(decision to view the shopping cart page) and finally purchase decision (i.e., shopping cart
payment or abandonment). Please note that the stages are sequential and consumers may drop
out as they progress and skip stages. We propose that consumer navigation orientation and
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reasons for visiting a commercial website and stimuli encountered during navigation impacts
decision to proceed through the shopping process and these impacts differ across the different
stages of the shopping process.
The Role of Unobserved Purchase Intent:
In the marketing literature, the shopping process has been analyzed from the context of
goal-directed vs. experiential shopping behavior, both in traditional (Babin, Darden and Griffin
1994) and online settings (Wolfinbarger and Gilly 2001). Shopping is characterized as either
“work” (high purchase intent) or “play” (low purchase intent) (Wolfinbarger and Gilly 2001)
based on whether motivation is extrinsic or intrinsic (Bagozzi, Davis and Warshaw 1992; Bloch
and Richins 1983; Celsi and Olson 1988) and involvement is situational or enduring (Bloch,
Sherrell and Ridgway 1986). Using clickstream data, Moe (2003) proposed a typology of online
shopping visits as buying, browsing, searching or knowledge-building that vary in terms of
purchasing likelihood and whether purchasing horizon is immediate or in the future and search
behavior is either directed or exploratory throughout the session. Further these visit goals are
manifested in differences in browsing behavior online. Bloch et al. (1986) suggest that shopping
orientation and unobserved purchase intent are influenced by many intrinsic and extrinsic
factors, and may manifest itself in a variety of outcomes. Hence investigation of the shopping
process itself is critical.
Prior research on purchase intent suggests that the stages of buyer readiness a consumer
is in, will determine the types of information sought at the site or at external sites, the time taken
to culminate the purchase process and the role of promotions in the purchase decision process.
Purchase intent may change within the session due to information content and stimuli
encountered while browsing (Montgomery, Li, Srinivasan and Liechty, 2004). The impact of
these stimuli on purchase intent differs across the stages and may accelerate or distract from
shopping process and purchase. For example, an offer of free shipping with minimum purchase
encountered during information search may motivate a consumer to consider putting an
additional book in the shopping cart to take advantage of the offer. However the same offer
displayed for the first time during checkout after the consumer has made final choice decisions
may lead the consumer to go back and potentially abandon his or her shopping cart. We can only
infer navigation orientation based on browsing characteristics in that stage and observe the
binary decision, whether consumers continued through or abandoned the shopping process.
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Information Search – Page view Product Shopping Page:
Consumer search has been studied extensively in the marketing literature. From a
decision-making perspective, prepurchase search has been defined as information seeking and
processing activities which one engages in to facilitate decision making regarding some goal
object (i.e., purchase) in the marketplace. Consumers may visit an online retail website using
their bookmark or type in the URL, in response to an email offer, shopping or search agent
referral and can be considered to be a mixture of “prepurchase searchers” and “ongoing
searchers” (Moe 2003). The consumer proceeds through the shopping process if this stage
culminates with the customer adding item(s) to her shopping cart, otherwise the consumer may
drop out by exiting the site.
Consumers may engage in directed search corresponding to planned purchasing behavior
where she is probably aware of specific product items, has substantial information, developed
preferences and is looking for product item- and purchase-specific information before placing the
item in her shopping cart. A consumer who logs in or registers to his or her account early in the
session indicates higher predisposition towards purchase. Search/deliberation visits are also goal-
directed with a planned future purchase in mind but the objective is to acquire relevant
information to enhance the quality of the purchase outcome (Putsis and Staelin 1983) and build a
consideration set. The consumer will browse relatively more category-specific pages than
product-specific pages, may use decision aids such as search engines and may deviate to
competing retailer websites to comparison shop for information, selection, price or deals (and
may or may not return). This stage will typically be used to look at available products, compare
their consideration utility to a threshold to determine whether a brand should be considered and
culminates when the consumer decides to put the item in the shopping cart. This may be done
one or more times and even after starting checkout until the consumer has found products that
satisfy his or her needs. This phase is intensely user-driven because the user is looking at and
assimilating information continuously. Promotion offers displayed at this stage may help or
distract the consumer from setting purchase-related goals for the session.
Ongoing searchers engage in search activity that is recreational or independent of specific
purchase needs or decisions and may involve two basic motives. The first “knowledge-
building”(Moe 2003) is to acquire a bank of product information potentially useful in the future
either for personal use “purchase efficiencies” or for dissemination to others (Hirschman and
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Wallendorf 1982). The second “hedonic browsing” is pleasure, recreation or intrinsic satisfaction
with the search activity itself. Unlike the bricks-and-mortar world, these ongoing or recreational
searchers with low purchase intent are likely to add items in their virtual shopping cart to
bookmark and organize information to form consideration sets for future use. Others may exit
the website without using the shopping cart altogether. Unlike earlier research, our modeling
framework allows us to discriminate between these types to account for “true” shopping cart
abandonment behavior.
The central difference between prepurchase and ongoing search is the consumer’s ability
and/or readiness to buy at the time of search activity. Because of their desire to acquire general
product knowledge, ongoing searchers will tend to focus more on informational pages and spend
more time processing informational content and hence have longer page view durations. They
are less likely to login into their account, and are more likely to deviate to related and unrelated
category external websites. Please note that an ongoing searcher browsing through a website
without any intent to buy may, nevertheless, make a purchase in response to an attractive price or
promotional offer (O'Guinn and Faber 1989). This parallels the traditional in-store purchase
context corresponding to the low involvement decision-making model. Kotler (1974: p. 50)
suggested that most purchases are unplanned and that pricing promotions, displays, information
on the package can be designed “to produce specific emotional effects in the buyer that enhance
his purchase probability.” Our modeling framework can capture the impact of stimuli on
unplanned purchase behavior through their impact on unobserved purchase intent.
Consideration Stage - Decision to Place Item in Shopping Cart
In the consideration stage, the outcome of interest is adding product item(s) to the
shopping cart. Please note that the sequential nature of the process implies that this stage is
contingent on the occurrence of the prior information search stage. Consumers with preplanned
purchase goals and well-defined choices are likely to add (fewer) items that more closely reflect
their choice set and are more likely to be purchased. Links to account pages make it easy for
consumers to follow through on their purchase goals. Prominent hyperlinked complementary
product suggestions may help consolidate purchases and increase purchase order value.
Prepurchase searchers trying to make optimal choices are likely to add items that satisfy their
consideration criteria so that they can be evaluated later in their shopping process without having
to search for them again. Consumers may jump to competing retailer sites to comparison shop
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after they have added an item to their shopping cart. Ongoing searchers may add items to their
shopping cart to form a “wishlist” or repository of product information they might be interested
in the future.
A wide variety of technologies and features both standard and proprietary exist in virtual
shopping carts across stores. Some shopping carts tout patented “one-click” features (e.g.,
Amazon.com and BN.com), click once to place an item in the cart and continue shopping. Others
require users to click several times every time they add a unique item to the cart before they can
resume shopping. Click a "Buy" button, view contents of cart (a deviation from browsing
activity), and then click again to continue shopping. Shopping carts may be persistent, i.e., retain
items placed in them across visits; or non-persistent, items in shopping cart are emptied once the
consumer leaves the site. The nature of persistency may vary based on whether the consumer has
logged in to their account prior to adding items to their cart. Items retained in persistent shopping
carts from prior visits may act as distractors or cues to more purchases. Similarly, consumers’
desire to comparison shop after placing considered items in a non-persistent shopping cart can
lead to frustration and unintentional cart abandonment after they return from competing sites.
Evaluation Stage (Decision to View Shopping Cart/ Start Checkout)
The information search and placing items in the cart phases discussed earlier are, in
essence, user-driven iterative browsing and selection tasks with (possibly) less well-defined
goals and a larger number of possible actions. The checkout phases are system-driven pre-
defined, linear tasks with well-defined goals and sub-goals, and with a smaller number of
predefined actions. Thus most consumers with low purchase intent drop out of the process prior
to this stage. Most consumers who have not already abandoned the shopping process and are
evaluating their shopping cart are likely to make a purchase.
Most online shopping carts show the items that the customer has already selected.
Typical provided attributes are: item code, item name or short description, quantity, price, extra
discount (if provided), availability, subtotal cost, shipping and other costs, total cost. When users
trigger the checkout stage, they may have formed their consideration set and want to make their
choice decision. A differentiating aspect of this stage is that consumers may use multiple
information processing strategies to choose among categories of products and also brands within
a category. Links to information that the user wants to read before completing the purchase e.g.:
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product description, shipping details, return policy, security policy, etc. if not provided earlier
must be provided at this stage to avoid frustration and abandonment later.
Hyperlinked item descriptions to item details can be very useful in avoiding frustration.
Consumers may return to information search stage after evaluating contents in their cart to locate
additional alternatives or verify information. Please note that this diversion to search additional
information either at the retailer or competing retailer site may also lead to abandonment. Most
shopping carts support operations for: adding items, removing items, emptying shopping cart,
comparing items, changing items’ quantities, updating shopping cart to allow consumers meet
intrinsic shopping and promotion-related goals. This stage may involve elaborate processing by
highly involved consumers to finalize purchase order.
Purchase Decision (Shopping Cart Payment or Abandonment)
The purchase decision phase has a single goal – completing the financial transaction (as
defined by the contents of their shopping cart and their shipping preferences) as quickly and
securely as possible with the minimum of disruption and roadblocks. Accordingly this phase has
a set of linear and intentionally fairly rigid sub-goals and is system-driven. The focus here is not
on user entertainment but on completing the transaction rapidly and securely – before shoppers
change their minds about their shopping carts and the related cost. Because errors could have a
more serious (security and financial) impact, a well-designed user help function and provision of
obvious and intuitive navigation clues by using progress or stage indicators are essential.
Consumers have to provide certain details with privacy implications, such as their
address and credit card details. Some websites have all stages integrated into one page (e.g.
www.amazon.com) but the implied functionality is the same – each of these categories of
information must be provided so that the transaction in the next stage can be carried out.
Simplifying this process will ensure that there will be a smaller incidence of purchase deferral
and shopping cart abandonment during this phase- providing additional costs such as shipping
and handling were shown earlier. Users who feel that they have lost control can simply abandon
their shopping cart and leave the site without any embarrassment, unlike a user standing at a
checkout in a supermarket.
EMPIRICAL CONTEXT
We applied our model to clickstream data of bookstore purchases at http://barnesand
noble.com (or books.com or bn.com). The dataset used for this analysis consists of 1,160 users
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who visited barnesandnoble.com between April 1, 2002 and April 30, 2002, as measured by
comScore Media Metrix
2
. Table 1 provides the demographic characteristics of consumers in our
sample.
_______________
Insert Table 1 here
The “one-click” online purchasing system at the B&N website is branded as B&N
EXPRESS CHECKOUT (described in the US Patent No. 5,960,411 owned by Amazon.com, Inc.
and legally contested by B&N’s Express Checkout feature). According to the patent, “once the
description of an item is displayed, the [user] need only take a single action to place the order to
purchase that item.” That “single action,” such as the clicking of a “Buy Now” icon, is sufficient
to consummate a sale because the user’s billing and shipping information is already stored in the
seller’s database. B&N’s online shopping cart is non-persistent, and displayed on every shopping
page. The descriptive statistics of the data are given in Table 2.
_______________
Insert Table 2 here
We have the following information on covariates for the panelists’ visits at B&N:
Shopping Cart Data. ID of person making purchases, the date and time of purchase.
Navigation Activity Data. Information on pages viewed by the consumer include date and time of
visit, whether weekend or not (Weekend), whether the consumer came to website after clicking
on an e-mail offer (Email), whether purchased on last visit (Last buy) and whether used wishlist
feature (Wishlist) in the present session. The sequence of activities during the session was
constructed from the page-by-page click data - number of pages browsed prior to current page
(Visit depth), cumulative exposures to pop-up ads (PopAds), and time since last page view. The
cumulative page views at comparison shopping websites such as bizrate.com during the session
(Comp. Shop), the total number of competitive bookstore sites the consumer visited during the
B&N session (Cumother) and cumulative number of non-bookstore websites visited (Cumnotbn)
captures the comparison-shopping behavior by consumers while shopping for books at B&N.
2
Shortly after compiling the dataset used in this analysis, Media Metrix was acquired by comScore Networks.
comScore subsequently implemented considerable improvements to both the data collection methodology and depth
of data measured. Improvements include a significant increase in panel size to accommodate analysis of home, work
and university audiences, and full measurement of transaction details including products purchased, prices paid and
shopping basket totals which are not available in our data used in this study.
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Page Data at B&N. Data on HTML content on each page was collected using Perl script for
presence of banner ad (Ad), price (Price) and promotional image (Promotion). The number of
links to various types of webpages at B&N – to home page, to account pages, to product pages,
and to information pages was also collected.
The 1,160 users had 1,704 sessions at the site, and viewed an average of 8.75 pages per
session. Ninety-four sessions ended in purchases. Hence the conversion rate is 5.5% (Table 3).
Preliminary analyses of the data indicates that consumers differ in their behavior in sessions
when they purchase compared to those when they do not purchase (1,610 sessions out of
11,139). In sessions when shopping carts were abandoned consumers are less likely to access
shopping pages (p<0.05), add items to their shopping cart, view their shopping cart and purchase
(all p<0.01). Further they were exposed to more promotion offers, banner ads to other products
than sessions when a purchase was made. Consumers who purchased their shopping cart items
visited more frequently, have a higher likelihood of visiting during weekends, browsed more
pages and visited more non-bookstore websites.
________________
Insert Table 3 here
We find that consumers don’t use the shopping cart on 90.2% sessions and rarely use the
wishlist feature (99.4%). The median number of items placed in the shopping cart or wishlist is
1, see Figure 1. The number of unique items in shopping cart has a non-linear effect on purchase
probability. Figure 2 indicates that the median number of items in shopping carts that are
purchased is 2. Carts with 1 item are more likely to be abandoned than purchased, carts with 2
items are more likely to be purchased than abandoned. The propensity to purchase or abandon
with more items in cart is insignificantly different thereafter.
____________________
Insert Figures 1 and 2 here
To illustrate how dependent measures were constructed from our data, we discuss the
decomposition of the four-stage shopping process for the user session reported in Table 4. The
user started by being exposed to a pop-up promotion window on free shipping. This corresponds
to the first stage of whether to view shopping pages. This first stage lasted for two page views
until the user looked at a shopping page to check item information on the page (i.e. on the second
page view). Then the user entered into the second stage of whether to add item(s) to the shopping
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cart. He searched around for various items until on the tenth page view, when he actually added
something to the cart for the first time (i.e. note the keyword “vcqty=1”). Next, the user entered
into the third stage of whether to view the shopping cart with item(s). The user viewed the
shopping cart on the thirteenth page view, but abandoned his shopping cart without a purchase.
The decomposition of users’ session into the four natural stages of shopping process could
provide more insights to managers on how to reduce online retailer’s shopping cart abandonment
rate.
________________
Insert Table 4 here
Figure 3 shows the attrition rate of consumers in our sample at the four shopping stages.
42% of consumers who enter the site leave without using the shopping cart. Of the remaining
58% almost half (42%) add an item to their shopping cart and abandon the site without checking.
Once consumers start checkout, very few (1.35%) leave while evaluating their shopping cart and
making their purchase selections. In the final purchase stage one-third of consumers leave
without completing their transaction. Hence, inducing consumers to enter stage 3 – page
viewshopping cart is key to reduce shopping abandonment. To quantify the impact of these
variables on shopping process outcomes variables we develop our estimation model of shopping
cart behavior next.
________________
Insert Figure 3 here
A DYNAMIC FOUR-STAGE MODEL OF ONLINE SHOPPING CART BEHAVIOR
Our exploratory analysis from the previous sections suggest that there are four natural
stages of online user’s shopping cart behavior starting with shopping page view where users can
add items to their shopping carts conditional on decision to visit the site (i.e. stage 1), followed
by decision to place or remove the item in the virtual shopping cart (i.e. stage 2), decision to
view shopping cart prior to site exit (i.e. stage 3), and finally decision to purchase item(s) in
shopping cart (i.e. stage 4). Therefore, we propose a four-stage model of binary probit to model
user’s decisions at each stage. As shown in Montgomery, Li, Srinivasan and Liechty (2004),
user’s browsing behavior has high persistency. Therefore, we use an autoregressive process of
the latent utility to capture this dynamic change over time. Additionally, consistent with past
17
research, we employ a hierarchical Bayesian framework to account for consumer heterogeneity
with the use of user characteristics and demographics to explain some of this heterogeneity.
Formally, we assume that user i has latent utility
t
j
iqt
U associated with page view a page in
stage j on page view occasion t of session q, where there are total of I users, Q
i
sessions for user
i, and T
iq
page views for the q
th
session of user i. j
t
(= 1, 2, 3, 4) refers to stage j on occasion t. In
our dataset, I=1,160, Q
i
ranges from 1 to 17, and T
iq
ranges from 1 to 238. If the latent utility is
greater than some threshold value (without loss of generality, this threshold value is normalized
to be zero), the consumer chooses to view a page at stage j
t
. Otherwise, not choose to view it.
We denote the user’s choice of a page at stage j
t
as Y
iqt
. Therefore, we have the following
observational equation:
>
=
otherwise0
0 if1
t
t
j
iqt
j
iqt
U
Y
. (1)
The latent utility (
t
j
iqt
U ) is modeled as an autoregressive process with order 1 (i.e., AR(1)
process, Paap and Franses 2000, Haaijer and Wedel 2001, Seetharaman 2004, Montgomery, Li,
Srinivasan and Liechty 2004):
)1()1(
)1()1(
t
t
t
t
t
j
iqts
j
tiq
j
is
j
tiqis
j
iqt
εXΓUU ++=
−−
−−
φ
,
]1 ,0[~ N
t
j
iqts
ε
(2)
where subscript s defines the user’s unobserved state (s=1, …, S) for user i during session q at
page view t. Also,
)1(
)1(
−
−
t
j
tiq
X
is a vector of the L-1 covariates given in Table 2 for user i during
session q at time t (L=19 as the first element of X is unity to incorporate an intercept),
t
j
is
Γ is a 1
× L parameter vector. The error terms
t
j
iqts
ε are assumed to be distributed as ]1 ,0[N while the
variance is normalized to be 1 for identification purpose.
Notice that the
)1(
)1(
−
−
t
j
tiq
X
covariates associated with the utility at time t, see equation (2),
correspond to the page contents of the previous page view at time t-1. We assume that a user
decides which category to view at time t largely based upon the information being viewed at time
t-1 (e.g., the number of links of the page, type of information display, time page viewed, etc.),
since the page at time t has not yet been displayed.
To identify the unobserved states and the parameters in equation (2), we let the expected
value of
t
j
iqt
U ,
t
j
iqts
U , increase in state s for all the four stages. That is, the higher the state, the
18
higher the user’s expected utility to choose to view a shopping page, add item to cart, view the
cart, and make a purchase in the four different stages, respectively (i.e.
ttt
j
iqtS
j
iqt
j
iqt
UUU ≤⋅⋅⋅≤≤
21
,
for j
t
= 1, 2, 3, 4).
Similar to Li, Liechty, and Montgomery (2002) and Montgomery, Li, Srinivasan, and
Liechty (2004), we formulate the first-order Markov process by assuming that there is a hidden,
continuous time Markov chain , D
iqt
, which indicates the state. Note that s is only defined at
integer time values, while D
iqt
is continuous and equal to s at integer values
3
. The waiting time
between transitions (w
iqt
) in our continuous time domain follows an exponential distribution:
[]
′
=−=
iqtSiqtiqtiqtDiqtiqtDiqtiqtiqt
iqtiqt
ww λλλλλ L
21,,
where},exp{]|Pr[ λλ
(3)
where
iqts
λ is an intensity parameter for state s for session q at occasion t, and the expected
waiting time till the next is the inverse of this parameter (
iqts
λ1 ). Given that a transition has
occurred, the transition matrix (
iqt
P ) that defines our first-order Markov process is:
[]
=>===
+
0
0
0
where,1 if ,,Pr
21
221
112
,
L
MOMM
L
L
iqtSiqtS
Siqtiqt
Siqtiqt
iqtigsiqtiqiqtwtiq
PP
PP
PP
tPgDsD
iqt
PPν
(4)
where P
iqtgs
denotes the conditional distribution for user i to switch to state s in session q on
occasion t given the previous state was g, hence the rows sum to one. Notice that the diagonal
elements are zero since same state transitions are captured through the waiting time. Finally, the
initial state probability for the first page view during a session is:
1 if ]Pr[
,
=== tvsD
iqt
Diqiqiqt
ν
.
(5)
where we redefine the probability vector
iq
ν as the initial starting probabilities.
Consumer Heterogeneity
Following the usual hierarchical Bayesian framework (Rossi, McCulloch, and Allenby
1996) we incorporate heterogeneity across users by assuming that
t
j
is
Γ ( j
t
= 1, 2, 3, 4) has a
random coefficient specification. Specifically,
t
j
is
Γ follows a multivariate regression:
3
We define time between page views as a standard time unit, and not as the time of day. The elapsed clock time
between page views is irregular, and may include page views at other sites or non-computer activities (e.g., getting a
19
) ,(~ ,
ttttt
j
s
j
is
j
isi
j
s
j
is
MVN Ψ0ςςRΠΓ +=
,
(6)
where
i
R is the K × 1 vector of demographic measures, plus an intercept, listed in Table 1 for
user i (K=10, since the first element is unity to incorporate an intercept),
t
j
s
Π
is a 1 × K
parameter matrix, and
s
Ψ is a L × L covariance matrix.
Finally, we assume that the row vectors of the transition matrix and the vector of initial
probabilities follow a Dirichlet distribution, and the waiting times follow a gamma distribution:
),(~ ),(~ ),(~
iqtsiqtsiqtsiqsiqsiqtjiqtj
DD λλλν
()
ΓατP
,
(7)
where P
iqtj
denotes the jth row of the matrix P
iqt
,
iqtsiqts
λλ
()
and
denote the shape and scale
parameters, respectively.
We also want to see if managers can intervene users’ hidden markov process. Thus, we
assume that the hyper-parameters (
iqtiqtiqiqtj
λλατ
()
, , , ) are functions of session context variables
or marketing variables. So we have:
iqtiqt
s
iqt
iqtiqt
s
iqt
iqiq
s
iq
iqtjiqt
j
iqtj
ιEλλ
ρEλλ
ξEαα
υEττ
+⋅=
+⋅=
+⋅=
+⋅=
((
))
, (8)
Where
iqt
E are session context variables or marketing variables for user i for session q at
occasion t. Since all the hyper-parameters (
iqtiqtiqiqtj
λλατ
()
, , ,
) should be positive, we assume the
following distributions for the error terms: ),0( ~
υ
Συ NormalTruncated
iqtj
,
),0( ~
ξ
Σξ NormalTruncated
iqtj
, ),0( ~
ρ
Σρ NormalTruncated
iqtj
, and
),0( ~
ι
Σι NormalTruncated
iqtj
. All of the four error terms are truncated above zero.
ESTIMATION RESULTS
Model Comparison
The hierarchical Bayesian estimation procedure with the prior setting is given in the
technical appendix. We ran the models coded in C++ for 30,000 iterations. The first 20,000
cup of coffee). The disadvantage of this approach is a loss of information. However, we do include elapsed time as
a covariate, but find that it is a poor predictor of browsing, which supports our standardization of time.
20
iterations were used as "burn-in" period to ensure convergence. The last 10,000 iterations were
used for parameter inference. To assess the performance of the proposed model, we considered
two benchmark models. Since we focus on virtual shopping cart abandonment, the first
benchmark model is a simple independent two-stage session-level model where users first decide
whether to add something into their shopping cart in the first stage, and then decide whether to
buy it given some item was added into the cart. This benchmark model is widely used in industry
practice. The second benchmark model is simply the independent four-stage model at the page
level without heterogeneity. In addition, in order to determine the number of hidden states that
our dynamic four-stage probit model should have (i.e., the value of S), we compute the Bayes
factors following Kass and Raferty (1995) for four different models: a one-state, two-state, three-
state and four-state version of the hidden Markov model. We divided each user’s sessions into
two parts, the earlier sessions are used for estimation and the later ones are used for out-of-
sample prediction. If a user has one session, then their data was only used for estimation. The
construction of the holdout sample is meant to closely approximate the type of information that
online retailer such as Barnes & Noble would have available for their users based on past
information. There are 1,160 users in the estimation sample and 268 users in the holdout sample
with 11,769 observations and 5,054 observations, respectively. The disparity in the number of
users is due to the large number of users with only one session. For the users in the holdout
sample we predict their parameters and the states of the hidden Markov models only using the
information from the estimation sample.
_______________
Insert Table 5 here
The comparison of log marginal density, in-sample and out-of-sample hit rates of the
above models are given in Table 5. The marginal posterior distribution (or marginal density) is
computed by taking the mean across the Gibbs iterations weighted by the corresponding priors
(Newton and Raftery 1994). The hit rate refers to the percentage of user choices that are
correctly predicted. For example, random guessing should yield 50% hit rate. In terms of both in-
sample and out-of-sample hit rates, the one-state dynamic four-stage model clearly outperforms
the two simple benchmark models. This shows that it is important to capture user’s page view
dependence and user heterogeneity.
21
We find that the two-state model of navigation orientation is favored over the one-state
model, the three-state model and the four-state model by odds of 151.9, 145.5, and 627.4,
respectively. This result is also supported in terms of both in-sample and out-of-sample hit rates.
Since the two-state Markov process is strongly favored, we only present the estimation results
for this model. Throughout the remainder of the paper we refer to state 1 as the browsing-
oriented state and state 2 as the shopping-oriented state following our identification conditions.
We now discuss substantive results from our model estimation.
Impact of Web Page-specific Variables (Price, Promotion, Banner Ad, Links to Product, Home
and Account pages)
The posterior means and standard deviations of the parameter estimates for the web page-
specific variables, session-specific variables, and comparison shopping activities for our two-
state dynamic four-stage probit model are given in Table 6.
_______________
Insert Table 6 here
The intercepts measure the user’s intrinsic utility of choosing to enter the four stages
during the shopping process holding everything else constant. Notice that users in a shopping-
oriented state tend to have more positive intercepts than those in the browsing-oriented state,
which indicates the shopping-oriented visitors will have higher probabilities of moving through
the shopping process and purchasing in the end. This is consistent with the identification
conditions for the unobserved states of the hidden Markov chain.
It is interesting to find that the presence of price information on a page encourages page
view of shopping pages but discourages adding items into shopping cart by browsing-oriented
users. In contrast, price information positively impacts visitors in shopping-oriented states to add
items to cart but discourages shopping page page view and final purchase. This suggests that
price serves an information cue incorporated into their knowledge bank by browsing-oriented
users before proceeding to search for other products. Shopping-oriented consumers use price
information to decide whether to add items to their shopping cart, thus moving to the next stage
of the shopping process, and culminating in purchase.
Promotional messages (graphical images that promote B&N’s free shipping if two or
more items are purchased) discourage all users from browsing shopping pages. However they
22
have opposite impact on adding items to the shopping cart based on consumers’ navigational
orientation. They may discourage browsing-oriented users from adding items to the shopping
cart, but positively impact shopping-oriented users. The presence of promotional information
distracts visitors from page view shopping pages and browsing-oriented users from adding items
to virtual carts. For shopping-oriented users, the presence of free shipping promotional
information has a positive influence on adding items to shopping carts, which is consistent with
manager’s intuition. Interestingly, we find that the presence of promotional information has no
significant impact on motivating users to check out the items in their shopping cart and finally
purchase.
Banner ads have a significantly positive impact on browsing-oriented visitors on
decisions to continue shopping except on page view the shopping cart. However, they have a
significantly negative impact on page view the shopping pages for users in the shopping-oriented
state. This may due to the fact that the banner ads may distract shopping-oriented visitors from
their goals in the early stages. Also banner ads are peripheral non-intrusive stimuli and are easier
to avoid.
The effect of hypertext links is mostly negative or insignificant. More links on a page
encourages browsing-oriented users to engage in wide non-linear search through different
product options and not follow the shopping process. However, more links to the home page for
users in a browsing-oriented state tends to have a positive impact on page view shopping page.
Also, more links to product pages increases the likelihood of selecting a shopping page, which
may indicate that these product links provide information scent (Pirolli and Card 1999)
activating users’ interests.
Impact of Session-Specific Variables (Previous purchase, Time duration, Visit depth, Wishlist,
Popup and Email)
We find that consumers who have made a previous purchase (Lastbuy) are less likely to
go through the early stages of the shopping process but are more likely to purchase if they are in
the shopping-oriented state. The user’s familiarity with the shopping process at the site and
specific shopping goals may reduce the user’s need to engage in extensive search.
Time duration (or the seconds since the last page view) does not seem to have a
significant impact on browsing, except longer time lags for shopping-oriented users tend to
23
increase the likelihood of purchase. Also, visit depth (or the cumulative number of page views
during the session) discourages users in both states from page view shopping pages or adding
items to their shopping cart. This suggests that the longer the user browses at the site the more
likely she is to leave without progressing through the shopping process. Browsing-oriented users
are more likely to browse more shopping pages and purchase on weekends, while shopping-
oriented visitors are less likely to progress through the shopping process and engage in more
browsing behavior than on weekdays.
Signing in the account tends to encourage browsing-oriented users to view shopping
pages and purchase but discourages them from adding items to cart and check them next. In
contrast, signing in has a significantly positive impact on adding items to shopping cart but has a
negative impact on purchase for shopping-oriented users. Shopping-oriented users who signin
are more likely to enter the middle stages of the shopping process compared to browsing-
oriented users. Accessing the wish list more often does not have any significant impact except to
encourage browsing-oriented users to view shopping pages and add items to cart. Exposure to
more pop-up ads and coming from email solicitation tends to divert users’ attention and
discourage them from advancing through the shopping process. However, users coming from
email solicitation are more likely to buy regardless of their orientation state due to own self-
selection.
Impact of Comparison Shopping Activities (Comp. Shop, Cumother, Cumnotbn)
Interestingly, we find that checking other comparison shopping sites such as bizrate.com
discourages all users to buy although it may increase shopping-oriented user’s likelihood of
adding items to the shopping cart at B&N. The cumulative number of page views at other
bookstore sites during a session has insignificant influence on all stages of the shopping process,
which may indicate high store loyalty for B&N. However, the cumulative number of page views
at other non-bookstore sites discourages shopping-oriented users from adding items to cart and
purchasing. This indicates that there could be a time competitive effect across different web sites
that a user visits during a session.
The estimates of the impact of previous latent utility (i.e., the AR(1) process) are
0.03(0.01) for browsing-oriented state and –0.01(0.01) for shopping-oriented state, respectively.
(Standard deviations are given in the parentheses) We find that there is significant positive
24
browsing persistence for the users in browsing-oriented states while the impact is insignificant
for shopping-oriented users. This indicates that shopping-oriented users move more quickly
through the shopping process to fulfill their goals compared to browsing-oriented users.
Impact of Demographics on Online Shopping Process
The posterior mean and standard deviation for the hyper-parameters associated with the
impact of the demographic variables on the web user’s response to promotion presence are given
in Table 7. The demographic variables help explain variation in browsing behavior across users.
For brevity we report the demographic relationships for whether promotion information is
present on the page (promotion presence) only, but have estimated all demographic responses.
_______________
Insert Table 7 here
First consider users in the browsing-oriented state. Younger individuals tend to be more
likely to add items to shopping cart but are less likely to check them when promotional
information is present on a page, but at a decreasing rate due to the significance of the
corresponding squared age variable. Most of other demographic variables such as gender, race,
presence of children, marital status, and college education have no significant impact. However,
higher income tends to increase the likelihood of adding items to shopping cart.
Second, let’s consider users in the shopping-oriented state. Younger individuals seem to
have higher response to promotion presence in terms of adding items to their shopping cart but at
an increasing rate. White individuals and users without child in their household are likely to add
items to shopping cart when promotion is present. Gender, marital status, college education, and
income have no statistically significant impact on user’s response to promotional presence.
In summary, we find that demographic characteristics do have some significant predictive
value in predicting a user’s browsing behavior as they move through the shopping process
online, particularly whether to add items to shopping cart. However, the effects are quite varied
depending upon whether the user in a browsing-oriented or shopping-oriented state.
Estimates of the Markov Model of the Mixture Process
The estimates for the starting probabilities of the two-state hidden Markov chain are
0.97(0.03) for the browsing-oriented state and 0.03(0.01) for the shopping-oriented state,
25
respectively. Notice that a user has a very high probability of starting in a browsing-oriented
state (97%). (Standard deviations are given in the parentheses). On average a user will stay in
this browsing-oriented state for about three page views (i.e., the inverse of waiting time intensity
estimate 0.37(0.03)). In contrast, a user in the shopping-oriented state tends to persist in this
state longer or about four page views (i.e., the inverse of waiting time intensity estimate
0.25(0.03)). The transition probability matrix is trivial for the two-state model, since there are
only two states and the switching behavior is captured by the waiting time in each state. This is
consistent with the findings in Montgomery, Li, Srinivasan and Liechty (2004).
Impact of Marketing Mix, Hypertext Links, and Behavioral Variables on Hidden Markov Process
The estimates for the marketing mix, the total number of the hypertext links on a page,
and behavioral variables on hidden Markov process are given in Table 8. These variables impact
the starting probability and the waiting time intensity of the hidden Markov process through their
hyper-parameters (i.e. equation 8). Since the transition probability matrix is trivial for the two-
state model, we do not have the estimates for the variables on transition probability matrix.
_______________
Insert Table 8 here
First let’s consider the impact of email solicitation on the starting probability of the
hidden Markov process. The starting probability follows a Dirichlet distribution with hyper-
parameters as a function of email solicitation. Therefore, in order to explain the impact of email
solicitation on the starting probabilities, we need to look at the estimates across both states.
Email solicitation seems to dramatically decrease the weight of the hyper-parameter for the
browsing-oriented state and only slightly reduce that of the shopping-oriented state, which
indicates that email solicitation significantly increases the starting probability of being in the
shopping-oriented state. Perhaps email solicitation motivates purchase goals among users.
Second, let’s consider the impact of marketing mix, number of hypertext links, and
behavioral variables on the waiting time intensity of the hidden Markov process. The waiting
time intensity follows a Gamma distribution with both its shape hyper-parameter and scale
hyper-parameter as a function of the marketing mix, the number of hypertext links on a page, and
behavioral variables such as account sign-in and frequency of accessing wish list. Therefore, the
expectation of the waiting time intensity is the division of its shape parameter by its scale
26
parameter. Take the price presence as an example. Price presence tends to decrease the scale
parameter (-79.64) a lot more than the shape parameter (i.e. -16.54) in the browsing-oriented
state. Therefore price presence will increase the waiting time intensity for the browsing-oriented
state. Since the average waiting time is the inverse of its intensity, price presence tends to
decrease user’s time duration in the browsing-oriented state. In contrast, price presence decreases
the shape parameter (i.e. -68.49) much more than the scale parameter (i.e. -25.62) in the
shopping-oriented state. Thus it tends to decrease the waiting time intensity and eventually
increase the time duration in the shopping-oriented state.
Following the same logic, we find that presence of promotional information, banner ads,
less hypertext links on a page, account sign-in, less frequent access to wish list, less exposure to
pop-up ads, and less page views at comparison shopping web sites seem to decrease the waiting
time intensity and hence increase user’s time duration in the browsing-oriented state. In contrast,
lack of promotional information, presence of banner ads, more hypertext links on a page, account
sign-in, more frequent access to wish list, less exposure to pop-up ads, and more page views at
comparison shopping web sites tend to decrease the waiting time intensity in the shopping-
oriented state and hence increase user’s time duration in such state. Presence of promotional
information and pop-up ads distract users from their goals and browse around. This supports
similar findings by Sismeiro and Bucklin (2004) for disruptive effects of pop-ads on user
completion of shopping tasks at an automobile site. Also presence of banner ads, more hypertext
links on a page, account sign-in, more frequent access to wish list, and more page views at
comparison shopping sites could encourage users to become shopping-oriented. This could be
important for managerial intervention in order to decrease the online retailer’s shopping cart
abandonment rate and increase sales as we discuss in the next section.
MANAGERIAL IMPLICATIONS
The superior performance of the two-state multi-stage model of online shopping behavior
provides a prescriptive tool for managers seeking to decrease their shopping cart abandonment
rates. As we noted in our results, each webpage a visitor accesses can be dynamically customized
to encourage her to progress through the shopping process, based on her navigation activity at
the site prior to the present page. We assume that the firm has estimated the multi-stage shopping
model on the estimation sample at the individual consumer level and targets them on their future
27
sessions at the site. For new consumers with no prior history at the site the firm uses population
estimates to customize webpages and updates them with actual response on subsequent visits.
We demonstrate the application of our proposed approach on (a.) predicting navigation
orientation when consumer starts the session and tracking evolution of orientation state as the
consumer navigates through the website, (b.) dynamic placement of marketing mix offers on
webpages to improve conversion rates at each of the stages of the shopping process and (c.)
prediction of shopping cart abandonment at the next page view given initial navigational paths.
_______________
Insert Table 9 here
We discuss the evolution of consumer’s navigation orientation first. Table 9 presents the
sensitivity estimates. If the user visits the site in response to an email solicitation, the probability
of starting in shopping –oriented state increases by 0.434% if she visited the site through other
routes (using bookmark, search engine or typed in the URL etc.) as Table 9 indicates. If a visitor
in shopping-oriented state signs in to her account the duration of her shopping oriented state will
be longer by 0.009 page views than if she does not sign-in. A visitor starting in browsing-
oriented state will persist shorter by 0.009 page views than if she did not sign-in. Hence sign-in
accelerates the evolution of navigation behavior towards purchase. Promotional and web page
stimuli also have an impact on the waiting time and hence switching behavior between the two
states. As an example, consider the direct effect of presence of price information on persistence
in a given state as equations (8) indicate. The presence of price information on a shopping page
decreases the duration in the shopping oriented state by 0.007 page views and increases the
duration of browsing oriented state by 0.019 page views. The combined effect of presence of
price information on a shopping page (i.e. the combined effects on both user’s utility and
navigation orientation) decreases duration in the shopping-oriented state by 0.009 page views
and increases duration in the browsing-oriented state by 0.10 page views.
_______________
Insert Table 10 here
We now consider the customized display of promotional images on web pages. Table 10
presents the change in predicted probabilities. The last paragraph illustrated how each visitor can
be classified as being either browsing-oriented or shopping-oriented at a particular page view. A
promotion displayed on a page for a browsing oriented visitor decreases the probability of page
28
view the next shopping page by 0.173%. The probability of adding items to the shopping cart
decreases by 0.79%, the probability of page view shopping cart by 0.131% and the probability of
making a purchase by 1.002%. Hence promotional images should not be displayed on web pages
till the consumer is in the final stages of purchase for a browsing –oriented consumer, however
they may be displayed when a shopping-oriented consumer adds items to her shopping cart.
Similar customization decisions can be taken for other web page and promotional stimuli. As
shown in Table 10, dynamic customization of web pages using different marketing mix or web
design tools can significantly improve user’s probabilities to move along the shopping process
and finally purchase.
To assess the overall performance of full customization using the proposed two-state
model, we did the following forecast exercise. Suppose B&N were to classify each user after
their first page view up to their fifth page view as either deliberation-oriented or browsing-
oriented, and then based upon this classification customize the subsequently requested pages
with the objective of reducing shopping cart abandonment. Specifically, we make the following
changes for the marketing mix and hypertext links using both the estimation and holdout sample:
if the covariate is a binary variable, add that covariate if the sign of its estimated coefficient is
positive; delete it if the sign is negative. If the covariate is continuous, double that covariate if
the sign of its estimated coefficient is positive; reduce it by half if the sign is negative.
The session-level shopping cart abandonment predictions at every page view given initial
paths navigated by the consumer are presented in Table 11. Applying these above rules to our
estimation sample we find that the shopping cart abandonment rate would decrease by 3.30%
(0.002) after the first page view and 2.50% (0.001) after the first five page views. (Standard
deviations are given in the parentheses) This indicates that it is more effective to intervene early
in user’s session than late due to the fact that users are more likely to exit the site as they
progress. This is also supported by the results using the holdout sample with 2.80% (0.002) and
0.8% (0.001) reduction of the shopping cart abandonment rate after the first page view and the
first five page views, respectively. These significant decreases in shopping cart abandonment rate
could have important impact on B&N’s sales and profitability.
_______________
Insert Table 11 here
29
CONCLUSIONS
This research proposes a multi-stage model of online shopping process with the goal of
predicting shopping cart abandonment at an online retailer website. We identified three sets of
factors that affect shopping cart abandonment: (1) consumer’s unobserved purchase intent that
influences navigation orientation, (2) exposure to hyperlinks, marketing mix and promotional
stimuli on web pages while browsing a website that can change navigation orientation at any
point during the session, and (3) comparison shopping activity that affects consumer’s progress
through the shopping process. Instead of predicting shopping cart purchase or abandonment at
the session level using a two-stage model, we predict the completion of each stage of the
shopping process that lead to a purchase. This allows us to model true shopping cart
abandonment, we can separate sessions where items placed in shopping cart were abandoned or
not purchased at the end of the session from no cart activity sessions which cannot result in
purchase and represent information gathering activity by consumers.
We identified four stages in an online shopping process for any online retailer website
which correspond to the well-established purchase decision making process: (1) view product
items on a shopping page, (2) add items to shopping cart, (3) checkout a shopping cart, and (4)
purchase item(s) in shopping cart. Each of these stages is managerially relevant and account for
consumer attrition from the purchase process. We propose a dynamic four-stage binary probit
model of consumer’s decision at each stage of the shopping process. An autoregressive process
of latent utility is used to capture persistency in consumer’s browsing behavior. Consumer
heterogeneity due to user demographics and characteristics is accounted for using a hierarchical
Bayesian framework. An important contribution is recognizing that navigation orientation varies
during the session in response to stimuli the consumer is exposed to during navigation. The
impact of latent purchase intent, which influences navigation orientation state is modeled by a
hidden, continuous time Markov chain which follows a first-order Markov process. Our model
has superior performance compared to a session level model and session-stable purchase intent
model and predicts 87% of out-of sample events correctly.
From a substantive perspective, our results for the hidden Markov chain suggest
consumer’s navigation goals can be characterized by two states, either browsing-oriented or
shopping-oriented. For the online retailer in this study, consumers are most likely to start in the
browsing oriented state. However consumers persist in the shopping-oriented state longer than in
30
the browsing-oriented state. Consumers arriving at the website in response to an email
solicitation are most likely to be shopping-oriented. Account sign-in; presence of price
information, banner ads, more hypertext links, frequent access of wishlist and comparison
shopping sites are associated with longer persistence in the shopping-oriented state. In contrast,
presence of promotion information, pop-up ads seem to distract consumers from their shopping
process and increase persistence in the browsing state.
We find that web page and marketing mix stimuli differ in their impact at different stages
of the shopping process for browsing and shopping-oriented consumers. Shopping-oriented
consumers are intrinsically more likely to progress through the shopping process compared to
browsing-oriented consumers. The view cart and begin checkout is the critical stage, the
abandonment rate drops drastically after consumers enter that stage. Price information acts as a
cue encouraging browsing-oriented consumers to view other shopping pages instead of adding
the item to the shopping cart. In contrast, price information helps shopping-oriented consumers
make consideration decisions and add the item to the shopping cart (at the least to bookmark
them) instead of searching around by page view other shopping pages. In addition to the impact
on navigation orientation, promotion messages and pop-up ads have a direct effect on detracting
consumers from proceeding through the shopping process. Hence pop-ups served at the
beginning of the session are less disruptive than those towards the end at least for browsing-
oriented consumers, similar to findings in Moe (2003). Surprisingly, banner ads in general, have
a positive impact on continuing through the shopping process for browsing-oriented and
shopping-oriented consumers (except page view shopping pages). Marketers can thus customize
website experience at each page view for an individual consumer by adding or deleting web-page
stimuli to encourage progress through the shopping process.
Prior purchase and longer time since last visit has negative impact on page view shopping
pages for all consumers but negative impact on adding to cart for shopping-oriented consumers
only. Visit depth has negative impact on progressing through the shopping process, which might
imply that consumers who navigate through many pages at the site are information-seekers and
are not likely to purchase in that session. Shopping-oriented consumers are less likely to buy
during the weekend, whereas browsing-oriented consumers are more likely to buy. Since
consumers responding to email solicitations are more likely to start in shopping-oriented state,
the firm may want to avoid scheduling its outbound email marketing dispatches right before or
31
during the weekend. We realize that customers may still choose to read and visit them during the
weekend. Comparison shopping at other bookstore sites has no impact in any of stages indicating
high consumer loyalty for the e-tailer B&N. However diversion to non-bookstore and shopping
agent sites is detrimental to purchase outcomes.
Our research has a number of limitations. This paper conceptualizes shopping cart
abandonment as a navigational event, hence factors affecting navigation progress at the site have
been considered. We did not consider the effects of price on purchase decisions. Actual price of
products and shipping and handling at the focal retailer and competing sites may have a
significant impact on shopping cart abandonment, however this data was not available to us.
These effects may be examined in controlled laboratory experiments since access to actual
clickstream datasets with all competing offers is difficult to obtain. We found that the number of
unique items in the shopping cart has a non-linear effect on shopping cart abandonment, however
we could not examine the total number of items in shopping cart since the data was not available.
Marketing mix stimuli at competing websites can affect the focal firm’s shopping cart
abandonment. We do not model the effect of stimuli on external sites explicitly, since we don’t
have data on those stimuli. However we capture some of those effects as page views of
comparison shopping content within and across category competitor sites during the session.
Consumer panel clickstream can be used to develop richer models to account for stimuli
observed at competing sites allowing the focal firm to develop customized offers and stimuli to
mitigate the distractive effects of competing sites. We do not model the e-store choice decision,
future research should be directed towards simultaneously modeling the e-store choice and
shopping process decisions, allowing researchers to profile websites based on their conversion
ability.
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35
Table 1. Demographic characteristics
Variable Mean Std Dev Min Median Max
Age 45.89 14.62 9 46 89
Age
2
(square of Age) 2326.48 1331.68 81 2209 7921
Male .47 .50 0 0 1
White .77 .42 0 1 1
Children under 18 in the house .40 .49 0 0 1
Married .29 .45 0 0 1
Some college education .82 .39 0 1 1
High Income (>$50,000) .32 .47 0 0 1
Medium Income ($25,000-$50,000) .35 .48 0 0 1
Table 2. Descriptive Statistics
Variable Mean StdDev Min Med Max
Presence of price information on page (Proportion) .45 .50 0 0 1
Promotional image present (Proportion) .83 .37 0 1 1
Presence of banner advertisement (Proportion) .03 .16 0 0 1
Number of links to a home page 2.4 1.0 0 3 5
Number of links to a product page 10.1 18.1 0 0 110
Number of links to an account page 2.0 1.1 0 2 9
Number of links to an information page 28.8 33.9 0 17 303
Whether made a B&N purchase during last session .03 .18 0 0 1
Time Since Last Page view (Seconds) 7.2 66.3 1 1 1193
Whether the Visit is on Weekend (Proportion) .28 .45 0 0 1
Cum. no. of page views at B&N during session (visit
depth)
8.8 16.4 1 5 238
Cum. no. of page views at other sites during session 44.3 84.6 0 17 891
Cum. no. of page views at other bookstores during
session
4.3 17.3 0 0 174
Whether signed in at B&N during session 0.17 0.37 0 0 1
Cum. no. of page views of B&N wish list during session 0.11 0.69 0 0 7
Whether came from comparison shopping site 0.18 0.79 0 0 1
Cum. no. of page views of pop-ups during session 0.82 1.12 0 1 15
Whether came from B&N email solicitation 0.04 0.18 0 0 1
36
Table 3. Comparison of Sessions with Purchase and without Purchase.
Purchase sessions Non-purchase sessions
Dependent variables:
Mean Std. deviation Mean Std. deviation
Page view shopping page* 0.67915 0.46686 0.63049 0.48269
Add to cart** 0.07814 0.26843 0.01427 0.11862
View cart** 0.3093 0.46226 0.05638 0.23066
Purchase** 0.02362 0.15188 0 0
Predictor variables:
Current webpage-specific variables
Price presence 0.41508 0.4928 0.44259 0.49672
Promotion
++
0.62663 0.48376 0.90699 0.29045
Ad presence
+
0.01583 0.12483 0.02998 0.17055
Links to home page* 2.43116 0.77049 2.34482 1.18721
Links to account page** 2.51156 1.25514 1.75913 1.10382
Links to product page 9.3093 17.73829 10.65383 18.61732
Other links
++
22.31131 27.19221 30.60777 36.25661
Current session-specific variables
Visit depth** 35.99749 38.0764 14.12865 22.14504
Weekend** 0.35955 0.47993 0.2651 0.44141
Time since last page
view
++
82.86034 1137 681.5467 3581
Cumnotbn* 55.15804 120.345 46.50705 77.79176
cumother 3.00352 8.23932 5.17596 20.26174
Last buy 0.16608 0.3722 0.0386 0.19266
Email reference 0.0608 0.239 0.02586 0.15871
Sign in 0.44548 0.49708 0.07649 0.26579
Product/Item-specific variables
Comp. shop 0.00628 0.07902 0.00862 0.09244
Cum page view of pop-
ups 0.80075 1.00601 0.82638 1.14516
* Mean in sessions when purchase was made is significant larger (p<0.05) than in sessions when
shopping cart was abandoned
** Mean in sessions when purchase was made is significant larger (p<0.01) than in sessions
when shopping cart was abandoned.
+
Mean in sessions when purchase was made is significant smaller (p<0.05) than in sessions
when shopping cart was abandoned.
++
Mean in sessions when purchase was made is significant smaller (p<0.01) than in sessions
when shopping cart was abandoned.
37
Table 4. Example of Decomposition of User’s Session*
Time URL Stage
1 8:36:11pm
/promo/coupon/popups/fs_usa_popup.asp?userid=xxx
1
2 8:36:29pm
/booksearch/results.asp?wrd=70%2d215&userid=xxx
1
3 8:36:48pm
/booksearch/results.asp?userid=xxx&mscssid=yyy&wrd=70%2d215&opr=a&sort=p
2
4 8:37:14pm
/booksearch/isbninquiry.asp?userid=xxx&mscssid=yyy&isbn=0072134445
2
5 8:38:10pm
/booksearch/results.asp?userid=xxx&mscssid=yyy&wrd=70%2d215&opr=a&sort=p
2
6 8:44:32pm
/textbooks/booksearch/isbninquiry.asp?userid=xxx&mscssid=yyy&isbn=0619034971
2
7 8:55:12pm
/promo/coupon/popups/fs_usa_popup.asp?userid=xxx
2
8 8:55:24pm
/booksearch/results.asp?wrd=70%2d215&userid=xxx
2
9 8:55:36pm
/booksearch/results.asp?userid=xxx&mscssid=yyy&wrd=70%2d215&opr=a&sort=p
2
10 8:56:37pm
/shop/cart.asp?userid=xxx&mscssid=yyy&vcqty=1
2
11 8:58:16pm
/booksearch/results.asp?userid=xxx&mscssid=yyy&wrd=70%2d215&opr=a&sort=p
3
12 8:58:40pm
/booksearch/isbninquiry.asp?userid=xxx&mscssid=yyy&isbn=0072224983
3
13 8:59:21pm
/shop/cart.asp?userid=xxx&mscssid=yyy
3
14 9:01:26pm
Exit
3
Source: comscore Media Metrix, 2002
*Listing of raw clickstream dataset associated with a selected session on April 28, 2002 for one
user. (All URLs are prefixed by
http://www.barnesandnoble.com
. As is customary, comScore
masked all personally identifiable information (PII) prior to releasing data for this analysis. The
userid and mscssid are listed as xxx and yyy, respectively, to protect the privacy of this user.)
Table 5. Model Comparison
Model Log Marginal
Density
In-Sample Hit
Rate (%)
Out-of-Sample Hit
Rate (%)
Two-Stage Model at
Session Level
83.91
(0.37)
68.91
(0.46)
Independent Models at
Page Level
-1993.1 94.16
(0.23)
83.65
(0.37)
One-State Model -1321.0 94.96
(0.22)
84.02
(0.37)
Two-State Model -1169.1 96.45
(0.18)
87.45
(0.33)
Three-State Model -1314.6 95.09
(0.22)
85.08
(0.36)
Four-State Model -1796.5 94.47
(0.23)
85.78
(0.35)
38
Table 6. Proposed Two-State Model of Four-Stage Online Shopping Process
1.View Shopping
Page
2. Add to cart 3. View Cart 4. Purchase
State
B
&
P
&
B P B P B P
Intercept -1.04
(0.09)
-0.77
(0.16)
-0.62
(0.13)
-0.46
(0.15)
-3.64
(0.75)
-1.10
(0.59)
1.20
(0.53)
1.95
(0.58)
Current web page-specific variables
Price
presence
0.80
(0.08)
-0.37
(0.14)
-0.39
(0.07)
0.96
(0.10)
n.s. n.s. n.s.
-4.81
(0.60)
Promotion
-0.84
(0.15)
-0.68
(0.14)
-2.57
(0.38)
0.45
(0.12)
n.s. n.s. n.s. n.s.
Ad
presence
1.19
(0.28)
-0.17
(0.07)
0.70
(0.18)
1.63
(0.19)
n.s. n.s. 2.29
(0.62)
n.s.
Links to
homepage
2.92
(0.20)
-1.66
(0.10)
-3.26
(0.15)
-1.19
(0.19)
n.s. 1.37
(0.65)
n.s. n.s.
Links to
account pg
-1.33
(0.10)
1.33
(0.12)
-0.23
(0.12)
-1.38
(0.17)
n.s. -1.34
(0.65)
n.s. -1.39
(0.53)
Links to
product pg
0.64
(0.16)
1.54
(0.22)
n.s. n.s. n.s. n.s. n.s. n.s.
Other links -0.42
(0.06)
-0.35
(0.09)
n.s. n.s. n.s. n.s. n.s. n.s.
Current session-specific variables
Last buy -0.23
(0.11)
-1.15
(0.09)
0.43
(0.14)
-0.83
(0.13)
n.s. n.s. n.s. 4.19
(0.37)
Time since
last page
view
n.s. n.s. n.s. -0.19
(0.10)
n.s. n.s. n.s. 1.04
(0.28)
Visit depth -2.13
(0.14)
-1.29
(0.12)
n.s. -0.26
(0.11)
n.s. n.s. n.s. n.s.
Weekend
1.27
(0.21)
-2.17
(0.19)
-0.75
(0.14)
-0.42
(0.18)
n.s. n.s.
3.63
(0.77)
-2.06
(0.49)
Sign in 0.71
(0.12)
n.s.
-1.11
(0.12)
1.64
(0.17)
-0.95
(0.41)
n.s.
1.95
(0.36)
-3.67
(0.37)
Wishlist 0.80
(0.09)
n.s.
0.54
(0.11)
-0.99
(0.15)
n.s. n.s. n.s. n.s.
Pop Ads n.s. -1.93
(0.12)
-1.33
(0.14)
-0.47
(0.15)
n.s. n.s.
-1.52
(0.81)
1.48
(0.49)
Email ref.
-1.82
(0.19)
0.94
(0.17)
-0.72
(0.24)
n.s. -2.72
(0.53)
-5.74
(0.76)
1.60
(0.72)
3.13
(0.35)
Comparison shopping activity
Comp.
shop.
-0.60
(0.20)
n.s. n.s. 0.88
(0.11)
n.s. n.s. -2.72
(0.26)
-1.06
(0.30)
Visit other
Bkstore
Site
n.s. n.s. n.s. n.s. n.s. n.s. n.s. n.s.
Visit other
non-bkstore
-0.44
(0.06)
n.s. n.s. -0.22
(0.07)
n.s. n.s. n.s. -0.77
(0.21)
&
B: Browsing-oriented state, P: Shopping-oriented state.
39
Table 7. Posterior mean and standard deviation of effects of demographics on Promotion.
Promotion
Inter-
cept
Age Age
2
Male White Child Married College
Med.
Income
High
Income
1. Shopping
Page
-.24
(.12)
.07
(.06)
-.08
(.04)
.07
(.13)
-.04
(.21)
.16
(.23)
-.04
(.22)
-.36
(.22)
-.15
(.27)
.14
(.28)
2. Add to
Cart
-.28
(.22)
-.39
(.04)
-.12
(.03)
-.05
(.22)
.01
(.25)
-.05
(.18)
.03
(.25)
.02
(.21)
-.08
(.25)
.30
(.15)
3. View Cart .19
(.28)
.31
(.11)
-.22
(.11)
-.03
(.31)
.05
(.30)
-.01
(.31)
-.02
(.26)
.04
(.26)
.07
(.28)
.01
(.25)
Browsing-oriented
State
4. Purchase -.05
(.27)
-.15
(.27)
.03
(.11)
.12
(.31)
.08
(.38)
.06
(.29)
.01
(.35)
.02
(.36)
-.01
(.27)
.08
(.25)
1. Shopping
Page
-.15
(.09)
-.11
(.09)
.04
(.06)
-.22
(.17)
-.54
(.14)
.08
(.15)
.24
(.21)
-.02
(.10)
-.03
(.18)
.05
(.25)
2. Add to
Cart
.05
(.11)
-.14
(.06)
.06
(.02)
.06
(.33)
.54
(.21)
-.27
(.13)
.19
(.21)
-.03
(.17)
.30
(.17)
-.03
(.15)
3. View Cart .08
(.29)
.04
(.16)
-.11
(.12)
-.04
(.30)
-.01
(.30)
.02
(.31)
-.02
(.33)
.02
(.38)
.01
(.28)
-.04
(.32)
Shopping-oriented
State
4. Purchase -.31
(.43)
-.09
(.27)
.15
(.21)
-.13
(.32)
.01
(.26)
.02
(.35)
.15
(.30)
-.12
(.35)
-.04
(.37)
.03
(.34)
Table 8. Posterior mean and standard deviation of effects of covariates on Hidden Markov chain
hyper-parameters
Variables
Inter-
cept
Email Price Promo. Ads.
Tot.
Links
Sing In
Wish
List
Cum.
Pop-up
Cum.
Comp.
Starting Prob.
Hyper-Param.
73.77
(.60)
-113.11
(.30)
Waiting Time
Intensity –
Shape Param.
-106.69
(3.61)
-16.54
(4.06)
-126.79
(2.94)
-60.20
(2.81)
-49.26
(3.43)
-73.45
(2.38)
-66.85
(5.22)
-17.83
(2.39)
-8.88
(3.59)
Browsing-oriented
State
Waiting Time
Intensity –
Scale Param.
-4.77
(2.27)
-79.64
(3.64)
-11.99
(2.95)
-2.93
(2.13)
-75.24
(8.69)
-48.02
(4.35)
-102.72
(4.36)
-58.81
(5.44)
-86.64
(5.51)
Starting Prob.
Hyper-Param.
-8.94
(.46)
-1.77
(.53)
Waiting Time
Intensity –
Shape Param.
-92.70
(4.02)
-68.49
(5.01)
-16.69
(3.30)
-44.59
(4.34)
-14.80
(5.26)
-53.22
(3.26)
-62.04
(3.49)
-1.73
(1.89)
-34.31
(5.32)
Shopping-oriented
State
Waiting Time
Intensity –
Scale Param.
-50.46
(5.20)
-25.62
(2.25)
-27.17
(3.34)
-.10
(.73)
24.48
(2.17)
-41.96
(2.77)
-48.33
(2.27)
-16.74
(2.58)
-31.51
(2.01)
40
Table 9: Applications – Hidden Markov Chain
Starting Probability (%) Waiting Time
Variables
Browsing Shopping Browsing Shopping
Email
Solicitation
-0.434
(0.006)
0.434
(0.006)
N.A. N.A.
Sign In
N.A. N.A. -0.009
(0.002)
0.009
(0.003)
Price Presence
(Combined
Effects)
N.A. N.A. 0.010
(0.001)
-0.009
(0.002)
Price Presence
(Hidden Markov
Only)
N.A. N.A. 0.019
(0.002)
-0.007
(0.002)
Note: Rules for the applications are: add the covariate for all users.
Table 10: Applications (%) – Four Stages
Variables 1. View
Shop. Page
2. Add to
cart
3. View Cart 4. Purchase
Price
Presence
0.171
(0.038)
0.792
(0.041)
0.599
(0.049)
0.971
(0.017)
Promotion
Presence
0.173
(0.037)
0.790
(0.040)
0.131
(0.033)
1.002
(0.097)
Ad
Presence
0.184
(0.039)
0.857
(0.035)
1.058
(0.086)
1.235
(0.094)
Marketing
Mix and
Web Design
Links to
Prod. Pages
0.178
(0.009)
0.801
(0.020)
2.133
(0.076)
0.920
(0.036)
Visit Comp-
Shop Site
0.172
(0.008)
0.794
(0.021)
0.003
(0.079)
0.924
(0.035)
Comparison
Shopping
Visit Non-
bkstore Site
0.150
(0.007)
0.785
(0.021)
0.620
(0.049)
0.713
(0.029)
Weekend
0.151
(0.008)
0.733
(0.020)
0.669
(0.033)
1.054
(0.043)
Last Buy
0.174
(0.009)
0.796
(0.020)
0.005
(0.079)
0.955
(0.037)
Session
Context
Visit Depth
0.187
(0.008)
0.833
(0.028)
1.107
(0.068)
0.310
(0.029)
Note: Rules for the applications are: If the covariate is a binary variable, add that covariate if the
sign of its estimated coefficient is positive; delete it if the sign is negative. If the covariate is not
a binary variable, double that covariate if the sign of its estimated coefficient is positive; reduce
it by half if the sign is negative.
41
Table 11. Predicted session-level shopping cart abandonment rate given initial paths for the two-
state dynamic four-stage probit model.
Forecast Origin/Number of page views
during session
Sample
Tot. No.
of
Sessions
No. of
Sessions
with item in
Cart
(Purchase)
Sample
Aband.
Rate
1 2 3 4 5
Estimation 1,257
107 (93)
13.1% 9.8% 10.7% 10.7% 10.6% 10.6%
Holdout 447
58 (49)
15.5% 12.7% 14.2% 14.5% 14.7% 14.7%
42
Figure 1: Shopping Cart and Wishlist Usage
0
20
40
60
80
100
012345678101112
Number of items in shopping cart/wishlist
Percentage of sessions
Shopping Cart
Wishlist
Figure 2: Purchase and Abandonment vs. Number of Items in Shopping Cart and Wishlist
0
5
10
15
20
25
30
35
40
45
50
123456789101112
No. of items in cart and wishlist in session
Number of session
s
Abandoned carts
wishlist usage
Carts purchased -
wishlist usage
Abandoned carts
- cart usage
Carts purchased -
cart usage
43
Figure 3. Attrition Rates at Each stage of Shopping Process.
1. Search shopping pages
2. Put items in cart
3. View cart
4. Checkout
42.02%
48.3%
1.35%
Exit
2.87%
Purchase
5.45%
44
Technical Appendix
Monte Carlo Markov Chain for Estimating the Dynamic Four-Stage Probit Model with a
Markov Mixture Process
The likelihood for the observed data, Y, conditional on the parameters that describe its
dynamics and the hidden Markov chains D is given by:
})(
2
1
exp{)
)2(
1
(),,,|(
)I(
2
)1()1(
11
sD
j
tiq
j
is
j
tiqis
j
iqt
ijqt s
iqt
tttt
UU
sqrt
f
=
−−
−−
−−−=
∏∏
XΓΣφΓDY φ
π
Where )I(⋅ is an indicator function and
t
j denotes the stage j at occasion t.
We assume a priori that the densities of the starting values for
iqt
D ,
iq
v
, and the density
of each row of the hidden chain transition matrix are Dirichlet densities. In addition, we assume
a priori that the intensity parameters,
iqs
λ , for
iqt
D follow a Gamma density. That is,
),(~
),(~
),(~
),(~
of row j theis vector,S1 a is ),(~
),(~
)(~
th
λ
λ
τ
α
λλ
λλ
λλλ
(
)
((
))
()
VMVN
VMVN
VτMVNτ
VαMVNα
Dirichlet
Gamma
Dirichlet
s
s
js
s
iqtiqtjiqtjiqtjiqtj
iqtsiqtsiqts
iqsiq
PPττP
αv
×
To complete our model we specify the following priors:
.for ],,[~
.for ],,[~
. and for ],,[ ~
2
1
sN
sWishart
sjMVN
sis
j
s
s
j
s
φ
ςς
σφφ
ρ VΨ
VΠΠ
Π
−
We apply data augmentation and MCMC methods (Gibbs sampler see McCulloch and
Rossi (1994) and reversible jump algorithm (Liechty and Roberts, 2001)) based on the following
full conditional distributions:
(1).
0000
},{},{},{},{},{|
00
iq
j
iqt
j
isis
j
iq
j
iqt
j
iq
DYUU
t
XΓφ
≠
45
+⋅⋅⋅+
⋅⋅⋅
+
+
⋅⋅⋅
=
−⋅⋅⋅−−−
⋅⋅⋅
−−
−
⇒
++=
⋅⋅⋅
++=
++=
−
−
−−
−−
−
−−
i
T
i
i
i
i
T
i
i
T
iii
T
i
i
T
i
i
T
i
i
T
i
T
i
i
T
i
j
siqT
j
siq
T
is
j
siq
j
siqis
j
siq
j
iq
T
is
is
is
j
Tiq
j
is
j
iq
j
is
T
is
j
iq
j
is
T
is
j
iqT
j
iq
j
is
j
iq
j
isis
j
iq
j
iq
j
is
j
iq
j
siqT
j
Tiq
j
is
j
Tiq
is
j
iqT
j
siq
j
iq
j
is
j
iqis
j
iq
j
siq
j
iq
j
is
j
iqis
j
iq
U
U
U
U
UU
UU
UU
εε
εε
ε
XΓXΓXΓ
XΓXΓ
XΓ
εXΓ
εXΓ
εXΓ
1
21
1
0
1
12
0
1
12
0
12
0
11
11
21212
1
0
1
0
1
1
1
21
1
0
2
)1(
1
2
0
1
102
01
)1()1(
2112
1001
φ
φ
φ
φ
φ
φφ
φ
φ
φ
φ
Let
−⋅⋅⋅−−−
⋅⋅⋅
−−
−
=
−
−
−−
1
12
0
1
12
0
12
0
11
)1(
1
2
0
1
102
01
i
T
i
i
T
iii
T
i
j
Tiq
j
is
j
iq
j
is
T
is
j
iq
j
is
T
is
j
iqT
j
iq
j
is
j
iq
j
isis
j
iq
j
iq
j
is
j
iq
U
U
U
XΓXΓXΓ
XΓXΓ
XΓ
A
φφ
φ
,
⋅⋅⋅
=
i
T
is
is
is
φ
φ
φ
2
B , and
+⋅⋅⋅+
⋅⋅⋅
+
=
−
i
T
i
i
j
siqT
j
siq
T
is
j
siq
j
siqis
j
siq
i
εε
εε
ε
ε
1
21
1
1
1
21
1
~
φ
φ
. Then )(~
~
ii
, MVN V0ε . Let '
1
eeV =
−
i
. We have:
εeBUeAe
~
'''
0
+=
i
0000
},{},{},{},{},{|
00
iq
j
iqt
j
isis
j
iq
j
iqt
j
iq
DYUU
t
XΓ
φ
≠
⇒
=
−−
−∞
−−
∞+
otherwise ))''( ),''()''((
1 if ))''( ),''()''((
~
11
)0 ,(
0
11
) ,0(
0
BeeBAeeBBeeB
BeeBAeeBBeeB
N
YN
j
iq
Where
0iq
Ds = and
t
j denotes the stage j at occasion t.
(2). 0,},{},{},{},{},{|
≠
−
−
tDYUU
iqt
j
iqt
j
isis
j
iqt
j
iqt
j
iqt
ttt
XΓφ
+
−
=
−
−−
⇒
+=−
+−=−−
⇒
++=
++=
+
+
+
−−
++
+
−−
++
+
−−
+
+
−−
++
−−
++
−−
1
1
)1(
11
11
)1(
11
11
)1(
11
)1(
)1(
)1()1(
)1()1(
)1()1(
)1()1(
)1()1(
1
U
t
t
t
tt
t
ttt
tttt
t
ttttt
tttt
t
ttttt
j
stiq
j
iqts
j
iqt
is
j
iqt
j
is
j
tiq
j
tiq
j
is
j
tiqis
j
stiq
j
iqtis
j
iqt
j
is
j
tiq
j
iqts
j
iqt
j
tiq
j
is
j
tiqis
j
stiq
j
iqt
j
is
j
iqtis
j
tiq
j
iqts
j
tiq
j
is
j
tiqis
j
iqt
U
U
U
UU
UU
U
UU
ε
ε
XΓ
XΓ
εXΓ
εXΓ
εXΓ
εXΓ
φ
φ
φ
φ
φ
φ
46
Let
−
−−
=
+
+
−−
+
−−
tt
t
ttt
j
iqt
j
is
j
tiq
j
tiq
j
is
j
tiqis
U
U
XΓ
XΓ
A
1
)1(
11
)1(
)1()1(
φ
,
−
=
is
φ
1
B
, and
=
+
+
1
)1(
~
t
t
j
stiq
j
iqts
it
ε
ε
ε
. Then )(~
~
itit
, MVN V0ε .
Let '
1
eeV =
−
it
. We have:
εeBUeAe
~
'''
0
+=
i
0,},{},{},{},{},{| ≠⇒
−
−
tDYUU
iqt
j
iqt
j
isis
j
iqt
j
iqt
j
iqt
ttt
XΓφ
=
−−
−∞
−−
∞+
otherwise ))''( ),''()''((
1 if ))''( ),''()''((
~
11
)0 ,(
11
) ,0(
BeeBAeeBBeeB
BeeBAeeBBeeB
N
YN
t
j
iqt
Where
iqt
Ds = and
t
j denotes the stage j at occasion t.
(3). ) ,(~,,},{},{},{},{|
2
babNDYU
it
s
j
iqt
j
is
j
iqt
j
iqtis
tttt
⋅
φ
σφφ XΓ ⋅I(
ttt
j
iqtS
j
iqt
j
iqt
UUU ≤⋅⋅⋅≤≤
21
)
)1(
)1(
)1(
)1(
*
2
11
*
)1(
1
1
2
1
2
)1(
)(
)
1
)(( Where
−
−
−
−
==
−
=
−
=
−
−=
+⋅=
+=
∑∑
∑∑
t
ttt
i
iq
t
t
i
iq
t
j
tiq
j
iqt
j
iqt
j
iqt
s
Q
q
T
t
j
iqt
j
tiq
Q
q
T
t
j
tiq
UU
UU a
Ub
XΓ
φ
φ
σ
φ
σ
Where
iqt
Ds = . The absolute values of
is
φ are restricted to be within unit circle.
t
j
iqts
U is the
expected value of
t
j
iqt
U for hidden state s.
(4). ) ,(~,,},{},{},{},{|
BABΨΠRXΓ ⋅
MVNYU
j
s
j
si
j
iqtis
j
iqt
j
iqt
j
is
ttt
φ
⋅ I(
ttt
j
iqtS
j
iqt
j
iqt
UUU ≤⋅⋅⋅≤≤
21
)
1
)1(
*
1
,
1,1
*
1
11
,
1,1
1
)(
))()'(( Where
−
−
−
==
−
−−
==
−
−=
+=
+=
∑
∑
ttt
iqi
tt
iqi
tt
j
tiqis
j
iqt
j
iqt
i
j
s
j
s
TQ
tq
j
iqt
j
iqt
j
s
TQ
tq
j
iqt
j
iqt
UUU
UI
I
φ
RΠΨXA
ΨXXB
(5). ) ,(~,,},{},{| VFVVΠΨRΠ
Π
⋅Γ MVN
s
j
si
j
is
j
s
∑∑
=
−
−−
−
=
−
+Γ=+=
I
i
s
j
is
j
si
I
i
i
j
si
R RR
1
1
11
1
1
'1
)(,))(( Where ΠVΨFVΨV
ΠΠ
(6)
)))')((( ,(~ ,},{, }{ },{|)(
1-
1
1
∑
=
−
−Γ−Γ++Γ
I
i
i
j
s
j
isi
j
s
j
isi
j
s
j
is
j
s
IWishart RΠRΠVVRΠΨ
ςςςς
ρρ
(7). ),(~,},{|
iqtsiqtsiqtsiqtsiqtsiqtsiqtiqts
TnGamma λλλλλ
()()
++D
47
where n
iqts
is the number of times D
iqt
was in state s and T
iqts
is the amount of time that D
iqt
was
in state s.
(8). ,},{},{},{},{},{|
iqtjiq
j
iqt
j
is
j
iqt
j
iqtisiqt
ttt
YU
PvXΓD φ
~ Reversible Jump Algorithm: independence
sampler, refinement sampler, and birth-and-death sampler.
We use the reversible jump Hasting Metropolis (HM) algorithms proposed by Liechty
and Roberts (2001) to generate samples of each hidden Markov chain
iqt
D . The difference
between their algorithm and ours is based on the distribution of U in this paper versus the
likelihood functions in theirs. We used three different algorithms for updating
iqt
D . The first
algorithm is an independence algorithm, which ignores the current realization of
iqt
D and
proposes realizations of by drawing from the prior density of
iqt
D . This results in proposed
realizations that are considerably different, in terms of the posterior density, and as a
consequence this algorithm tends to result in large but infrequent moves.
The other two algorithms create proposed realizations of
iqt
D by making small
modifications to the current realization of
iqt
D . The second algorithm is a refinement algorithm
where the proposed realization of
iqt
D is created by modifying one of the jump times of the
current realization of
iqt
D . The third algorithm is a birth-death algorithm where the proposed
realization of
iqt
D is created by either inserting a new interval into the current realization of
iqt
D
– a birth – or removing an interval from the current realization of
iqt
D – a death. The
independence algorithm has obvious advantages when the posterior distribution is multi-modal
or when a poor initial value of
iqt
D has been chosen, where as the refinement algorithm and the
birth-death algorithm have the advantage of more efficiently exploring the modes of the posterior
distribution.
In order to take advantage of the properties of these three algorithms, one of these three
algorithms is randomly chosen at each iteration of the MCMC algorithm to update each hidden
Markov chain. Although our model itself is different from theirs, we apply the algorithms
proposed by Liechty and Roberts (2001) and refer to their description of the algorithms and the
formulas for calculating the acceptance probabilities.
(9).
∑
=
=++
S
1j
11
1 with , ... , ~},{|
iqjiqSiqSiqiqiqiqtiq
v)ddDirichlet( αααDv
=
otherwise 0
qsession in iuser for s is state starting if 1
iqs
dwhere
(10). 1 with , ... ,~ }{},{},{|
1
11
=++
∑
=
S
k
iqtjkiqtjSiqtjSiqtjiqtjiqtjiqiqtiqtj
P)mmDirichlet( τττvDP
q.session in occasion tat iuser for k state toj state from jumps ofnumber theis where
iqtjk
m
The draws of P
iqtj
can be sampled from Gamma distribution with
iqtjkqtjk
mshape +=τ and scale
= 1 for all k. Then normalize each draw using the sum of all of the draws.
48
(11). , ,, },{|
ι
λλ
ΣEλD
iqt
s
iqtsiqtsiqtiqts
,λ
()(
] ,[ e
)(
)(
~
),0(
*
1
iqts
ι
λλ
λ
λ
λ
λ
ΣEλ
iqt
s
iqts
iqts
iqts
NormalTrunacatedλ
iqts
iqts
iqts
⋅⋅
⋅⋅
Γ
+∞
−
−
(
)
(
(
)
)
iqts
λ
(
can be generated using standard Metropolis-Hasting algorithm.
(12). , ,, },{|
ρ
λλ ΣEλD
iqt
s
iqtsiqtsiqtiqts
, λ
)()
] ,[ e
)(
)(
~
),0(
*
1
iqts
ρ
λλ
λ
λ
λ
λ
ΣEλ
iqt
s
iqts
iqts
iqts
NormalTrunacatedλ
iqts
iqts
iqts
⋅⋅
⋅⋅
Γ
+∞
−
−
)
)
(
(
)
)
iqts
λ
)
can be generated using standard Metropolis-Hasting algorithm.
(13). , ,, },{|
ξ
α
ΣEvD
iq
s
iqiqtiqs
α
] ,[ 1~
),0(
1
1
1
1
1
ξ
α ΣE
iq
s
αα
iqs
α
iqs
iqs
S
k
iqkiqs
S
k
iqk
NormalTrunacated)v(v
)ααΓ()Γ(α
)αΓ(
iqs
S
k
iqk
iqs
⋅⋅
−⋅⋅
−⋅
+∞
−−
∑
−
=
=
=
∑
∑
iqs
α can be generated using standard Metropolis-Hasting algorithm.
(14).
, },{|
iqtjiqtiqtsj
τ
PD
, ,
υ
τ
ΣE
iqt
s
−⋅⋅
−⋅
−−
∑
−
=
=
=
∑
∑
1
1
1
1
1
1~
iqtsj
S
k
iqtkj
iqtsj
ττ
iqtjs
τ
iqtjs
iqtsj
S
k
iqtkjiqtsj
S
k
iqtkj
)p(p
)ττΓ()Γ(τ
)τΓ(
] ,[
),0( υ
τ ΣE
iqt
s
NormalTrunacated ⋅⋅
+∞
49
iqtsj
τ can be generated using standard Metropolis-Hasting algorithm.
(15). ,,},{ },{|
αξ
VαΣEα
iqiqs
s
α
],[] ,[ ~
),0( αξ
α
VαΣE
MVNNormalTrunacated
iq
iq
s
⋅
⋅
∏
+∞
s
α can be generated using standard Metropolis-Hasting algorithm.
(16).
,,},{ },{|
λ
VλΣEλ
)
)))
ρ
λ
iqtiqts
s
],[] ,[ ~
),0(
λ
VλΣEλ
)
))
MVNNormalTrunacated
iqt
iqt
s
⋅
⋅
∏
+∞ ρ
s
λ
)
can be generated using standard Metropolis-Hasting algorithm.
(17).
,,},{ },{|
λ
VλΣEλ
(
(((
ι
λ
iqtiqts
s
],[] ,[ ~
),0(
λ
VλΣEλ
(
((
MVNNormalTrunacated
iqt
iqt
s
⋅
⋅
∏
+∞ ι
s
λ
(
can be generated using standard Metropolis-Hasting algorithm.
(18). ,,},{ },{|
τυ
τ VτΣEτ
iqtiqts
s
],[] ,[ ~
),0( τυ
VτΣEτ MVNNormalTrunacated
iqt
iqt
s
⋅
⋅
∏
+∞
s
τ can be generated using standard Metropolis-Hasting algorithm.
(19).
ξξξ
ρ
V,},{ },{,|
iqiqs
s
α Eα
Σ
],[] ,[ ~
),0( ξξξ
ρα VΣE hartInverseWisNormalTrunacated
iq
iq
s
⋅
⋅
∏
+∞
ξ
Σ is a diagonal matrix and can be generated using standard Metropolis-Hasting algorithm.
50
(20).
υυυ
ρτ
VEτΣ
,},{ },{,|
iqtiqts
s
],[] ,[ ~
),0( υυυ
ρ VΣEτ hartInverseWisNormalTrunacated
iqt
iqt
s
⋅
⋅
∏
+∞
υ
Σ is a diagonal matrix and can be generated using standard Metropolis-Hasting algorithm.
(21).
ρρρ
ρλ VEλΣ
,},{ },{,|
iqtiqts
s
))
],[] ,[ ~
),0( ρρρ
ρ VΣEλ hartInverseWisNormalTrunacated
iqt
iqt
s
⋅
⋅
∏
+∞
)
ρ
Σ is a diagonal matrix and can be generated using standard Metropolis-Hasting algorithm.
(22).
ιιι
ρλ VEλΣ ,},{ },{,|
iqtiqts
s
((
],[] ,[ ~
),0( ιιι
ρ
VΣEλ hartInverseWisNormalTrunacated
iqt
iqt
s
⋅
⋅
∏
+∞
(
ι
Σ is a diagonal matrix and can be generated using standard Metropolis-Hasting algorithm.
