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Optimizing Web Sites for Customer Retention*

Michael Hahsler
Department of Information Systems and Operations
Vienna University of Economics and Business Administration


Abstract
With customer relationship management (CRM) companies move away from a
mainly product-centered view to a customer-centered view. Resulting from this
change, the effective management of how to keep contact with customers throughout
different channels is one of the key success factors in today’s business world.
Company Web sites have evolved in many industries into an extremely important
channel through which customers can be attracted and retained. To analyze and
optimize this channel, accurate models of how customers browse through the Web
site and what information within the site they repeatedly view are crucial. Typically,
data mining techniques are used for this purpose. However, there already exist
numerous models developed in marketing research for traditional channels which
could also prove valuable to understanding this new channel. In this paper we
propose the application of an extension of the Logarithmic Series Distribution (LSD)
model repeat-usage of Web-based information and thus to analyze and optimize a
Web Site’s capability to support one goal of CRM, to retain customers. As an
example, we use the university’s blended learning web portal with over a thousand
learning resources to demonstrate how the model can be used to evaluate and
improve the Web site’s effectiveness.

1. Introduction
Today, the World Wide Web is a very important channel for attracting new customers and for
retaining customers. For example, a company Web site can be used for conveying service and
product information, for advertising and for selling products. Optimizing the Web appearance
and integrating it into an overall customer relationship management (CRM) strategy is a key
success factor in today’s business world. Therefore, it is crucial to gain an insight into how
customers use the Web site.
Analyzing large volume Web usage data is normally done by data mining specialists using their
own techniques. However, there exist numerous models developed in marketing research for
traditional channels which could prove valuable to understand this new channel. It is important
to examine how well existing models perform on such data and, if necessary, to adapt the models
accordingly. A further challenge is to make the application of the models efficient enough so
they can be used together with other data mining techniques for large amounts of data (e.g., by
simplification or by applying computationally more efficient estimation techniques from
machine learning).
*In Bing Liu, Myra Spiliopoulou, Jaideep Srivastava, and Alex Tuzhilin, editors, Proceedings of the 2005
International Workshop on Customer Relationship Management: Data Mining Meets Marketing, November 18-19,
2005, New York City, USA, 2005

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In marketing research, a well-known group of models for repeat-buying behavior are the
family of NBD-type models. Such a model was first introduced for consumer goods by Chatfield
et al. [1] and later extended and applied by various authors. For example, Lee et al. [2] used the
NBD model to describe the visit frequencies of users for a Web site and gave an empirical
illustration using the visit frequencies extracted from the transaction log of the Yahoo! Web
portal. Moe and Fader [3] modeled the visit frequencies of visitors for the online retailers
Amazon and CDNOW with an NBD-type model they extended to incorporate a stochastic
process of changes in visit frequencies over time. On their data sets from an online panel
collected directly by the visitors' Web browsers, the new model provides a slightly better fit than
a stationary NBD model. Notable is that their model can split the visitors into a group with
decreasing visit rates and a group with increasing rates, where in their data set frequent visitors
with an increasing visit frequency show an up to 40% higher conversion rate than the other
visitors. These two applications of the model are analogous to brick-and-mortar store visiting
behavior which is known to be covered well by NBD-type models (see e.g. [4]).
In this paper we focus on the application of a NBD-type model for repeat usage at the level of
individual Web pages or collections of Web pages that belong together and serve a common
purpose (e.g., product descriptions, support information) rather than on the visits of whole Web
sites. With this approach it is possible to analyze and compare different parts of a Web site,
differences between products or product classes in Web-based catalogues, or different ways of
organizing and presenting information and services. Also, analyses of the impact of other CRM
activities, promotions, and changes in the customer behavior over time are possible.
To simplify model estimation and thus make it more suitable for larger data volumes, we
suggest using the Logarithmic Series Distribution (LSD) model, a simplification of the zero-
truncated NBD model. We also extend the repeat usage model to include one-time users which
seem to play an important role in Web usage data.
The paper is organized as follows: In section 2 we discuss differences between Web-based
information and consumer products to analyze how models originally developed for consumer
products can be applied to Web-based information. In section 3 the LSD model is presented and
we extend the model to account for one-time users. In section 4 we present the empirical results
for fitting the model to a data set from an educational portal. In section 5 we describe how the
model can be used by managers to analyze and optimize parts of their Web site.
2. Web-based Information vs. Consumer Products
The NBD model and the repeat-buying theory were developed for consumer products and not for
information. In this section we compare consumer goods with so called ‘information goods’ and
motivate why NBD-type models can also be applied to such information goods. Shapiro and
Varian [4] suggest defining information very broadly by stating that everything that can be
digitized is information. Therefore examples of information goods are books, music, movies,
stock quotes, and so on. This definition clearly also comprises online product or support
information, downloads, etc. In the online world an information good can be a collection of Web
pages which belong together (information is spread over different Web pages for better access or
includes additional media in separate files). Furthermore, online information goods can be
dynamic, they can be personalized or consist of search results for a user’s query.

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Similar to consumer products, information goods can be offered, sold and consumed. For the
model used in this paper an important characteristics of consumer goods is that they are
consumed in regular intervals (e.g., a family buys some milk almost every week). Many
information goods create similar usage patterns, for example a person might check her cell
phone provider’s Web site almost every week to see what new ring tones or logos are available.

Table 1: Differences between using consumer panels and Web usage data for NBD-type
models.
Consumer Panel Web Usage Data
Items consumer products information goods
(Web sites, collections of Web pages, dynamic
content, multimedia content, etc.)
Unit of Analysis market baskets browser sessions
Analyzed Behavior purchase incidences following links to Web sites or documents,
downloads, etc.
Ignored Behavior quantity bought,
package size
repeat usage per session, number of pages
browsed within an information good, time
spent on a page
Identity of Customers known varies between anonymous user sessions and
complete personalization
Purchase History known unknown or partially known
Non-buyers known unknown
Incorrect Recording omission, over-reporting
dynamic IP addresses, caching mechanisms,
proxy servers, Web robots


The data originally used for the NBD model stem from consumer panels. Although, there
exist online panels which use modified Web browsers to record the user behavior (e.g. comScore
Media Metrix), this approach is very cost intensive and it probably only provides enough
information for the analysis of the most popular Web sites. The most common and inexpensive
way to collect consumer data is analyzing the transaction data logged by the company's Web
server. Most of the differences between panels and transaction logs are just the names used to
refer to the same concepts (see Table 1), but there are also some fundamental differences. For
example, in panels the whole purchase history of each customer is known, for anonymous use of
information on Web sites this is usually not the case. Even if the Web site uses personalization,
often the whole usage history of the user cannot be reconstructed since users tend to use a site
anonymously as long as possible and only reveal their identity when it is absolutely necessary.
Another important difference is the errors known to occur during data recording. Even though
data recording at the level of an application server (content server, e-commerce system, etc.) is
becoming more common, still online data recording is far from perfect. Known problems include
user and session identification with dynamic IP addresses, caching mechanisms and proxy
servers as well as the presence of Web robots (e.g., see [6] and [7]). The NBD-type models are
used on consumer panel data which are also known to be imperfect and contain omission and
over-reporting of purchases [8] which produce similar distortions like online data recording. The

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reason why the model still works reasonably well lies in its inherent robustness which is a very
important property for analyzing Web usage data.
3. The LSD/OTB Model
In this section we develop a simple and robust NBD-based model for the usage frequencies of
information goods which uses the LSD approximation of the NBD extended by users who only
access a specific information once and then never again. Although we model usage, in the spirit
of repeat-buying theory, we refer to such users as one-time “buyers” (OTB). We start with an
introduction of the NBD-type model and then derive the LSD/OTB model. We also review the
assumptions of the NBD model to argue why the model is appropriateness for the data analyzed
in this paper and under which circumstances the model can or can not be applied.
Chatfield, Ehrenberg and Goodhardt introduced in [1] a simple but very successful model of
stationary purchasing behavior, the so-called negative binomial distribution (NBD) model,
which Ehrenberg [8] used to describe repeat-buying behavior for consumer products. The model
uses the following simplifications:
1. Only one brand (product) is analyzed at a time. Therefore, the relations between different
brands (products) are irrelevant and brand choice and product heterogeneity are not
modeled. This simplification carries over unchanged to online data where only one
information product is analyzed at a time.
2. The aggregated purchasing behavior of all customers is stable (stationary) during the
analyzed period of time, meaning there is no trend present. This has been found to hold
approximately for frequently bought consumer goods, however, it certainly does not hold
for the introduction of new products. This assumption can be problematic since online
information goods can be short-lived. However, since the production cost of high quality
information is high, these information goods will be present long enough to reach a near
stationary market after an introduction phase. Furthermore, the stationary model can be
used as a reference to detect trends in a non-stationary situation.
3. The model uses the concept of purchasing occasions and purchase incidences. A purchase
incidence occurs, if a consumer purchases one or more units of a product in a specific trip
to a store (a purchasing occasion). The number of items bought and the package size are
ignored. The frequency of purchases proved to be more useful for modeling than the
quantity bought or the price paid. Applied to information goods this means that repeat
visits per session, the number of pages browsed within an information good and the time
spent on these pages, is ignored.

For the NBD model we consider one specific product for a single time period t. Set C
represents the customers. The purchases of the product for each individual customer Cci ∈ are
modeled by Poisson processes with parameters ciµ :


Customer heterogeneity is accounted for by different parameters ciµ . The distribution of the
long-run ciµ over all customers is assumed to follow a truncated Γ-distribution. The Γ-

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distribution has 3 parameters and can fit various shapes. Following this assumption, the
distribution of the number of purchases per customer is a special case of a compound Poisson
distribution, namely the negative binomial distribution (NBD). See [8] for the proof.
The NBD has 2 parameters, the mean m and the exponent k. The following equation gives the
probability of observing a customer purchasing the product r times in period t.



The mean m is the average number of purchases per customer. PNBD(R=0) is the proportion of
active customers who just do not buy the analyzed product in the observed period of time. The
proportion of customers b who buy is therefore 1- PNBD(R=0) and the average number of
purchases these customers is ω =m/b.
The NBD can be fitted to empirical data using the method of moments, maximum likelihood
estimation and some other estimation methods [9], but in general parameter estimation is
cumbersome. Especially, if the proportion of customers who do not buy the item PNBD(R=0) is
not observable, which is often the case for Web usage data. However, the zero-truncated NBD
tends (for k<0.2) toward the logarithmic series distribution (LSD) with only one parameter, q
(see [10]). The LSD gives a very good approximation to the NBD if the proportion of customers
who buy the item in the population is less then 20% (b<0.2) [8]. This is almost always the case
for Web usage data with a large number of items. For the LSD, the probability of observing
customers buying r-times in period t is given by:

Where the average number of purchases per customer ω is a function of q:

The LSD is easy to fit to empirical data. For the maximum likelihood estimation the mean ω is
estimated by the sample mean and then the equation above is used to compute the estimate for
the parameter q. The parameter q cannot be calculated directly from ω, however, standard
numeric approximation can be applied efficiently.
In some situations, real-world data sets contain a proportion of observations at r=1 which is
much higher than expected. Since the model only describes repeat-usage behavior, the
discrepancy at r=1 can be explained by users who only use a certain information product once
and then never again. Fader and Hardie [11] incorporated such one-time buyers (OTB) into the
NBD model and develop the NBD/OTB model to describe purchases in a tea store. In the same
way we expand the LSD model to model one-time users. The aggregate distribution of purchases
of the LSD/OTB model is:

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π is the proportion of one-time buyers and δr,1 is the Kronecker delta with δr,1 =1 if r=1 and 0
otherwise. The mean and variance are given by:


If the proportion π is 0 then the LSD/OTB model collapses into the simple LSD model. The
parameters of the LSD/OTB model can be estimated using the method of maximum likelihood.
The log-likelihood function is given by:

fr represents the observed count of users with r repeat-buys. To estimate the parameters,
standard numerical optimization is used to maximize the log-likelihood function. Alternatively,
the real number of repeat-users with r=1 could be seen as unknown and it could be estimated
iteratively together with the distribution parameter q using the Expectation Maximization (EM)
algorithm [12].
4. Fitting the Model
To provide evidence that the LSD/OTB model can describe usage of information from a Web
site, we analyze one year (2001) of transaction data from the application level log of an
educational portal, the Virtual University information system at the Vienna University of
Economics and Business Administration (see http://vu.wu-wien.ac.at). The portal provides
access to online information (lecture notes, research material, enrollment information, etc.) for
students and researchers. An item in this setting is defined as a collection of Web pages
(including also other media like word processor files) that present a logical unit of information
on a specific topic, e.g., Course material on International Marketing. The items are stored on
different Web servers in the university's Intranet as well as on the Internet. The portal provides
an interface to find items and records when a user follows the hyperlink to an item. The system
is comparable to a Web-based catalogue or a small, very specialized search engine.
Since the portal does not require user identification (which is also common for commercial
Web sites), we have to use heuristics (filter Web robots, analyze IP addresses and use permanent
cookies stored in the users’ Web browsers) to identify different users [6]. To compute sessions,
we used a timeout of 20 minutes (a common timeout for this purpose, see [13]). This is a very
coarse approach because of dynamic IP addresses and proxy servers. However, we will see that
this data still provides useful insights for understanding aggregated Web usage behavior.

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Table 2: Results of fitting the LSD and the LSD/OTB models*
model items
no
q
no χ2 test
(α=0.05)
no significant
differences
significant
differences
% of fitting
models
LSD 2226 713 786 475 252 65.34%
LSD/OTB 2226 834 838 516 38 93.14%


0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25 30
fre
qu
en
cy
number of clicks per user (r)
observed count
LSD
LSD/OTB

0
20
40
60
80
100
120
140
160
180
0 5 10 15 20 25 30
fre
qu
en
cy
number of clicks per user (r)
observed count
LSD
LSD/OTB

Figure 1: Two examples (C++ Standard Library to the left and Freshmeat to the right).
For better visibility of the differences both plots are truncated at r=30.

In the data set we observed usage of 9671 different items from 15340 different IP addresses.
The data contained 56278 sessions. We selected again items with more than 10 observations.
This reduced the items to 2226. For these items we estimated the parameters of the LSD and
LSD/OTB model and used the χ2-goodness-of-fit test to analyze the fit of the model for our data.
The results of the analysis are shown in Table 2. For the items with enough observations and
repeat-usage to estimate the parameter q and to conduct the χ2 test, the observations of 65.34%
of the items do not differ significantly from the LSD model. The introduction of one-time users
improves the results. For the LSD/OTB model more than 90% of the items do not differ
significantly from the model.
In Figure 1 we inspect 2 items in more detail. The left plot is for an item which contains
information about the C++ Standard Library for programming in the language C++. The
LSD/OTB model (p=0.954, π=0.390) fits the data well with χ2=1.922 at 5 degrees of freedom
(no significant differences at α=0.05). Following the model, 39% of the clicks are from one-time
users who only needed the information once or found the pages not informative so they never
returned. The simple LSD model is significantly different from the observed data since it can not
fit the high number of observations at r=1.
The plot to the right in Figure 1 is for the item Freshmeat, a repository of free software. The
LSD/OTB model (q=0.956, π=0.471) describes the observed data better than the LSD model,
however, the χ2-value is 15.134 at 6 degrees of freedom which means that there are significant
differences between the model and the data. The reason for the differences are that in the
observed data there are several users who use the site more than 30 times (this is not visible in
Figure 1 since the plot is truncated at r=30). These observations distort the estimates for the
* Numbers are corrected in this version of the paper.

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parameters which leads to a underestimation at r=2 and 4. An explanation for the observed high
repeat-users could be recording errors due to the user identification heuristic.
5. Using the LSD/OTB Model for Analyzing Web Sites
The parameters of the model directly provide important diagnostics for the usage of different
items. A proportion of one-time users (parameter π) which is considerably higher for some items
than for the rest in a Web Site indicates that the items do not provide the consumer with the
expected information or are not fulfilling their expectations, thus do not contribute to the aim of
retaining customers. An analysis of these items or the navigation structure for these items can
provide information to improve the Web site or the item and thus help to convert one-time users
to repeat-users.

Table 3: Parameters of the LSD/OTB model over time for 3 selected items
1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
user q π user q π user q π user q π
Enrolment System 67 0.72 0.79 20 0.87 0.91 46 0.70 0.79 27 0.96 0.95
C++ Class 111 0.81 0.36 93 0.84 0.56 36 0.80 0.95 26 0.99 0.75
Online Dictionary 241 0.92 0.51 213 0.90 0.41 161 0.87 0.30 173 0.83 0.31


0
0,2
0,4
0,6
0,8
1
1 2 3 4
Quarter
q
Enrolment System C++ Class
Online Dictionary

0
0,2
0,4
0,6
0,8
1
1 2 3 4
Quarter
pi
Enrolment System C++ Class
Online Dictionary

Figure 2: Parameters of the LSD/OTB model over time

The parameter q can be interpreted as the proportion of usage by repeat-users. By considering
more than one time-period with the LSD model, this repeat-usage behavior can be analyzed. We
divided the data set containing data for 1 year into 4 quarters and estimated the LSD/OTB model
for each quarter individually. In Table 3 we present the number of different users who used the
items and the estimated model parameters for three selected items. The items are the university
wide online enrolment system, an introductory class on the programming language C++ and a

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online English-German dictionary. The changes of the parameters over the 4 quarters are shown
in the plots in Figure 2.

For the strictly stationary LSD model, the values of q should not change over time unless there
are changes in the underlying user behavior. The usage behavior for the online dictionary
exhibits approximately stationary behavior. However, parameter q declines steadily which means
the item is losing repeat-users. For the remaining two items we found greater changes of the
parameter q over time. The changes of both items are similar and can be explained by
seasonality in the data set. The 3rd quarter (July to September) are holidays at the university
where only few students are on campus and with the 4th quarter (October) the new study year
starts. Therefore, we observe for the 2 items a lower q in the 3rd quarter and a very high q in the
4th quarter.
Changes of the parameter π, the proportion of one-time users, over time also indicates changes
in usage behavior. In the data for the selected 3 items (see Figure 2) no clear trend can be
identified. For the enrolment system the proportion seams to stay almost constant at a very high
rate. This might indicate that navigating to the system through the portal page is cumbersome
compared to the prominently placed link on the university’s home page. For the online
dictionary π it is steadily degreasing. For the C++ class we observed the biggest changes which
can be explained by the behavior of its main user group, students who can take the class. The 1st
quarter is dominated by students studying for the final exam in February, hence the low one-time
only user rate. The class is not offered in the 2nd and the 3rd quarter resulting in a higher π with
the peak in the 3rd quarter where many students check out if they want to take the class in the
next term starting with the 4th quarter.
If stationary usage behavior (a constant number of users and a constant parameter q) can be
assumed approximately the model can be used for predicting repeat-usage (analogous to repeat-
buying in [8]). The theory considers two consecutive periods of the same length where by
definition the parameter q stays constant. Individual users change their behavior but the
aggregated numbers stay the same. In this situation users who use an item in both periods are
called repeat-users (repeat-buyers). New users (new buyers) use an item in period two but not in
period one. Lost users (lost buyers) used an item in the first period but do not use it in the second
period. From the parameter q of the LSD model several characteristics of repeat-usage behavior
can be calculated. First, the proportion of repeat-users bR in the total number of observed users b
can be calculated by:

Note that this proportion is more than just the number of users who used an item more than
once during the observation period. It also contains a proportion of the users who used the item
only once in the observation period but are predicted by the model to use the item again in the
following period.
The proportion of times an item is used by repeat-users mR in each time period equals q:

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The average usage per repeat-user ωR is given by:

And finally, the average number of times an item is used by lost or new users (they are equal
in the stationary state) can be calculated by:


Table 4: Repeat-usage characteristics for 3 selected items
q ωR bR/b mR/m ωL=ωN
Enrolment System 0.717 2.519 0.572 0.717 1.327
C++ Class 0.807 3.205 0.640 0.807 1.364
Online Dictionary 0.916 5.456 0.737 0.916 1.409


We calculated the corresponding values using q estimated from the 1st quarter and present the
results in Table 4. For the C++ class the average repeat-user uses the class Web pages 3.205
times in the 1st quarter. 64.0% of the observed users (excluding the one-time users) are repeat-
users who account for 80.7% of the usage of the class pages. The new and lost users on average
use the pages 1.364 times, a number close to 1. In the same way the numbers for the other items
can be interpreted where the online dictionary has very loyal repeat-users (73.7% of its users)
accounting for over 90% of the observed usage.
Even if stationary or near-stationary behavior cannot be assumed (e.g., for the C++ class), the
above characteristic are still meaningful to analyze the composition of the user base from usage
data. The values are more useful than simple statistics normally generated by Web analyzer
tools. Standard analyzer tools report summary statistics as the total number of page views, visits
and hits in a time period. These numbers can give an idea about the development of the usage
over several periods but the structure of repeat-usage is not visible. Clearly, retained customers,
i.e., customers who repeatedly visit some Web pages are more valuable for commercial Web
sites than customers who never come back after the first visit. With the LST/OTB model
observed usage from a single time period can be divided into a part resulting from one-time users
and another part resulting from repeat users. This provides a very important insight into how
effective parts of the Web site are in converting visitors into loyal repeat-visitors.
6. Conclusion
In this paper we concentrated on analyzing usage-behavior of information provided by a
commercial Web sites in order to work towards one of the main CRM goals, customer retention.
Instead of applying standard data mining technology, we applied a NBD-type model from
marketing research to model usage frequencies of collections of Web pages (Web-based
information). In order to be able to deal with larger volumes of data, we applied the LSD model,
the most simple and easy to estimate version of the NBD-type models. To account for one-time

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users (OTB), we expanded the model and developed the LSD/OTB model. Using an example
data set, we show that the LSD/OTB model gives a very good fit for the items (for over 90% of
the items).
The parameters of the extended model are directly usable for the manager of a Web site. For
example, big differences between the proportion of one-time users within a Web site give a hint
to problems with the item quality or the navigational structure (e.g., an item is reachable by a
link with a misleading name). Changes of the users' repeat-usage behavior over time can be also
automatically analyzed by detecting changes in the parameters in successive periods. These
insights into the composition of usage-behavior are way beyond the capabilities of standard Web
analyzer tools.
Especially, the estimation of the proportions of repeat-users and one-time users directly shows
the ability of different parts of the Web site to retaining customers and thus indicates where
improvements are required. This is a valuable input for the CRM processes.
7. References
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