1
Modeling the Network of Loyalty

Profit Chain
Carl Lee, Central Michigan University, Mt. Pleasant, MI
Tim Rey, The Dow Chemical Company, Midland, MI
Olga Tabolina, The Dow Chemical Company, Midland, MI
James Mentele, Center for Applied Research & Technol
ogy,
Central Michigan University Research Corporation, Mt. Pleasant, MI
Tim Pletcher,
Center for Applied Research & Technology,
Central Michigan University Research Corporation, Mt. Pleasant, MI
ABSTRACT
This article presents
a case study on modeling th
e network of cause

and

effect relationships of
the loyalty

profit chain for
the
chemical industry.
The modeling of the loyalty

profit chain has
become an important research topic in marketing due to the dynamic change of the global
economical marketing.
T
h
e article
first
present
s
a
project model and strategy
and discuss how it
is applied to this case study.
I
n order to model the complex network of the
potentially nonlinear
and asymmetric
cause

and

effect
relationships
, a modified neural network technique, s
tructural
neural network is developed
. D
etailed strategy of modeling building and evaluation is presented.
A comparison between this modified neural network, the traditional neural network
and
regression models is presented
.
1.
INTRODUCTION
This article presents a case study for
predicting the profit through
modeling
the network
of loyalty

profit chain
for a company in the chemical industry, which will be named as Company
A through out the article. The complete m
odeling proces
s
included three stages which spanned
several years of elapsed time and was conducted
in three stages
.
The first stage was to establish
the network of the cause

and

effect relationships in the individual business study specifically for
the attitudinal or p
erformance portion of the performance

sa
tisfaction

loyalty
chai
n (Rey and
Johnson
2002;
Rey
2002).
Structured equation model and partial least square model were applied
to build the loyalty construct
based on theoretical
loyalty
framework available in the
marketing
literature (e.g.
, Dick and Basu, 1994; Oliver, 1994; Oliver, 1997; Gustafsson and Johnson, 2000;
2
Gustafsson and Johnson, 2004).
.
The second stage
took the conceptual loyalty construct from
stage one as the basic network and
used customer attitud
inal performance data, perceived values,
satisfaction, image and customers’ characteristics across the accumulation of 40+ individual
business studies spanning four
years to build a predictive model of loya
lty index (Lee, Rey,
Mentele &
Garver, 2005).
The
third stage was to model
the complete loyalty

profit chain for
predicting the profit for Company A. The complete loyalty

profit network is built on the loyalty
network obtained from
the stage two
with additional network structure connecting the loyalty
con
struct with variables ob
employee satisfaction, market orientation, and financial data.
This
article
focuses on the third stage of
modeling the
complete
network of loyalty

profit chain.
Recent
research findings
in the marketing research literatures
have c
onfirmed
that
customer satisfaction,
customer loyalty
and retention
are related to key me
asures of financial
performance,
such as
increased sales, lower costs, and more predictable profit streams are some
of the tangible benefits to the company of having l
oyal customers (Bejou and Palmer 1998;
Terrill et al. 2000). Customer loyalty has also been documented as a source of competitive
advantage and a key to firm survival and growth (Bharadwaj et al. 1993; Reichheld 1993;
Reichheld, 1996; Terrill, 2000 ).
Reic
hheld and Sasser (1990) identified numerous bottom line
benefits of customer retention
due to loyal and satisfied
customers
including willing to
purchase
more, pay
ing
higher prices, easier to service (thus reducing operating costs), and help
ing
to
expand
the customer base by giving positive referrals.
The bottom line is that
Building and
enhancing long

term relationships with customers generates positive returns to a company
.
On
the other hand, how a firm should do in order to build satisfied and loyal cus
tomers? Empirical
evidence in the satisfaction literature has shown that performance attributes of a firm, such as
product quality, customer services, technical support, cost, and so on, are associated with
customer satisfaction, which in turn impact the
loyalty (see, e.g.,
Hanson
1992; Mi
ttal, Ross, and
Baldasare 1998,
Anderson and Mittal
2000).
The marketing literature also suggests that different customer segments may place
different levels of importance on product and service attributes, and that for
different segments
attribute may have more or less impact on predicting satisfaction, loyalty, and retention.
Further,
different level of retained customers may have different impact on the firm’s
profitability
.
For
example, Mittal and Katrichis (2000) arg
ue that newly acquired and loyal customers should be
3
treated as distinct segments. They present three case studies from the automotive, mutual fund,
and credit card industry to show that attribute importance varies significantly between these two
segments.
Reichheld
(1996) showed that for the credit card and insurance industry,
the
relationship between a customer’s duration with
the firm and profitability varied significantly.
By
calculating the cost of
maintaining customers in each segment and the revenue
they generated,
the firm
will be
able to calculate the differential
profitability rates for each segment.
F
ailure to
consider segment

specific differences may lead a firm to optimize performance on the wrong
attribute for a given segment
(
Anderson
and Mitt
al
2000)
.
The modeling strategy used for this project consists of a large task of data preparation,
data harmonization and data processing. As indicated in data mining literature
(e.g., Berry and
Linoff 2000; Han and Kamber 2001)
, the data cleansing stage
took over 80% of the project
period.
The network of cause and effect relationship for describing the ‘path’ that leads to profit
is complicated. A
modification of the
neural network technique, namely,
structural
neural
network (SNN) is developed
for modeling the loyalty

profit chain.
Section
t
wo
presents the
complete loyalty

profit network structure and
discusses the motivation behind the development
of the SNN technique for modeling the loyalty

profit chain.
Section three
discusses the project
pl
an
and the issues related to data preparation, harmonization and processing. Section four
describes the
SNN technique
and the
SNN modeling
strategies for building the SNN
model
using
the data provided by
Company A. Section
five
summaries the results and gives a brief discussion
of the findings.
A brief conclusion and remarks
of the
SNN techniques
and the lesson learned
is
discussed in
s
ection
s
ix
.
2.
THE NETWORK O
F THE LOYALTY

PROFIT CHAIN
There is a long history of development of the loyalty and profitability framework in the
marketing research literature (e.g., Dick and Basu, 1994; Oliver, 1994; Oliver, 1997; Gustafsson
and Johnson, 2000; Gustafsson and Johnson,
2004).
The complete loyalty

profitability
framework adopted in stage
t
hree is given in Figure
1
.
This framework was developed by testing
and modifying various theoretical frameworks in the marketing literature using company A’
s
data. For more detailed disc
ussion of the development of the framework, one may refer to Rey
and Johnson (2002), Rey (2002) and Lee, et al (2005).
Consistent with the literature
(e.g.,
4
Gustafsson and Johnson, 2000
)
, customer perceptions of product and service attributes (technical
su
pport, customer service, availability and delivery, product quality, and cost) lead to customer
perceptions of value. In turn, perceived value, ease of doing business, and the business
relationship influence and predict customer satisfaction. Loyalty inten
tions (intentions to
repurchase and recommend) are predicted by the firm’s perceived image in the marketplace,
customer characteristics (type of buyer, type of firm, etc.), and their current level of customer
satisfaction. Loyalty intention predicts loyalt
y behaviors, which in turn affects the customer’s
purchase volume, level of price sensitivity, and retention. Various profitability measures are
directly predicted by these variables.
Figure
1
: The Complete
Network of the
Loyalty

Profit
Chain
2.
1
THE NEED FOR NEW TECHNIQUES FOR MODELING
THE
LOYALTY

PROFIT
CHAIN
Regression techniques such as multiple regression and principle component regression
are typical techniques for modeling profit without taking into account
the network structure.
S
tructural equation modeling (SEM) and partial least square (PLS) techniques
are typical
techniques for modeling profit when the network structure is considered
(e.g., Johnson and
Gustafsson, 2000)
.
Gustafsson and Johnson
(
2004)
co
mpared multiple regression, partial least
5
square and principle component regression techniques for three different service industries. They
suggested that one should not solely rely on one technique until they are carefully compared. This
is mainly due to
the fact that the modeling structure and the underlining assumptions are different
and serve for different purposes.
Lee, et. al. (2005) discussed the strengths and weakness of these
traditional techniques and indicated that the s
trengths of these traditio
nal techniques include
(1)
parameter/weight estimates are
more easily
interpret
ed
, (2)
models are
easy to construct, and (3)
in most cases, confidence level and hypothesis testing can be performed. The weakness of these
techniques include
(1)
inability to
model nonlinear
relationship between inputs and targets
, (2)
in
ability to model h
igh
er
order
interactions
effectively,
(3)
requir
ement of
distribution
assumptions such as normality, and (4)
inability to effectively model large amount
s
of messy
data..
Ande
rson and Mittal (2000) gave a thorough discussion about the nature of nonlinearity
and asymmetry in the chain relationship between
the constructs of
attribute performance,
satisfaction, loyalty and profit, and showed that the relation between each link oft
en is nonlinear
and asymmetric.
For instance, the nonlinear link between attribute performance and satisfaction
constructs may
occur when
performance increases in certain
types of attributes
have less of an
impact on satisfaction
at some point, while a
t ot
her points in the chain, there are
increasing
returns
. The nonlinear link between satisfaction and profit construct may appear in the
form of
diminishing returns
. That is, each additional one

unit increase in an input has a smaller impact
than the
precedin
g one

unit increase.
Asymmetric lin
k occurs when
the impact of an increase is
different from the impact of an equivalent decrease, not
only in terms of direction but also in
terms of size
(e.g., Anderson and Mittal, 2000)
.
Empirical evidences have been rep
orted in the
literature
in a variety of industries such as health care ((Mittal and Baldasare 1996), airlines and
telephone directory service (Danaher 1998), automotive (Mittal, Ross, and Baldasare 1998), and
business

to

business marketing (Kumar 1998).
In
the Chemical industry, similar nonlinear and
asymmetric relationships also exist based on
exploring the
Company A’s data
(Rey 2002)
.
M
arketing literature has suggested that many marketing characteristics such as customer’s
satisfaction, retention rates,
and profit measurements do not follow
a
normal distribution. In
addition, the fast growth of data collected by firms not only results in a complex and messy data
structure but also in a large amount of data. The traditional statistical inference and hypot
hesis
6
testing may no longer be appropriate
in these situations
. In various data mining literature (e.g.,
see, Hand, et, al, 2001; Hastie, 2001; Riply, 1996
; Han and Kamber, 2001
) a variety of
techniques have been developed for dealing with problems involv
ing large amounts of
non

normal,
nonlinear,
and
messy data
.
A key feature of
the
loyalty

profit
chain (Figure
1
)
is that the attribute performance,
satisfaction, loyalty and financial constructs in the model are inherently abstract or latent
variables.
Ap
propriate modeling
techniques need to accommodate the fact that the model is a
network of cause

and

effect relationships that contains latent variables. Traditional SEM and
PLS techniques are natural choices for modeling such a network
(e.g., see Johnson a
nd
Gustafsson, 2000;
Hahn, et al, 2002; Gustafsson and Johnson, 2004)
.
However, the weaknesses
mentioned above have caught the attention of various researchers. Alternative modeling
techniques have been developed to deal with these drawbacks. For instance,
Hahn, et al (2002)
proposed a mixture PLS model for taking into account the difference of business segments.
Ansari, et, al.
(2000) proposed a hierarchical Bayesian methodology for treating heterogeneity in
structural equation models.
Hruschka (2001) appl
ied a one hidden layer neural network to model
net attraction.
The ultimate goal of the loyalty

profit modeling project is:
“
To develop a predictive model for predicting profit that is capable of taking into the
nonlinear and asymmetric cause

effect rel
ationships in the loyalty

profit framework
without the assumptions such as normality and homogenous variance for large and
messy data
for Company A.
”
Lee, et, al, (2005) proposed a modification of the traditional neural network, namely, a
struct
ural
neural network technique (SNN) to model the loyalty construct in stage two of the project. They
demonstrated that the SNN technique performs better than traditional NN models as well as
regression modeling techniques. The proposed SNN technique mimics
the theoretical loyalty
framework, and takes into account the nonlinear and asymmetric relationships between
constructs (i.e., performance to satisfaction to loyalty). Building on the success of the SNN
model for the loyalty construct, it was decided to a
pply the same technique for modeling the
complete loyalty

profit chain
in stage three of this project
.
The major advantage of a neural network technique is that it is a universal approximat
or
7
(Riply, 1996) for any type of function. However, since the weig
ht estimates of the neural network
model are not meaningful for interpreting the impact of the inputs (or independent variables), it
has been criticized as a ‘Black Box’ approach. Therefore, in the development of the
structural
neural network sys
tem, some strategies are implemented to deal with the issue of validity of the
technique.
3. THE
PROJECT PLANNING AND
DATA PREPARATION
AND EXPLORATION
3.1: Project Model and Strategy for Data Mining Project
A successful data mining project requires the i
ntegration of three
skills: information
technology skill, domain knowledge skill and analytic skill. A data mining project team therefore
must be multi

disciplinary. The project model implemented for this and other data mining
projects is summarized in Fig
ure 2.
Figure 2: Project Model for Conducting Data Mining Project
As shown in Figure 2,
our project model is a collaboration team approach from both business
client and academic researchers. The project team for the loyalty

profit project con
sists of
information technology support from both the research center and Company A. Similarly, the
domain experts for marketing research in loyalty and profitability is also from both Company A
and researchers at the center. The analytic experts are from
the research center.
Table 1
Client
Research
Center
& IT
Discipline
Expertise
•
Establish Requirements
•
Monitor Results
•
PROJECT
TEAM
•
Interpret Results
•
Identify Actionable Events
•
•
Summarize and Analyze
•
Quality Control
•
Discover and Explore
•
Identify data to extract
•
Create Models
•
Tools & IT Skills
•
Project Management
•
External Data
•
Integrate Data
•
Security & Confidentiality
•
Link to Busin
ess Strategy
•
Data Knowledge
•
Provide Corporate Data
•
Prioritize Need
8
summari
z
es our data mining project strategy, including this loyalty

profit project. Such a strategy
is common in business intelligence (e.g., Berry and Linoff, 2000).
Table 1: The Data Mining Project Strategy
1. Define busines
s problem
2. Build data mining database
3. Explore data
4. Prepare data for modeling
5. Build model
6. Evaluate model
7. Deploy model and results
8. Take action
9. Measure the results
3.2 Data Sources and
Data
Preparation
In order to build a predicti
ve model
based on the framework in Figure 1, a variety of data
sources were required. These data include customer satisfaction surveys, employee satisfaction
surveys, customer complaint data, market orientation survey, purchasing volume data, price data,
r
evenue data and cost data. Some data were at customer level and some were collected at
business account level. Some data were cross

sectional, and some were longitudinal. All of the
data were transformed into business
account level and aggregated into
a
cr
oss

sectional data
structure
.
T
able
2
summarizes the
data sources
and brief characteristics of the data.
Table 2: Data Sources for the Loyalty

Profit Predictive Model
Data Source
Characteristics
Customer Satisfaction
and
Loyalty
•
Cross sectional, Conduct
ed in different sectors in different time period (a total of 40+
survey studies)
•
100+ variables
,
20,0
00+ observations (by individual
within a business customer
)
Market Orientation
•
Cross sectional
•
20+ variables
,
300+ observations
(business sector in Compan
y A)
Employee Satisfaction
•
Multiple time frames
•
20+ variables
,
30
,000+ observations
(business sector in Company A)
Customer
Complaint
s
•
Quarterly Over time
•
30 variables
, 180
,000+ observations (customer level)
Account Sales/Volume
•
Quarterly Over time
•
40
+ of variables
,
100
,000+ observations
(account level)
Price
•
Quarterly over time
•
30+ variables
,
1,40
0,000+ observations (customer level)
Profit
Quarterly Over time
•
25+ of variables
,
300
,000+ observations (customer level)
The quarterly data were collaps
ed into annual average data. By going through the steps of data
collapsing, merging, titration data quality checking, and missing data processing,
data
transformation, new variable creation, and variable selection, the final data set consist of 2976
cases
and 63 inputs and five target variables.
The target variable presented in this article is the
9
adjusted 2001
Economic Profit (
A_
EP
01
), which is the measure of the ‘pure’ profit
for the year
of 2001
at the account level defined by Company A.
As suggested in
data mining literature (e.g.,
Berry and Linoff, 2000), we also experienced that o
ver 80% of the project time was spent on the
data preparation
.
Table 3 summarizes the inputs for each latent variable shown in the loyalty

profit chain network in Figure 1.
Table 3: The Input Variables for each Latent Variable of
the Network of Loyalty

Profit Chain
Latent Variable
# of Inputs
(data source)
Latent Variable
# of Inputs
(Data Source)
Costs
4
(Survey)
Product Quality
2
(Survey)
Availability
5
(Survey)
Customer
Service
4
(Survey, Complaint data)
Technical Support
4
(Survey)
Perceived Value
2
(Survey)
Ease of Doing Business
7
(Survey)
Commercial Relation
6
(Survey, Internal data)
Customer Characteristics
3
(Survey, Internal data)
Customer Satisfaction
4
(Surv
ey)
Image
6
(Survey)
Purchase Intent
2
(Survey)
Business Competition
3
(Internal data
Retention, Attrition
8
(Internal data)
Purchase Behavior
1
(Internal data)
Volume Index
1
(Internal data)
Price Index
1
(Internal data)
The
se
inputs were determin
ed using both the domain knowledge from the loyalty

profit
framework and the empirical data collected by Company.
Most of the survey
questions are
in the
scale of 1 to 10 with one being ‘extremely negative’ and ten being ‘extremely positive’. These
data a
re usually
distributed skewed to the left (that is
, more customers were in positive or
extremely positive category).
The distributions of volume, price, the EP indices and other
financial variables are highly skewed to the right. Accounts that are outside
the 99
th
percentile
were considered outliers.
Th
ese variables are
adjusted
by the 99
th
percentile
defined as:
.
Where
VNAME
i
is the
variable name with the original
scale for the
i
th
account, and
VNAME
_P99
is the 99
th
percentile
of th
e corresponding variable
.
The transformed data values that are greater than one were treated as outliers and were deleted.
Other inputs were also standardized using range normalization:
. This transformation
eliminates the effec
t of the different
scales of the original data, and retains the variation structure of individual input.
10
3.2.1: Missing Data Processing
Missing data processing is often one of the tricky issues in the data preparation. This
project involves with over 40 d
ifferent surveys
from both business customers and internal
employees
in diffe
rent time periods with
different questions
or different ways of asking the same
questions, as well as different time periods of financial data and profit data. In the process of
p
reparation of data at the account level, we encountered various missing data problems. For each
type of missing data, a strategy was developed using both the domain knowledge and the
property of the type of data. Some missing data were set to zero, some we
re deleted and some
were imputed. Two imputation techniques were applied. One was by using the tree imputation
technique
with surrogate variables. The other was by trend analysis. For instance, missing in
price a
t different quarter des not mean
there was n
o price
n
or zero price. A time series trend
imputation was used to impute the price data.
Figure 3 shows an example of price imputation.
Figure 3: Price Imputation using Trend Analysis
Before Imputation
After Imputation
3.2.2: Hostage
and
Mercenary Customer
Identification
Lee, et, al, (2005) developed an SNN model for the loyalty construct and mentioned an
unsolved issue about hostage and mercenary customers. Hostage customers are those who are
dissatisfied, but, have to purchase the produc
t, while mercenary customers are those who are
satisfied but tend to shopping around regardless. In modeling the profit, it is important to
carefully examine these two types of customers. I
t was decided to take loyalty

specific
segmentation approach by seg
menting the customers into hostage, mercenary and ‘logical’
customers. The ‘logical’ customers segment was then used for the profit model building. A set of
criteria was developed within Company A for segmenting the three types of customers.
Such a
segment
ation strategy is nece
ssary and was also recommended in the marketing literature (e.g.,
Anderson and Mittal, 2000).
11
4.
MODELING
STRATEGY FOR BUILDING A
STRUCTURAL
NEURAL NETWORK
4.1: A Brief Overview of a Neural Network Model
A neural networ
k (NN) can be considered as a two

stage nonlinear or classification
model, usually represented by a network diagram. The two

stage process is, first, to derive a
hidden layer of variables through a nonlinear function acting upon the linear combination of t
he
inputs:
, where g is the activation function and
is the weight matrix of
the inputs. Additional layers can be derived using
as inputs to create two or more hidden
layers.
Commonly used activation functions are: Hyperbolic tangent:
,
Logistic function:
, Arctangent function:
and Elliott function:
.
The
target
is modeled as the function of the linear combination of
defined as
,
where
is the activation function connecting hidden layers with the targets. The fu
nction
can
be taken the same as
or as an identity function. If f is taken as an identity function, Y is a linear
combination of H. In modeling with a NN model, one usually normalizes both targets and inputs
to eliminate the prob
lem of different units and magnitudes among the variables.
T
he
Backpropagation algorithm
is one of the earlier techniques developed to estimate the weights
.
Many alterative algorithms have been developed (Ripley,1996). Most algorithms for estimating
the we
ight matrices
and
minimize certain objective functions, which are defined as the
functions of the difference between the observed values
and predicted values
. For detailed
description of
neural network,
one may refer to
, for example,
Fausett (1994)
,
Ripley (1996)
, and
Han and Kamber (2001).
4
.2
SNN Model
for
t
he Loyalty

Profit Chain
The following strategy is applied to build a
structur
al
neural network model for fitting the
theoretical framework of cause

effect relationship.
(1)
Network Identification: The framework in Figure 1 is used as the underlying network for
building the SNN model
.
Each node in the SNN model represents a latent vari
able in the
framework. The layout and the number of hidden layers are determined by the framework
itself.
For example, the Product Quality, Cost, Customer service, Availability/Delivery and
Technical Support are the nodes for the first hidden layer, which
are the inputs for the second
12
Input
H1
H2
Target
Input
Input
H1
H2
Target
hidden layer “Perceived Value”. The “Ease of Doing Business” is also a
first
Hidden Layer,
which is the input for “Biz/ Commercial Relation. The “Perceived Value” and
“
Biz/Commercial Relationship” are the inputs for the
thir
d
hidden layer, “Satisfaction”.
(2)
Determination of
the n
umber of
n
eurons for each hidden node (latent variable): For each
hidden node, the number of neurons decides the degree of approximation of the inputs to the
node. The more the neurons, the better the
approximation supposes to be, but the risk of over
fitting also increases. Therefore, it is important to determine an adequate number of neurons
for each node. Principle Component Analysis is applied to determine the number of the
principle components of
the input variables for each hidden node as the number of neurons
for the hidden node. The percent of variation explained for choosing the number of neurons is
80% or higher. Hence, the eigenvalues may be less than one in some cases.
The following Figur
e (Figure
4
)
is an example of
traditional NN and a
Structural
Model
Figure
4
: Traditional NN model
and SNN Model
Traditional NN Model
Structural
NN Model
The data mining software,
SAS Enterprise Miner
®
is used to building the SNN model. Figure 5
gives the SNN architecture of the SNN model for the target variable, pure economic profit.
Figure 5: The SNN
Architecture for the Loyalty

Profit Network Using SAS
/EM
13
The light blue blocks in Figure
5
represent the input variables, and the dark blue squares are the
hidden layers representing the latent variables. The
adjusted 2001 Pure Economic Profit
(A_E
P01) is the target variable
(yellow block). The number inside each hidden layer is the
number of neurons applied to the hidden node
, which is determined using factor analysis as
described in step (2) above.
Notice that the structure in Figure
5
mimics
the framework
in
Figure 1.
The price and volume are combined into one latent variable.
The marketing
orientation is combined into the business competition latent variable.
[Olga and Rey: Please
revise this. I am not so
sure about the Gap and Competition inputs].
Thus, based on the
loyal
ty

profit
framework, the SNN model for modeling the target
A_EP01
(
2001 adjusted Pure
Economic Profit
) has
seven
hidden layers.
4.
3
THE MODELING
STRATEGY AND ASSE
SSMENT
The
modeli
ng
st
rategy
and evaluation
are
the ste
ps 5,
6, and 7
shown
in
our
data mining
project strategy in Table 1
.
The fol
lowing processes are considered during modeling
.
(a)
Starting Weights and Stopping Rule:
Five preliminary networks are conducted using random
samples based on different seeds. The weight estimates that give the smallest error is chosen
to be the initial value
s. This is done using the neural network options in the SAS/EM.
(b)
Control over fitting: A
s
imple cross validation approach is applied to guide against over
fitting. The data are split into Training (60%), Validation (20%) and Testing (20%). Other
partitions
are also conducted. No noticeable differences are noticed.
(c)
The objective function for model comparison: Three objective functions are used for model
comparison. The primary objective function is the
Root
Average
Square
Error, which is also
used by EM as
the default for determining the final model, is defined as:
A
S
E = SUM(y
i
–
y
i(Pred)
)
2
/n , where n is the total number of cases
.
The
other two criteria are
Root Mean Square Error (RMSE)
and
Schwarz Bayesian Criterion
(SBC)
:
MSE = SUM(y
i
–
y
i(Pred)
)
2
/
(n

p), where p is total number of estimated weights.
14
(d)
Dummy Variable Handling: For
n
ominal input, deviation coding is used. For
o
rdinal input,
bathtub coding is used. For each case in the
i
th category, the
j
th dummy variable is set to
for
i
>
j
,
o
r otherwise to
otherwise (see SAS Enterprise Miner
Reference Manual for details).
(e)
Activation Functions: The hyperbolic tangent is used to connect the inputs and hidden nodes.
Logistic activation function
is used to link hidden layers and the target variable.
(f)
The competing models considered include (1) Linear Model
with complete two

way
interaction. Stepwise variable selection is applied for selecting variables.
(2) Traditional NN,
that is, all of the input
variables are feeding into the first hidden layer. To make a proper
comparison, three hidden layers, similar to the SNN, are also used. The number of neurons
for each hidden layer is three, which is the SAS
®
neural network default,
and
(
3
) SNN having
mult
iple neurons per node, where the number of neurons are determined using Principle
Component Analysis.
5. RESULTS AND DISCUSSION
U
sing the 60%/20%/20% data partition, the fit statistics for the
traditional NN, regression
and SNN models are given in Table
4.
The objective function is the Average
Square
Error
(ASE)
. The best model is the model that gives the smallest
ASE
for the validation data. Figure
6
gives the average errors for different iterations in the modeling process. The best is obtained near
the
135
th
iteration. The test data is not included in the modeling process. It is used as an
independent evaluation of the model.
Table 4: The Goodness of Fit Statistics for the Three Models
[Olga and Rey, please revise this table if the n
umbers are not correct.
I get them from the
power point presentation you presented at the final
presentation
. In the slides, there are
several different summary tables. The results are all different.
I am not sure if these
Model
Degrees of
Freedom
Root ASE
(Training)
Root ASE
(Validation
)
Schwarz Bayesian
Criterion
Adjusted
R

Square
Traditional NN
(3 nodes)
0.2394
0.2412

1159.6
Regression (with two

way interactions)
0.1877
0.1928

2768.3
0.86
Structural NN
0.1719
0.1719

2614.9
15
numbers I took are the
correct
on
es.
I can not find the degrees of freedom from your final presentation.
Are they available?
Figure 6
: The Average Square Error of each Iteration of modeling process for the
Validation Data
The target, adjusted 2001 Economic Profit is
range nor
malized. Values are between 0 and 1. The
root
average
square error
for the SNN model is the lowest, which is about 17%. Regression
model has error at 19%, while the traditional NN model has error at 24%.
F
igure 7 gives the plot between predicted profit (
left) and residual plot (right) against the
original profit. The residual plot shows some extreme accounts that are not fit properly.
Figure 7:
Plots for Predicted Profits (left) and Residuals (right) against Original Profits
16
The stepw
ise regression technique is also applied to select key factors that have significant
impact to the prediction of profit.
The adjusted R

square for the final model is at 86%.
Using the
adjusted R

square as the selecting criterion, Figure 8 give
s
the selecte
d variables
based on the
Adjusted R

square (left)
and the t

statistics
(right)
.
Figure 8: Selected Input Variables (left) and the corresponding t

test statistics (right)
Rey and Olga: Please note:
(1)
The variables selected are: ____________________
__________________________
[
Rey and Olga, please fill this, and give some discussion about these variables.
]
6. CONCLUSION
This article presents a data min
ing
project strategy and proposes a modified neural
network techniqu
e, a
structur
al
neural netwo
rk. The strategy and modeling technique are applied
to model the network of loyalty and profit chain for a chemical company.
The project
m
anagement model
and strategy
described in this article ha
ve
been successfully applied
to
various projects
in our research center
, including chemical industry, automotive
industry,
information technology industry, health care
industry
,
pharmaceutical indust
ry and others.
This article discusses how
t
he
SNN
architecture is built to
mimics the theoretical
framework that describes the cause

and

effect relationships
between the constructs of
performance, satisfaction, loyalty and profit
chain.
The SNN technique takes into account the
17
potential nonlinear and asymmetric relationships that can not be handled using the traditional
SEM and PLS modeling techn
iques. If the relationship is nonlinear and asymmetric, then, the
SNN model is shown that it performs better than others.
The results of this loyalty

profit
modeling project seem to suggest that the SNN technique performs better than the traditional NN
mo
del and somewhat better than the regression models.
This insight is important in several
aspects for the chemical industry:
(1)
The small advantage of SNN model against the simpler regression model suggests that the
nonlinear and
asymmetric
relationships
between constructs of the loyalty

profit chain may
be a
s strong as originally expected
.
(2)
N
eural network technique
is mainly for prediction purpose.
Understanding that the cause

and

effect relationships are less nonlinear
suggests that one can take
a
two stage modeling
strategy: first apply
the more traditional response surface modeling methodology to search
for the key drivers of
between constructs
and to understand the global trend of the
relationship,
and then, apply the SNN technique to
fine turn t
he prediction of
profit
to
obtain more localized profit prediction that
may be more useful
decision making in
different divisions
within
the company
.
(3)
Literature also showed that the relationship
s
between constructs
var
y
in different
industries
.
For
instance,
t
he study by
Goodman and associates (1995)
for
estimat
ing
the importance of
attributes of the U.S. postal service
indicated that linear relationship
between attributes
of
the postal servi
ce and overall satisfaction
is adequate.
However, this does
not mean that one
should
restrict to apply
ing
only linear techniques for modeling
the loyalty

profit chain. In
stead, it is important to apply a more general modeling technique that is robust to
assumptions and capable of handling large and messy data str
ucture.
The traditional NN model is an empirical modeling technique.
In general, the underlying
th
eoretical framework is not taken into consideration.
Instead, t
h
e
trad
itional NN
model
attempts
to allow the data to speak for itself. The failure of th
e traditional NN
model sends an important
message that when applying the ‘black box’ neural network modeling, it is essential to take into
account the context
ual and theoreti
cal
knowledge. For the loyal
ty

profit
modeling case, it is clear
that the theoretical framework provides a great deal of insight about the cause

and

effect
relationships among the latent variables and input data and the targets. Structur
al
neural netwo
rk
18
techniques should be considered for any predictive modeling problems when the context
ual and
theoretical
knowledge is available to assist
in
the designing the structure
.
Th
is technique is
applicable to other modeling problems where frameworks are well defined.
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ACKNOWLEDGEMENTS
This project was conducted at the Center for Applied Research & Technology Central Michigan
University Research Cooperation (CMURC) at Central Michigan University. The fin
ancial
support came from the Dow Chemical Company. The authors are grateful for the support of both
CMURC and the Dow Chemical Company.
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