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 & Technology,
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 the 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. The article first presents a project model and strategy and discuss how it
is applied to this case study. In order to model the complex network of the potentially nonlinear
and asymmetric cause-and-effect relationships, a modified neural network technique, structural
neural network is developed. Detailed 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 modeling process 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 performance portion of the performance-satisfaction-loyalty chain (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;
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Gustafsson and Johnson, 2004). . The second stage took the conceptual loyalty construct from
stage one as the basic network and used customer attitudinal 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 loyalty 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
construct 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 confirmed that
customer satisfaction, customer loyalty and retention are related to key measures 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 loyal 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 ). Reichheld and Sasser (1990) identified numerous bottom line
benefits of customer retention due to loyal and satisfied customers including willing to purchase
more, paying higher prices, easier to service (thus reducing operating costs), and helping 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 customers? 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; Mittal, 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) argue that newly acquired and loyal customers should be
2
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. Failure to
consider segment-specific differences may lead a firm to optimize performance on the wrong
attribute for a given segment (Anderson and Mittal 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 two 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
plan 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 section six.
2. THE NETWORK OF 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 three 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 discussion 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.,
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Gustafsson and Johnson, 2000), customer perceptions of product and service attributes (technical
support, 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 intentions (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 loyalty 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.
Structural 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) compared multiple regression, partial least
4
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 strengths of these traditional techniques include (1)
parameter/weight estimates are more easily interpreted, (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)
inability to model higher order interactions effectively, (3) requirement of distribution
assumptions such as normality, and (4) inability to effectively model large amounts of messy
data..
Anderson 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 often 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 at other 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 preceding one-unit increase. Asymmetric link 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 reported 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).
Marketing 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 hypothesis
5
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 involving large amounts of nonnormal, 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. Appropriate 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 and
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) applied 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 relationships 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 structural
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 apply 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 approximator
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(Riply, 1996) for any type of function. However, since the weight 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 system, 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 integration 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 Figure 2.
Figure 2: Project Model for Conducting Data Mining Project
Client
•Link to Business Strategy
•Data Knowledge
•Provide Corporate Data
•Prioritize Need
•Establish Requirements
•Interpret Results
•Monitor Results
•Identify Actionable Events
Research
Discipline
PROJECT •
•
Center & IT
Expertise
TEAM
•Tools & IT Skills
•Project Management
•Summarize and Analyze
•
Identify data to extract
•External Data
•Quality Control
•
Create Models
•Integrate Data
•Discover and Explore
•Security & Confidentiality
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 consists 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
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summarizes 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 business problem
4. Prepare data for modeling
7. Deploy model and results
2. Build data mining database
5. Build model
8. Take action
3. Explore data
6. Evaluate model
9. Measure the results
3.2 Data Sources and Data Preparation
In order to build a predictive 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,
revenue 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 cross-sectional data
structure. Table 2 summarizes the data sources and brief characteristics of the data.
Table 2: Data Sources for the Loyalty-Profit Predictive Model
Data Source
Customer Satisfaction
and Loyalty
Market Orientation
Employee Satisfaction
Customer Complaints
Account Sales/Volume
Price
Profit
Characteristics
• Cross sectional, Conducted in different sectors in different time period (a total of 40+
survey studies)
• 100+ variables, 20,000+ observations (by individual within a business customer)
• Cross sectional
• 20+ variables, 300+ observations (business sector in Company A)
• Multiple time frames
• 20+ variables, 30,000+ observations (business sector in Company A)
• Quarterly Over time
• 30 variables, 180,000+ observations (customer level)
• Quarterly Over time
• 40+ of variables, 100,000+ observations (account level)
• Quarterly over time
• 30+ variables, 1,400,000+ observations (customer level)
 Quarterly Over time
• 25+ of variables, 300,000+ observations (customer level)
The quarterly data were collapsed 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
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adjusted 2001 Economic Profit (A_EP01), 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 over 80% of the project time was spent on the
data preparation. Table 3 summarizes the inputs for each latent variable shown in the loyaltyprofit 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
Availability
Technical Support
4 (Survey)
5 (Survey)
4 (Survey)
Product Quality
Customer Service
Perceived Value
2 (Survey)
4 (Survey, Complaint data)
2 (Survey)
Ease of Doing Business
Customer Characteristics
7 (Survey)
3 (Survey, Internal data)
Commercial Relation
Customer Satisfaction
6 (Survey, Internal data)
4 (Survey)
Image
Business Competition
6 (Survey)
3 (Internal data
Purchase Intent
Retention, Attrition
2 (Survey)
8 (Internal data)
Purchase Behavior
Price Index
1 (Internal data)
1 (Internal data)
Volume Index
1 (Internal data)
These inputs were determined 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 are 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 99th percentile
were considered outliers. These variables are adjusted by the 99th percentile defined as:
A _ VNAMEi  VNAMEi / VNAME _ P99 . Where VNAMEi is the variable name with the original
scale for the ith account, and VNAME_P99 is the 99th percentile of the 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:
S _ NAME  NAME /( Max  Min) . This transformation eliminates the effect of the different
scales of the original data, and retains the variation structure of individual input.
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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 different surveys from both business customers and internal
employees in different 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
preparation 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 were 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 at different quarter des not mean there was no price nor 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
15
15
10
10
5
5
0
0
0
2
4
6
8
10
12
14
16
0
2
4
6
8
10
12
14
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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 product, 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. It was decided to take loyalty-specific
segmentation approach by segmenting 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
segmentation strategy is necessary and was also recommended in the marketing literature (e.g.,
Anderson and Mittal, 2000).
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4. MODELING STRATEGY FOR BUILDING A STRUCTURAL NEURAL NETWORK
4.1: A Brief Overview of a Neural Network Model
A neural network (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 the
H i.  g  Z ' X i. ' , i  1,2,
inputs:
,N ,
where g is the activation function and Z is the weight matrix of
the inputs. Additional layers can be derived using H i. as inputs to create two or more hidden
layers. Commonly used activation functions are: Hyperbolic tangent:
tanh a   e a  e  a   e a  e  a  ,
Logistic function: 1 1  e  , Arctangent function:  2   tan  a  and Elliott function: a 1  a  . The
1
a
target
Yi .
where
f
is modeled as the function of the linear combination of
H i.
defined as
Yi.  f W ' H i. '  
is the activation function connecting hidden layers with the targets. The function
,
f
can
be taken the same as g 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 problem of different units and magnitudes among the variables. The
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 weight matrices
Z
and
W
minimize certain objective functions, which are defined as the
functions of the difference between the observed values
Y
and predicted values
Ŷ
. 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 the Loyalty-Profit Chain
The following strategy is applied to build a structural 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 variable 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
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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 third hidden layer, “Satisfaction”.
(2) Determination of the number of neurons 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 Figure (Figure 4) is an example of traditional NN and a Structural Model
Figure 4: Traditional NN model and SNN Model
Traditional NN Model
Input
H1
Structural NN Model
Input
H2
H1
H2
Target
Target
Input
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
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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_EP01) 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
loyalty-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 ASSESSMENT
The modeling strategy and evaluation are the steps 5, 6, and 7 shown in our data mining
project strategy in Table 1. The following 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 values. This is done using the neural network options in the SAS/EM.
(b) Control over fitting: A simple 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:
ASE = SUM(yi – yi(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(yi – yi(Pred))2/(n-p), where p is total number of estimated weights.
 SSE 
SBC  n ln 
  p ln  n 
 n 
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(d) Dummy Variable Handling: For nominal input, deviation coding is used. For ordinal input,
bathtub coding is used. For each case in the ith category, the jth dummy variable is set to
1.5C /(C 2  1)
for i >j, or otherwise to
 1.5C /(C 2  1)
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
multiple neurons per node, where the number of neurons are determined using Principle
Component Analysis.
5. RESULTS AND DISCUSSION
Using 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 135th 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
Model
Traditional NN
(3 nodes)
Regression (with twoway interactions)
Structural NN
Degrees of
Freedom
Root ASE
(Training)
Root ASE
(Validation)
Schwarz Bayesian
Criterion
0.2394
0.2412
-1159.6
0.1877
0.1928
-2768.3
0.1719
0.1719
-2614.9
Adjusted
R-Square
0.86
[Olga and Rey, please revise this table if the numbers 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
14
numbers I took are the correct ones.
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 normalized. 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%.
Figure 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
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The stepwise 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 gives the selected 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 mining project strategy and proposes a modified neural
network technique, a structural neural network. The strategy and modeling technique are applied
to model the network of loyalty and profit chain for a chemical company. The project
management model and strategy described in this article have been successfully applied to
various projects in our research center, including chemical industry, automotive industry,
information technology industry, health care industry, pharmaceutical industry and others.
This article discusses how the 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
16
potential nonlinear and asymmetric relationships that can not be handled using the traditional
SEM and PLS modeling techniques. 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
model 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 as strong as originally expected.
(2)
Neural network technique is mainly for prediction purpose. Understanding that the causeand-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 the 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 relationships between constructs vary in different industries.
For instance, the study by Goodman and associates (1995) for estimating the importance of
attributes of the U.S. postal service indicated that linear relationship between attributes of
the postal service and overall satisfaction is adequate. However, this does not mean that one
should restrict to applying 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 structure.
The traditional NN model is an empirical modeling technique. In general, the underlying
theoretical framework is not taken into consideration. Instead, the traditional NN model attempts
to allow the data to speak for itself. The failure of the traditional NN model sends an important
message that when applying the ‘black box’ neural network modeling, it is essential to take into
account the contextual and theoretical knowledge. For the loyalty-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. Structural neural network
17
techniques should be considered for any predictive modeling problems when the contextual and
theoretical knowledge is available to assist in the designing the structure. This 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 financial
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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