Download A CUSTOMER-PREFERENCE UNCERTAINTY MODEL FOR DECISION-ANALYTIC CONCEPT SELECTION

Proceedings of the 4th Annual ISC Research Symposium
ISCRS 2010
April 21, 2010, Rolla, Missouri
A CUSTOMER-PREFERENCE UNCERTAINTY MODEL FOR DECISION-ANALYTIC
CONCEPT SELECTION
ABSTRACT
Analysis of customer preferences is one of the most important
tasks in new product development. How customers come to
appreciate and decide to purchase a new product impacts
market share and, therefore, the success of the new product.
Unfortunately, when designers select a product concept early in
the product development process, the market share of the new
product is unknown. Conjoint analysis is a statistical
methodology that has been used to estimate the market share of
a product concept from customer survey data. Although
conjoint analysis has been increasingly incorporated in design
engineering as a tool to estimate market share of a new product
design, it has not been fully employed to model market share
uncertainty. This paper presents two approaches, which use
conjoint analysis data to model market share uncertainty:
bootstrap and binomial inference. Demonstration and
comparison of the two approaches are presented using an
illustrative example.
1. INTRODUCTION
In product development, engineers select a product concept
before they develop detailed designs and prototypes [1]. At the
time of concept selection therefore, future market size, market
share, competition, warranty cost, and product cost are
uncertain. Uncertainties directly relevant to concept selection
are modeled. These uncertainties include market share,
warranty cost, and product cost. The present research addresses
market share uncertainty modeling as a means to select a
concept with the maximum expected utility of profit.
Conjoint Analysis (CA), a method to measure consumer
judgments, has been used in a variety of applications and has
received considerable attention since the early 1970s. This
method has most often been applied in the fields of applied
psychology, decision theory, and economics [2]. Robinson [3]
reports a multinational conjoint study of North Atlantic air
travel involving airfare, discounts and travel restrictions. This
study indicates that CA can accurately predict market shares.
Benbenisty [4] published a conjoint study involving AT&T’s
entry into the data terminal market. His simulator forecasted an
8% share for AT&T four years after launch and obtained an
actual share of just under 8%. These developments have been
discussed by Paul E. Green and V. Srinivasan [5]. Hildebrand
[6] has used CA for market definition, which is instrumental for
the assessment of market power and central to competition
policy. Currently however CA generates only one value for the
percentage of market share for a particular concept or concepts.
To overcome this limitation, the first approach, we
propose uses bootstrap [7], which is a sampling with a
replacement method that permits calculation of sample
statistics. Researchers have applied bootstrap to make statistical
inferences in clustering analysis and in phylogenetic trees [813]. Felsenstien [8] and Efron et al. [9] incorporated k-by-p
data matrix consisting of k species and p sites. They generated
bootstrapped samples of data matrices by sampling columns
with replacement.
By applying bootstrap to the results obtained from CA, a
continuous distribution is obtained, which improves results.
Furthermore, the continuous distribution can be discretized to
obtain probabilities by using the Extended Pearson-Tukey
method [14].
The second approach, which we propose as an
approximation to bootstrap, is binomial inference. Binomial
inference may be explained using a coin-flipping analogy [15].
In coin flipping, if we observe H heads and T tails in H+T flips,
an uncertainty of probability of head is modeled by a beta
distribution with parameter (H, T). Applying a similar analogy,
this work proposes that the uncertainty of market share of a
concept selected by M customers out of N total customers is
modeled by a beta (M, N–M) distribution.
This paper is organized as follows: Section 2 briefly
describes conjoint analysis, bootstrap, and a framework to
model market share uncertainty by integrating the two. Section
3 demonstrates and compares the proposed two approaches
(bootstrap and binomial inference) in an illustrative example.
Section 4 concludes the paper with a discussion of future work.
2. METHODOLOGY
2.1. Conjoint analysis
Conjoint analysis for estimating the market share of a new
product concept involves the following steps:
1
Copyright © 2010 by ISC
Concept definition: Identify product attributes and their
levels that are important for customers to make purchasing
decisions. Define new product concepts and competitors’
products as combinations of attributes and their levels. Product
attributes may be identified by interviewing customers and
translating the customer needs into product attributes.
Attribute level identification: Benchmark existing products
in the marketplace or forecast future customer needs for a new
product to identify attribute levels included in conjoint analysis
survey.
Conjoint survey design: Determine which conjoint method
will be used. That is, select the respondents’ concept evaluation
method (rating/ranking or choice), completeness of profile to be
used to describe concepts (full or partial profile), and decide
whether or not to use a Bayesian approach (Hierarchical Bayes
or non-Hierarchical Bayes). Create concept profiles to be
displayed to respondents according to the chosen method.
Market share estimation: Estimate the market share of the
concepts by analyzing respondents’ concept evaluation results.
2.2. Bootstrap
Bootstrap is a computer-based sampling-with-replacement
method that has been used to obtain a confidence interval of an
estimate as illustrated using a simple example in Fig. 1.
Suppose we wish to estimate a population average from a
randomly sampled data set {1, 2, 3, 4, 5, 6, 7}. We calculate a
sample average 4 and use this as an estimate of population
average. Because this is a point estimate of population average,
no confidence interval of this estimate can be obtained from the
initial data set alone; bootstrap samples of the same data size
must be generated by sampling with replacements from the
initial data set to obtain confidence intervals. For example, the
first bootstrap sample may be {5, 1, 7, 1, 2, 4, 4}, the second
Sample statistics
Data
(average)
Sampling with
replacements Initial sample : { 1 , 2 , 3 , 4 , 5 , 6 , 7 } →
4
Inference
(95% confidence interval)
Bootstrap samples
1 st
: { 5,1,7,1,2,4,4 } →
3.4
2 nd
: { 6,4,2,5,7,3,6 } →
4.7
3 rd
: { 2,3,5,2,1,1,1 } →
2.1
200 th
: { 4,6,4,7,3,4,2 } →
4.3
Distribution
1
4
7
bootstrap sample may be {6, 4, 2, 5, 7, 3, 6}, and so forth.
Fig. 1 Bootstrap procedure
In the bootstrap samples, the same data may appear more
than once or do not appear at all due to the sampling-withreplacement procedure. Each of these bootstrap samples
provides a sample statistic (i.e., average). If 200 bootstrap
samples are generated, 200 sample averages will be created.
These sample averages permit a construction of a confidence
interval or a distribution of sample statistics. For example, the
5th percentile and the 95th percentile of these bootstrap
averages provide a range of 95% confidence interval of the
point estimate 4, and a histogram of bootstrap sample averages
provides distribution of sample statistics, as illustrated in Fig. 1.
2.2. Bootstrap application to conjoint analysis
In conjoint analysis, respondents are randomly selected
from populations of customers as illustrated in Fig. 2.
Although conjoint analysis yields a concept’s true market share
if it is applied to the entire population of customers, surveying
the entire population is not feasible. By asking randomly
selected customers to evaluate product concepts and
competitors’ products, a point estimate of the market share of a
concept is obtained, as illustrated by the middle flow from left
to right in Fig. 2. Using a point estimate for the analysis is
equivalent to assigning a probability of one to the point
estimate.
Population
Customer {1, 2, 3, …, N}
Conjoint analysis
Probability
1
"True" market share, S True
0.5
Random
sampling
Sample
Customer {1, 2, 3, …, n}
STrue
Probability
Conjoint analysis
Point estimate of market share, s Estimate
Bootstrap
{ 1st sample}
Conjoint analysis
{ 2nd sample}
Market share, s 2
{ B-th sample}
Market share, s B
Market share, s 1
50%
Market
100% share
1
0.5
s Estimate 50%
Probability
Market
100% share
1
0.5
50%
Market
100% share
Figure 2 Application of bootstrap to conjoint analysis
In contrast, if bootstrap is applied to conjoint analysis,
bootstrap samples are generated from an initial set of randomly
sampled customers, as illustrated in the bottom flow in Fig. 2.
In the bootstrapped samples, a customer may appear more than
once or may not appear at all because of the sampling-withreplacement procedure. By applying conjoint analysis to the
bootstrap samples, market share estimates are obtained from
which a distribution of market share can be constructed as
illustrated in Fig. 2.
3. Illustrative example
This section illustrates and compares two market share
uncertainty modeling approaches: the application of bootstrap
and binomial inference to conjoint analysis. This example
presents non-Bayesian full-profile conjoint analysis with
customers’ evaluations in rating scales using automobile
concept selection as an illustrative example; however, both
approaches can be applied to any conjoint analysis approach.
3.1.Concepts and competition
For an illustrative purpose, this example assumes that a
firm wishes to estimate the future market share of a new
automobile (N) that will compete with two competitor vehicles
(C1 and C2). The concept of a new automobile is defined by its
type and fuel efficiency. Type refers to its form and the
maximum number of passengers that it can accommodate, and
2
Copyright © 2010 by ISC
fuel efficiency is associated by an engine type (a gasoline
engine or a hybrid engine). Furthermore, the firm selects a
basic warranty and a price both of which influence market
share.
The firm selects a sport utility vehicle (SUV) as a type of
the concept, 25 miles per gallon as a fuel efficiency, 5/60,000
(years/miles) as a basic warranty, and $35,000 as a price as
summarized in Fig. 3.
Concept
Warranty
Type
SUV
Fuel Efficiency
25
5 / 60,000
8 passengers
passengers
(miles/gallon)
(years/miles)
warranties are selected for the conjoint analysis study: 3/36000,
4/50000, and 5/60000 years/miles.
Warranty
SUV
Convertible
Sedan
3/36,000
58
13
28
4/50,000
20
14
21
5/60,000
8
2
6
4/60,000
1
0
2
(Years/Miles)
Price
Table 2 Basic Warranty Frequency
N
$ 35,000
Figure 3 Selected combination of concept, warranty, and price
Finally, Table 3 shows the minimum, average, median, and
maximum price of the benchmarked vehicles. Based on the
benchmarking results, three price levels are selected for the
conjoint analysis study: $20,000, $35,000, and $50,000.
Figure 4 summarizes the features of the two competitor
vehicles. The first competitor car (C1) is a convertible that gets
10 miles per gallon (gasoline engine). It has a basic warranty
of 3 years/36,000 miles and a price of $20,000. The second
competitor car (C2) is a sedan that gets 40 miles per gallon
(hybrid engine). It has a basic warranty of 4 years/50,000 miles
and a price of $50,000.
Type
Convertible
Fuel Efficiency
Non-hybrid
Warranty
Price
10
3 / 36,000
$20,000
C1
2 passengers
(miles per gallon) (years/miles)
Hybrid
Sedan
C2
40
5 passengers
4 / 50,000
$50,000
(miles per gallon) (years/miles)
Figure 4 Competitor cars C1 and C2
3.2.Market share point estimate
To estimate market share by applying non-Bayesian fullprofile conjoint analysis with customer evaluations in rating
scales, the firm first identifies possible levels of fuel efficiency,
warranty, and price to be analyzed in conjoint analysis. Based
on the automobiles introduced to the market between 2003 and
2009 (87 SUVs, 29 convertibles, and 57 sedans), fuel
efficiency, warranty, and price are benchmarked as summarized
in Tables 1 through 3. Table 1 shows the minimum, average,
median, and the maximum fuel efficiency of the benchmarked
vehicles. Based on the benchmarking results, three levels of
fuel efficiency are selected for the conjoint analysis study: 10,
25, and 40 miles per gallon.
SUV
Convertible
Sedan
Min
13
17
17
Average
17
23
22
Median
17
22
21
Max
24
33
44
Table 1 Fuel Efficiency (Miles per Gallon)
Table 2 summarizes the frequency of basic warranties
offered for the benchmark vehicles.
Based on the
benchmarking results, the three most widely offered basic
SUV
Convertible
Sedan
Min
20,972
17,365
20,342
Average
36,900
41,579
36,798
Median
36,105
35,513
28,045
Max
67,820
105,855
90,200
Table 3 Price ($)
To estimate market share, the firm must identify
81(=3×3×3×3) part worths of three levels of four attributes
(type, fuel efficiency, warranty, and price) for each respondent.
Based on the part worths, the firm predicts each respondent’s
utilities of the concept (as well as warranty and price) in Fig. 3
and two competing vehicles in Fig. 4. By comparing the utility
of the concept (and warranty and price) against utilities of
competing vehicles, the firm can predict which of the concept
and competitors’ vehicles each respondent will choose. From
the predictions of respondents’ choices, the firm estimates the
market share of a concept as well as that of each competitor
vehicle.
Part worths can be identified by asking respondents to rate
a total of 81(=3×3×3×3) combinations of attribute levels and
analyze the rating results by, for example, ordinary least square
regression analysis. However, evaluations of 81 alternatives
may impose a significant burden on respondents. To reduce
that burden, the firm may use an L9 orthogonal array so that
respondents evaluate only the nine combinations.
From 10 respondents’ evaluations of these nine
combinations using a 9-point rating scale (with 1 being the least
preferred and 9 being the most preferred), the firm can obtain
the respondents’ part worths. Figure 5 shows the part worth of
a respondent.
This individual prefers an SUV over a
convertible or sedan, as indicated by its part worth (1.3), which
is larger than that of the convertible (–2.3) or the sedan (1.0).
Similarly, the highest fuel efficiency of 40 miles/gallon, the
best warranty of 5 years/60,000 miles, and the lowest price of
$20,000 are the preferred levels, with the highest part worth
within each attribute.
The part worths in Fig. 5 are added to obtain the utilities of
concept N in Fig. 3 and the two competitor vehicles C1 and C2
3
Copyright © 2010 by ISC
in Fig. 4. For example, the utility of C1 (a convertible with a
fuel efficiency of 10 miles/gallon, a warranty of 3 years/36,000
miles, and a price of $20,000) is calculated by adding the part
worths of a convertible vehicle type, a fuel efficiency of 10
miles/gallon, a 3 years/36,000 miles warranty, a price of
$20,000, and the intercept: – 2.3 – 1.0 – 0.7 + 2.3 + 4.7 = 3.
Part Worth
3
1.3
1.0
0
-2.3
-3
Convertible
SUV
Type
Sedan
3
Part Worth
1
0
0
-1
10
25
40
Fuel Efficiency (Miles per Gallon)
Part Worth
3
-0.7
1st
2st
3rd
4th
5th
·
·
·
200th
bootstrap sample
bootstrap sample
bootstrap sample
bootstrap sample
bootstrap sample
=
=
=
=
=
{
{
{
{
{
R7
R1
R3
R8
R3
,
,
,
,
,
R10
R8
R10
R6
R4
,
,
,
,
,
R8
R7
R10
R10
R5
,
,
,
,
,
R10
R6
R9
R1
R10
,
,
,
,
,
R9
R2
R4
R8
R4
,
,
,
,
,
R6
R7
R5
R9
R3
,
,
,
,
,
R6
R5
R2
R8
R9
,
,
,
,
,
R9
R6
R3
R10
R10
,
,
,
,
,
R9
R8
R4
R10
R3
,
,
,
,
,
R6
R1
R2
R8
R7
}
}
}
}
}
bootstrap sample = { R5 , R1 , R9 , R9 , R2 , R4 , R1 , R10 , R4 , R5 }
Fig. 7 Bootstrap samples of respondents
-3
0
3.3. Market Share Uncertainty Modeling: Bootstrap
Bootstrap distributions of market share can be obtained by
applying bootstrap to the conjoint analysis data. Using the
original sample of 10 respondents (R1-R10), the samplingwith-replacement procedure is applied to generate 200
bootstrap samples. Each bootstrap sample consists of data from
10 respondents; however, each respondent may appear more
than once or may not appear at all as shown in Fig. 7.
0.7
0.0
By mapping respondents in 200 bootstrap samples to their
predicted choices, as illustrated in Fig. 8, the firm obtains 200
market share estimates for concept N and for the competitor
vehicles C1 and C2. From these market share estimates, the
firm constructs distributions of market share for its concept N
and for the competitor vehicles; as illustrated in Fig. 9.
-3
3/36,000
4/50,000
5/60,000
Warranty (Years/Miles)
Part Worth
3
Bootstrap samples
1st
2st
3rd
4th
5th
•
•
•
200th
2.3
0.7
0
-3.0
-3
20,000
35,000
Price ($)
50,000
=
=
=
=
=
{
{
{
{
{
C2
N
C1
C2
C1
,
,
,
,
,
C2
C2
C2
C2
C2
,
,
,
,
,
C2
C2
C2
C2
N
C2
C2
C2
N
C2
,
,
,
,
,
C2
N
C2
C2
C2
,
,
,
,
,
C2
C2
N
C2
C1
,
,
,
,
,
C2
N
N
C2
C2
,
,
,
,
,
C2
C2
C1
C2
C2
,
,
,
,
,
C2
C2
C2
C2
C1
,
,
,
,
,
C2
N
N
C2
C2
}
}
}
}
}
= { N , N , C2 , C2 , N , C2 , N , C2 , C2 , N }
Fig. 8 Predicted choices
Relative Frequency
Figure 5 Part worth example
Attribute levels
Fuel efficiency Warranty
Type
Price R1 R2
(miles/gallon) (years/miles)
N
SUV
25
5/60,000 $35,000 7.3 7.3
C1 Convertible
10
3/36,000 $20,000 3.0 2.0
C2 Sedan
40
4/50,000 $50,000 3.7 6.3
,
,
,
,
,
Market share (%)
N
C1
C2
0
0
100
40
0
60
30
20
50
10
0
90
10
30
60
•
•
•
•
•
•
•
•
•
50
0
50
Utility
R3 R4 R5 R6 R7 R8 R9 R10
5.7 3.3 5.7 6.0 3.7 3.0 4.7 4.7
9.0 3.0 3.0 2.0 4.0 5.0 2.0 2.0
4.0 4.0 4.0 7.0 5.7 5.3 7.3 5.7
1
0.8
0.6
0.4
0.2
0
0 10 20 30 40 50 60 70 80 90100
Market Share (%)
Figure 6 Utilities of N, C1, and C2 for the ten respondents,
R1–R10
(a) N
Relative Frequency
After calculating utilities of N, C1, and C2 for each
respondent, the firm can estimate market share of the concept
N. Figure 6 summarizes the utilities of concept N and the
competitor vehicles C1 and C2 for all 10 respondents; the
largest utility of each respondent is highlighted. Respondents 1,
2, and 5 choose N because it has the highest utility of all three
alternatives. On the same basis, respondent 3 chooses C1 and
respondents 4, 6, 7, 8, 9, and 10 choose C2. Based on these
results, the firm would estimate the market shares of these three
alternatives to be 30% for N, 10% for C1, and 60% for C2.
1
0.8
0.6
0.4
0.2
0
0 10 20 30 40 50 60 70 80 90100
Market Share (%)
(b) C1
4
Copyright © 2010 by ISC
0.6
0.4
0.2
0
0 10 20 30 40 50 60 70 80 90100
Market Share (%)
(c) C2
Fig. 9 Market share distributions
3.4. Market share uncertainty modeling: binomial
inference
Based on the binomial inference, the market share
distributions of N, C1, and C2 may be approximated by
Beta(3,7), Beta(1,9), and Beta(6,4) distributions; as illustrated
in Fig. 11. The probability distribution shows in Fig. 10 (b) was
obtained by discretizing the cumulative distribution in Fig. 10
(a) into 11 brackets (i.e., [–0.05, 0.05], [0.05, 0.15], …, and
[0.95, 1.05]), calculating the probability of market share (m) in
each bracket, and assigning the probability to the middle value
of the bracket: For example, Pr(m=0.10)=Pr(m≤0.15) –
Pr(m≤0.05).
Cumulative probability
N: Beta(3,7)
C1: Beta(1,9)
3.5. Comparison of bootstrap and binomial inference
An important goal of decision analysis is the
approximation (or discretizations) of continuous distributions
by discrete probabilities. The extended Pearson-Tukey method
is a simple yet accurate three-point approximation in which a
continuous distribution is represented by the 5th percentile,
50th percentile (i.e., median), and 95th percentile of the
distribution, with probabilities of 0.185, 0.63, and 0.185
respectively. Figure 11 compares the distributions obtained
from bootstrap with those from binomial inference (i.e., beta
distributions). Table 4 compares statistics of the bootstrap and
beta distributions: three points (5th percentile, 50th percentile,
and 95th percentile), the means, and the standard deviations of
the discretized distributions. The differences of statistics (the
percentiles, means, and standard deviations) are small, and
differ only by a maximum of 3.4 percentage points.
Cumulative probability
Relative Frequency
1
0.8
C2: Beta(6,4)
1
0.8
N: Beta(3,7)
C1: Beta(1,9)
C2: Beta(6,4)
N: Bootstrap
C1: Bootstrap
C2: Bootstrap
1
0.8
0.6
0.4
0.2
0
0
0.6
0.2
0.4
0.6
0.8
1
Market share
0.4
Fig. 11 Cumulative distributions
0.2
0
0
0.2
0.4
0.6
0.8
1
Market share
(a)
N: Beta(3,7)
C1: Beta(1,9)
N
C1
C2
Beta Bootstrap Diff. Beta Bootstrap Diff. Beta Bootstrap Diff.
-0.002 0.006
0.006 0.345
0.045
5th percentile 0.098
0.1
0
0.3
-0.014 0.074
-0.026 0.607
0.007
50th percentile 0.286
0.3
0.1
0.6
-0.050 0.283
-0.017 0.831
-0.069
95th percentile 0.550
0.6
0.3
0.9
-0.018 0.10
-0.018 0.6
0
Mean
0.30
0.32
0.12
0.6
-0.015 0.09
-0.003 0.15
-0.034
St. dev.
0.14
0.15
0.09
0.18
C2: Beta(6,4)
Table 4 Statistics of discretized distributions
1
Table 5 compares distributions in Figure 11 using a chisquare goodness-of-fit test with a 5% confidence level.
According to the results of this test, the null hypothesis that two
distributions have a good fit cannot be rejected for all three
cases (N, C1, and C2); as shown by the p-values larger than
0.05 in Table 5.
Probability
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
p-value
Chi-square
test
Test statistic
1
Market share
N
0.27
3.92
C1
0.09
2.81
C2
0.18
6.23
Table 5 Comparison of distributions
(b)
Fig. 10 Binomial inference
5
Copyright © 2010 by ISC
7. CONCLUSION AND FUTURE WORK
Conjoint analysis is a statistical methodology that has been
increasingly incorporated in design engineering as a tool to
estimate the market share of a new product design; however,
the use of conjoint analysis data to model market share
uncertainty has not been fully explored in the past design
engineering research. This paper has presented two approaches
(bootstrap and binomial inference as an approximation of
bootstrap distribution) to model market share uncertainty using
conjoint analysis data obtained from non-Bayesian full-profile
conjoint analysis with customers’ evaluations in rating scales.
Once discretized using the extended Pearson-Tukey
method, the beta distributions (obtained from binomial
inference) were compared with the bootstrap distributions. The
results indicated that there are small differences in the statistics
(the 5th percentiles, 50th percentiles, 95th percentiles, means,
and standard deviations) of discretized distributions.
Furthermore, chi-square goodness-of-fit tests of beta
distributions and bootstrap distributions indicated that these
distributions have good fits. These results support the use of a
beta distribution, which is obtained from a binomial inference
of conjoint analysis data, as a means to approximate bootstrap
distribution; thus, to model market share uncertainty.
Continuation of this avenue of research, which is to support this
preliminary finding with a larger number of respondents, is
future work.
This paper used conjoint analysis data obtained from nonBayesian full-profile conjoint analysis with customers’
evaluations in rating scales. Market share uncertainty modeling
using data obtained from other conjoint analysis
methodologies, in particular, non-Bayesian and Bayesian
choice-based conjoint analysis, is a topic for future work.
The accuracies of a market share forecast depend on
competitors’ products simulated in the conjoint analysis.
Furthermore, the future actions of competitors in response to
firm’s new product influence the accuracy of market share
forecasts [16, 17]. Future work, therefore, should study the
integration of competition uncertainty modeling into market
share uncertainty modeling in conjoint analysis.
8. ACKNOWLEDGMENTS
We would like to thank the Intelligent Systems Center at
Missouri University of Science and Technology for supporting
this research.
9. REFERENCES
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Analysis in Consumer Research: Issues and Outlook”
Journal of Consumer Research, Vol. 5, pp. 103-120.
[3] Robinson, P. J. 1980, “Application of Conjoint Analysis to
Pricing Problems,”
in Proceedings of the First
ORSA/TIMS Special Interest Conference on Market
Measurement and Analysis, D. B. Montgomery and D. R.
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