Conjoint Analysis

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Conjoint Analysis

• Dr. Milne

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Basic Problem

• Metric/non-metric input (preferences) converted
  to interval scaled output (utility)
• I like lobster more than catfish, which I like
  more than octopus. What does it mean to say that
  my liking for lobster over catfish is greater
  than my liking for salmon over tuna?
• An interval level scale for preferences is needed.

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Parting of ways

• Psychometrics rigorous and idealistic
• Marketing research approximate and pragmatic
• Conjoint is becoming very much removed from
  theoretical roots
• Numerical measurement of behavior
• Additive
• Compound stimuli
• Factorial designs
• Testing is rapidly ignored
• Moving from non-metric to metric
• Conjoint measurement vs. conjoint analysis

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Managerial Uses of Conjoint Analysis

• Find the product with the optimum set of features
• Determine the relative importance of each feature
  in consumer choices
• Estimate market share among products
• Identify market segments
• Evaluate the impact of price changes or other
  marketing mix decisions.

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A Simple Example

• Scenario a man buying a basic cartridge camera
  (faced with eight choices)
• Major brand 80
• Major brand 50
• Major brand 30
• Major brand 20
• Store brand 80
• Store brand 50
• Store brand 30
• Store brand 20

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Respondents Ranking of Eight Camera
Brands Price() Major Brand Store
Brand Average Rank 20 8 6 7.0 30 7 4 5.
5 50 5 2 3.5 80 3 1 2.0 Average
rank 5.75 3.25 Note, 8 is most preferred and
1 is least preferred
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Respondents Utility Values of Eight Camera
Brands Price() Major Brand Store Brand Average
Rank Utility 20 8 6 7.0 1.00 30 7 4 5.5 .7
0 50 5 2 3.5 .30 80 3 1 2.0 .00 Average
rank 5.75 3.25 Utility .75 .25
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Rank Order of Respondents Total
Utilities. Price() Major Brand Store
Brand Marginal Utility 20 8 (1.75) 6
(1.25) 1.00 30 7 (1.45) 4 (.95) .70 50 5
(1.05) 2 (.55) .30 80 3 (.75) 1
(.25) .00 Marginal Utility .75 .25
1.75 .75 (major brand utility) 1.00 (20
utility)
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Utility Values for Three Respondents Adam Bob
Carl Brand x .60 .80 .33 y .80 .35 .33 z
.40 .10 .33 Price () 20 1.00 .70 1.00 30
.80 .60 .80 50 .00 .20 .50 80 .00 .00
.00 Coupon Value() 2 .20 .20 .20 5 .75 .20
.30 10 .95 .60 .80
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Utility Values for Respondent Adam Brand (x) .60
(y) .80 (z) .40 Price (30) .80 (20) 1.00 (50)
.00 Coupon Value (2) .20 (2) .20 (2) .20 Tota
l Utility 1.60 2.00 .60
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Respondents Estimated Preferences for Three
Camera Brands Brand Price () Coupon Value
() Preferring X 40 5 50 Y 20 2 35 Z 80
10 15
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Effects of Change in Marketing Mix on
Respondents Preferences Preferring Each
Preferring Each Brand for Original Brand After
Xs Brand Situation Change in Price Change
() X 50 55 5 Y 35 35 0 Z 15 10 -5
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Conjoint Analysis

• Decompositional modelAn individuals overall
  preference or evaluation for a product (expressed
  as a combination of attributes) is decomposed by
  relating the know attributes to the evaluation.
• Best suited for understanding consumers
  reactions to and evaluations of predetermined
  attribute combinations that represent potential
  products or services.
• An applied method used in marketing research

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Which of the two flights described below would
you chose? A B-707 flown by New Zealand Air that
will depart within two hours of the time you
would like to leave and that is often late in
arriving in Sydney. The plane will make two
intermediate stops, and it is anticipated that it
will be 50 full. Flight attendants are warm
and friendly and you would have a choice of
multiple movies for entertainment. A B-747 flown
by Quantas that will depart within four hours of
the time you would like to leave and that is
almost never late in arriving in Sydney. The
flight is nonstop, and it is anticipated that the
plane will by 90 full. Flight attendants are
cold and curt and only magazines are provided
for entertainment.
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Compositional versus Decompositional Techniques
Compositional Y w1 X1 w2 W2 Collect x1
and x2 and relate it to Y.
Estimate weights to create a predictive
model Decompositional Y w1 X1 w2 W2
Collect Y and relate it to X1 and X2 which are
already fixed, and determine weights. Note
computationally similar, but design and
conceptually very distinct.
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Unique Features of Conjoint

• Specifiying the Conjoint Variate
• The only data provided by the subject is the
  dependent variable. The independent variable is
  prespecified.
• Separate Models for Each Individual
• A unique model is specified for each individual.
• Predictive accuracy is made for each individual.
• Not limited to linear relationships.

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Objectives

• To determine the contributions of predictor
  variables and their respective values to the
  determination of consumer preferences.
• To establish a valid model of consumer judgments
  useful in predicting the consumer acceptance of
  any combination of attributes, even those not
  originally evaluated by consumers.

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Questions to resolve

• Defining the total worth of the object
• Need to select attributes that accurately reflect
  judgment process.
• Need to include both potential positive and
  negative factors
• Specifying the determinant factors
• Attributes must also be selected so that they
  differentiate between the objects. These are the
  key to decision making.

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Research Problem Define Stimuli (factors and
levels) Basic model form Data collection Full
profile Trade off Pairwise Data Collection
(Create stimuli) Factorial design Fractional
factorial Select preference measure Form of
Survey Administration Assumptions Select
estimation technique Evaluate results Interpret
results Validate Apply results
Conjoint Analysis Decision Process This
technique requires a lot of upfront work to think
through the design, data collection, and analysis
options.
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Determining Factors and Selecting the Levels for
each Factor

• Actionable measures
• Communicable measures
• Number of attributes
• Balanced number of attributes
• Rate of attribute levels
• Attribute multicollinearity

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Specifying Model form

• Additive add up the values to each attribute
  (partworth) to obtain the overall worth of the
  model. This is the most common approach.
• Composition with interaction is possible the sum
  may be more or less than the wholebut not as
  common and the prediction is not as good.

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Part-worth
Selecting the Part-worth relationship
Preference
Level
Quadratic or idea
Linear
Preference
Preference
Level
Level
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Trade-off Approach
Factor 1 Price
1.19
1.39
1.49
1.69
Generic KX-19 Clean-all Tidy-UP
Factor 2 Brand Name
Pros Easy, simple, few cognitive
decisions Cons Sacrifice in only see a few
attributes at a time, large number of judgments,
easy to get confused and pattern response, cant
use pictoral or non written stimuli, only non
metric responses, cant use fractional factorial
designs.
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Full Profile Approach
Brand Name KX 19 Price 1.19 Form
Powder Color brightener Yes
Shows all attributes at once
Pros Better, more realistic, flexible scaling,
fewer judgments. Cons As the number of factors
increases so does the possibility of information
overload--can be overwhelming if have gt 6
attributes. The order in which the factors are
listed on the stimulus card may have an impact on
the evaluation.
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Paired Comparison
Brand Name KX-19 Price 1.19 Form Powder
Brand Name Generic Price 1.49 Form Liquid
VERSUS
A combination of approaches. Does not show all
the attributes. It is similar to trade-off in
that pairs are evaluated. But, like profile, the
judgments are made about combinations of
attributes. Approach used in adaptive conjoint
analysis.
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Creating Stimuli

• Factorial design 4 variables with 4 levels each
  would result in 256 stimuli. (4x4x4x4).
• Fractional factorial design selects a sample of
  stimuli (16 in this case). Can only be used for
  estimating the main effects. The stimuli are
  chosen for orthogonality.
• Designs are published.
• Software can be used.

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Two Fractional Factorial Designs Stimulus F1 F2 F3
F4 f1 f2 f3 f4 1 3 2 3 1 2 3 1 4 2 3 1 2 4 4 1 2
4 3 2 2 1 2 3 3 2 1 4 4 2 2 3 2 2 4 1 5 1 1 1 1 1
1 1 1 6 4 3 4 1 1 4 4 4 7 1 3 2 2 4 2 1 3 8 2 1 4
3 2 4 2 3 9 2 4 2 1 3 2 3 4 10 3 3 1 3 3 4 1 2 11
1 4 3 3 4 3 4 2 12 3 4 4 2 1 3 3 3 13 1 2 4 4 2 1
3 2 14 2 3 3 4 3 1 4 3 15 4 4 1 4 1 2 2 2 16 4 1 3
2 4 4 3 1 orgthogonal - no correlation among
levels across attributes and balanced each level
in a factors appears the same number of times.
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Selecting a measure of consumer preference
Trade-off uses only ranking data Full profile
uses both ranking and rating data Metric methods
are easily analyzed and easily administered even
by mail and allow conjoint estimation by multiple
regression. For ranking data have 11 point scales
for 16 or fewer stimuli and 21 point scale for
greater than 16 stimuli.
Survey Administration
Pencil and paper and computer based surveys.
Computer Disks. Web pages.
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Assumptions

• Very few statistical assumptions
• However, theory drives design, estimation, and
  interpretation.

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Estimation and Assessing Overall Fit

• Rank order calculated with MANANOVA or LINMAP
• Metric can be estimated with regression or
  special programs. The standardized betas are the
  part-worths.
• Preference b1 F1b2 F2 bn Fn
• Reliability can be estimated by correlating the
  predicted with the actual ratings for each
  individual.
• Corr (pref, Y hat.)

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Interpret Results

• Part worths are standardized Beta Weights so they
  can be compared.
• Relative importance of each factor should be
  calculated. Relative importance is the range of
  the partworths over the sum of the ranges across
  all factors.
• B1H-B1L /(B1H-B1L) (B2H-B2L)(BNH-BNL)

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Example Packaged Soup
Factors Levels Flavor Onion Chicken Veg
Calories 80 100 140 Salt
Free Yes No Price 1.89 2.49
Dependent Variable is preference (0-10) 3x3x2x2
36 possibilities in a full factorial
design Model can be estimated using dummy
variable regression where the estimated beta
weights are utility preferences
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Establish the Dummy Variables
D1 1 if onion, 0 otherwise D2 1 if chicken,
0 otherwise D3 1 if 80 calories, 0
otherwise D4 1 if 100 calories, 0
otherwise D5 1 if salt-free, 0 otherwise D6
1 if price 1.89, 0 otherwise Example Onion,
80 calorie, Saltfree soup for 1.19 would be
coded as ( 1 0 1 0 1 1)
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Run Regressions for Each Individual
Y B1 D1 B2 D2 B3 D3 B4 D4 B5 D5 B6 D6
? Card Pref Dummy Coding 1 8 1 0 0 1 1
0 2 6 0 1 1 0 1 0 3 3 1 1 1 0 0 0 . . .
. . . . . . . . . . . . . 36 5 0 1 1 1 1 1
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Check the fit for each regression for each
individual
Calculate Y for each individual Corr ( Y , Pref)
for each individual This is a measure of
internal consistency to see if there is a strong
relationship between the revealed preference and
the stated preference. Include individuals with
high correlations.
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Standardized Beta weights are the part worths
Attributes Part worth Flavor onion 3.50 Chicken
0 Vegetable 3.58 Calories 80 2.17 100 .67 14
0 0 Salt Free Yes 1.89 No 0 Price 1.19 .67 1
.49 0
Note the partworths can be rescaled relative to
each other. For example if onion -.08,
chicken -3.58 and Veg 0 adding 3.58 to each
changes the coding to make chicken 0. Utility
for an Alternative sum of the utilities
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Graphing Individual Part worths
Utility
Utility
Flavor
Calories
0
Chicken Onion Vegetable
80 100 140
Utility
Utility
Salt-Free
Price
No Yes
1.89 2.49
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Importance Weights
Attributes Range Percent Flavor 0
3.58 43 Calories 0 2.17 26 Salt 0
1.89 23 Price 0 - .67 8 Total 8.30 100
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Aggregate Analysis

• Estimate market share for existing attribute
  combinations in the market
• Simulate shifts in share with changes of existing
  product combinations (Brand A with a higher
  price).
• Estimate potential share that a new entrant might
  obtain (with unique set of attributes)
• Use the part worths to segment the market with
  Cluster analysis.