Introduction to
Choice-Based Conjoint (CBC)
Copyright Sawtooth Software, Inc.
Conjoint Methods: Card-Sort Method (CVA)
Using a 100-pt scale where 0 means definitely
would NOT and 100 means definitely WOULD…
How likely are you to purchase…
Coke
6-pack
$1.89
Your Answer:___________
Conjoint Methods: Pairwise Method
(ACA or CVA)
Which would you prefer?
Coke
6-pack
$1.89
Strongly Prefer
Left
1 2 3 4
Pepsi
8-pack
$2.29
5
Strongly Prefer
Right
6 7 8 9
Choice-Based Conjoint Question
Comparing the Methods (cont.):
Traditional Card Sort:
– Respondent task is not as realistic as CBC
– Ranking or ratings typically provide enough information to
compute utilities (preferences) for each individual
– Usually only compute Main Effects (no interactions)
Comparing the Methods (cont.):
Pairwise Presentation:
– Respondent task is often not as realistic as CBC
– Ratings typically provide enough information to compute
utilities (preferences) for each individual
– Usually only compute Main Effects (no interactions)
Comparing the Methods (cont.):
Choice-Based Conjoint Pros:
– Making choices in CBC questions is similar to what
buyers do in the marketplace
– CBC can include a “None” option, so respondents who
have no interest in purchasing can opt out of the
question
– Because we can analyze results by pooling respondent
data, CBC permits measurement of Main Effects AND
Interactions. More overall parameters can be estimated.
Comparing the Methods (cont.):
Choice-Based Conjoint Pros (cont.):
– Because we can pool respondent data, each respondent can
answer as few as just 1 question
– Respondents can answer at least up to 20 choice questions
with high reliability
– Randomized designs permit showing respondents all
combinations of levels and are quite efficient
– Particularly well suited to pricing studies
Comparing the Methods (cont.):
Choice-Based Conjoint Cons:
– Choices are inefficient: they indicate only which
product is preferred, but not by how much
– Aggregate models assume respondent homogeneity,
which may be inaccurate representation for a market
(but Latent Class analysis and new developments in
Bayesian estimation techniques help resolve this issue)
– Usually requires larger sample sizes than with CVA or
ACA
Comparing the Methods (cont.):
Choice-Based Conjoint Cons (cont.):
– Tasks are more complex, so respondents can process
fewer attributes (early academics recommended six or
fewer, but in practice it seems respondents can evaluate
a few more than that if the text is concise and the tasks
are laid out well)
– Complex tasks may encourage response simplification
strategies
Comparing the Methods (cont.):
Analyzing the Data:
– ACA: Ordinary Least Squares regression (OLS) or
Hierarchical Bayes (HB)
– CVA: OLS (ratings), Monotone regression (rankings) or
Hierarchical Bayes (HB)
– CBC: Counting analysis, Multinomial Logit, Latent Class,
or Hierarchical Bayes (HB)
– Adaptive CBC (ACBC): Hierarchical Bayes (HB),
Monotone regression
Main Effects Versus Interactions
Main Effects:
- Isolating the effect (impact) of each attribute, holding
everything else constant
Assume two attributes:
– BRAND: Coke, Pepsi, Store Brand
– PRICE: $1.50, $2.00, $2.50
Main Effects Versus Interactions (cont.):
Hypothetical Main Effects Utilities:
Levels
Utilities
Coke
50
Pepsi
30
Store Brand
10
$1.50
80
$2.00
40
$2.50
10
Interpretation: Across all brands
(holding brand constant), $1.50 is
worth 80 points, etc.
Main Effects Versus Interactions (cont.):
$1.50
$2.00
$2.50
Coke
50 + 80 = 130
50 + 40 = 90
50 + 10 = 60
Pepsi
30 + 80 = 110
30 + 40 = 70
30 + 10 = 40
Store Brand
10 + 80 = 90
10 + 40 = 50
10 + 10 = 20
We can add the main effect utilities together and infer the
preference for each brand at each price. But this assumes the same
price function for each brand.
Main Effects Versus Interactions (cont.):
Utility
Main Effect Price x Brand Curves
140
120
100
80
60
40
20
0
$1.50
Coke
Pepsi
Store Brand
$2.00
$2.50
Price
This may not be an accurate representation of how price changes
affect preference for each brand. Perhaps price changes have a
different impact depending on the brand. That would imply an
interaction.
Main Effects Versus Interactions (cont.):
$1.50
$2.00
$2.50
Coke
.58
.50
.41
Pepsi
.46
.32
.23
Store Brand
.31
.10
.02
CBC counts the percent of times each brand/price combination
is chosen. Each cell in the grid above is directly and
independently measured (two-way interaction).
Main Effects Versus Interactions (cont.):
Choice Probability
CBC Brand x Price Interaction
70%
60%
50%
40%
30%
20%
10%
0%
$1.50
Coke
Pepsi
Store Brand
$2.00
$2.50
Price
The Store Brand is more price sensitive to changes in price
compared to Coke and Pepsi. Coke buyers are most loyal in the
face of price changes.
Main Effects Versus Interactions (cont.):
There are many other kinds of interactions besides Brand x
Price:
Interaction: Cars and Colors
Choice Probability
70%
60%
50%
Lincoln
Continental
40%
Mazda Miata
30%
Honda Accord
20%
10%
0%
Black
Red
Color
Blue
Preference for
color depends
upon the car
Sawtooth Software’s CBC Systems
• Windows- or Web-based computer-administered interviews or
paper surveys
• Capacity: 30 attributes with up to 250 levels each (with Advanced
Design Module)
• Experimental design produced automatically
• Prohibitions between attribute levels can be specified
• Fixed designs can be specified
• Choice sets can include a “none” or “constant” option
• Data analyzed automatically by counting or multinomial logit,
optional modules for Latent Class and HB
• Market simulator included
The CBC System: Advanced Modules
• Paper and Pencil Module
– Assists in creating and analyzing data for paper and pencil
interviews
• Latent Class Segmentation Module
– Detects and models market segments
– Helps relax the assumption of homogeneity, but still does not
achieve individual-level data
– Permits specification of linear terms, and respondent
weighting
• Hierarchical Bayes Analysis CBC/HB
Advanced Design Module
• Advanced Design Module:
– Support “brand-specific attribute” designs and estimation (some
researchers refer to these as “true” discrete choice designs)
– More than one “Constant Alternative” (None) option
– Expanded number of attributes to accommodate brand-specific
attribute designs (up to 30 attributes)
– Ability to conduct/analyze partial-profile experiments
Why Latent Class and HB?
• To reduce the Red Bus/Blue Bus (IIA) Problem, one must account
for:
– Substitution effects
– Differential cross-elasticities
– Differential self-elasticities
Aggregate Logit
• Assume an aggregate logit solution where:
– Utility (Train) = Utility (Red Bus)
On any given day, difficult to predict which way any one
respondent will travel to work.
Resulting in the following aggregate shares:
– Train  50%; Red Bus  50%
Aggregate Logit:
• Assume we add another alternative where:
– Utility (Train) = Utility (Red Bus) = Utility (Blue Bus)
Again, difficult to predict which way any one respondent
will travel to work.
• Train  33.3%; Red Bus  33.3%; Blue Bus 
33.3%
• Net Bus ridership increased from 50% to 66.7% by
offering a bus of a different color
Two-Group Latent Class Solution:
• Left Half of Room
– Strongly Prefer Buses
• Right Half of Room
– Strongly Prefer Trains
In aggregate, it still appears that Utility (Bus) = Utility (Train)
Two-Group Latent Class Simulation:
• Now offer both Red and Blue buses
• Net Bus ridership still 50% (no Share Inflation)
Capturing heterogeneity has resulted in differential
substitution effects
Differential Cross-Elasticity under Latent
Class
• Now raise price of Blue Bus
– Many Blue Bus riders shift to Red Buses
– Train ridership unaffected
Capturing heterogeneity has revealed differential
cross-elasticity
Differential Elasticity under Latent Class
• Assume:
– Train riders = Not price sensitive
– Bus riders = Very price sensitive
Differential Elasticity under Latent Class
• If raise Train price
– Few train riders shift to buses
• If raise Red and Blue bus prices
– Many bus riders shift to trains
Capturing heterogeneity has captured
differential elasticities
Conclusions
• Capturing heterogeneity under Latent Class or HB
– Reduces Red Bus/Blue Bus problem
– Automatically accounts for differential substitution,
elasticities and cross effects with simple main-effects
models
• If those effects are due to differences in preferences
between people
Adaptive Extension of CBC
• In 2008, Sawtooth Software released an
adaptive form of CBC called ACBC. It is
quickly gaining acceptance.
• Shares the strengths of CBC, but provides a
more engaging respondent experience.
• Can extend CBC’s ability to study more
attributes and levels.