Conjoint Analysis
In conjoint analysis, researchers describe products or
services by sets of attribute values or levels and then
typically measure respondents' purchase interest. The
primary purpose of conjoint analysis is to model human
behaviour, usually purchase behaviour. By measuring
purchase interest in a “complete” product or service,
conjoint analysis captures the essential dilemma of
market choice: The perfect product is seldom available,
but lesser alternatives are. By forcing respondents to
trade off competing values and needs, conjoint analysis
uncovers purchase motivations respondents may be
unwilling to admit to and may not even realise they have.
1
Conjoint Analysis - Caution
A potential concern for any approach that
accommodates a large number of attributes is attribute
additivity. Seldom mentioned in the literature, attribute
additivity is the phenomenon where a large number of
less important attributes may overwhelm one or two
extremely important ones. For example, a feature-rich
product may have more total utility than a low-priced
one simply because all the small utility weights of the
various product features, when summed, exceed the
utility weight of the price attribute.
McCullough D., A User's Guide To Conjoint Analysis,
Marketing Research, 2002, 14(2), 18-22.
2
Conjoint Analysis
Within medicine, understanding how patients and other
stakeholders value various aspects of an intervention in
health care is vital to both the design and evaluation of
programs. Incorporating these values in decision making
may ultimately result in clinical, licensing,
reimbursement, and policy decisions that better reflect
the preferences of stakeholders, especially patients.
Aligning health care policy with patient preferences
could improve the effectiveness of health care
interventions by improving adoption of, satisfaction
with, and adherence to clinical treatments or public
health programs.
3
Conjoint Analysis
Methods using ranking, rating, or choice designs (either
individually or in combination) to quantify preferences
for various attributes of an intervention (often
referred to as conjoint analysis, discrete-choice
experiments, or stated-choice methods).
Conjoint-analysis methods are particularly useful for
quantifying preferences for nonmarket goods and
services or where market choices are severely
constrained by regulatory and institutional factors, such
as in health care.
4
Conjoint Analysis
The checklist should be used to understand the steps
involved in producing good conjoint-analysis research in
health care.
Bridges, J.F.P., Hauber, A.B., Marshall, D., Lloyd, A.,
Prosser, L.A., Regier, D.A., Johnson, F.R. and Mauskopf,
J., Conjoint Analysis Applications in Health-a Checklist:
A Report of the ISPOR Good Research Practices for
Conjoint Analysis Task Force, Value In Health, Volume:
14 Issue: 4, Pages: 403-413, 2011.
5
Conjoint Analysis
See also
Constructing Experimental Designs for Discrete-Choice
Experiments: Report of the ISPOR Conjoint Analysis
Experimental Design Good Research Practices Task
Force
Johnson, F.R., Lancsar, E., Marshall, D., Kilambi, V.,
Muhlbacher, A., Regier, D.A., Bresnahan, B.W., Kanninen,
B. and Bridges, J.F.P
Value In Health, 16(1), 3-13, 2013.
But beware of
Discrete Choice Experiments Are Not Conjoint Analysis
Louviere J.J., Flynn T.N. and Carson R.T.
6
Journal of Choice Modelling, 3(3), 57-72, 2010.
Conjoint Analysis
1. Was a well-defined research
question stated and is conjoint
analysis an appropriate method
for answering it?
1.1 Were a well-defined
research question and a
testable hypothesis
articulated?
1.2 Was the study perspective
described, and was the study
placed in a particular decisionmaking or policy context?
1.3 What is the rationale for
using conjoint analysis to answer
the research question?
7
Conjoint Analysis
2. Was the choice of attributes
and levels supported by
evidence?
2.1 Was attribute identification
supported by evidence
(literature reviews, focus
groups, or other scientific
methods)?
2.2 Was attribute selection
justified and consistent with
theory?
2.3 Was level selection for each
attribute justified by the
evidence and consistent with
the study perspective and
hypothesis?
8
Conjoint Analysis
3. Was the construction of
tasks appropriate?
3.1 Was the number of
attributes in each conjoint task
justified (that is, full or partial
profile)?
3.2 Was the number of profiles
in each conjoint task justified?
3.3 Was (should) an opt-out or a
status-quo alternative (be)
included?
9
Conjoint Analysis
4. Was the choice of
experimental design justified
and evaluated?
4.1 Was the choice of
experimental design justified?
Were alternative experimental
designs considered?
4.2 Were the properties of the
experimental design evaluated?
4.3 Was the number of conjoint
tasks included in the datacollection instrument
appropriate?
10
Conjoint Analysis
5. Were preferences elicited
appropriately, given the research
question?
5.1 Was there sufficient
motivation and explanation of
conjoint tasks?
5.2 Was an appropriate elicitation
format (that is, rating, ranking, or
choice) used? Did (should) the
elicitation format allow for
indifference?
5.3 In addition to preference
elicitation, did the conjoint tasks
include other qualifying questions
(for example, strength of
preference, confidence in
response, and other methods)? 11
Conjoint Analysis
6. Was the data collection
instrument designed
appropriately?
6.1 Was appropriate respondent
information collected (such as
socio-demographic, attitudinal,
health history or status, and
treatment experience)?
6.2 Were the attributes and
levels defined, and was any
contextual information
provided?
6.3 Was the level of burden of
the data-collection instrument
appropriate? Were respondents
encouraged and motivated?
12
Conjoint Analysis
7. Was the data-collection plan
appropriate?
7.1 Was the sampling strategy
justified (for example, sample
size, stratification, and
recruitment)?
7.2 Was the mode of
administration justified and
appropriate (for example, faceto-face, pen-and-paper, webbased)?
7.3 Were ethical considerations
addressed (for example,
recruitment, information and/or
consent, compensation)?
13
Conjoint Analysis
8. Were statistical analyses and
model estimations appropriate?
8.1 Were respondent
characteristics examined and
tested?
8.2 Was the quality of the
responses examined (for
example, rationality, validity,
reliability)?
8.3 Was model estimation
conducted appropriately? Were
issues of clustering and
subgroups handled
appropriately?
14
Conjoint Analysis
9. Were the results and
conclusions valid?
9.1 Did study results reflect
testable hypotheses and
account for statistical
uncertainty?
9.2 Were study conclusions
supported by the evidence and
compared with existing findings
in the literature?
9.3 Were study limitations and
generalizability adequately
discussed?
15
Conjoint Analysis
10. Was the study presentation
clear, concise, and complete?
10.1 Was study importance and
research context adequately
motivated?
10.2 Were the study datacollection instrument and
methods described?
10.3 Were the study
implications clearly stated and
understandable to a wide
audience?
16
Conjoint Analysis - Example
This presentation is loosely based on notes from
IBM/SPSS main and statistics examples.
In a popular example of conjoint analysis (Green and
Wind, 1973), a company interested in marketing a new
carpet cleaner wants to examine the influence of five
factors on consumer preference - package design, brand
name, price, a Good Housekeeping seal, and a money-back
guarantee.
17
Conjoint Analysis - Example
There are three factor levels for package design, each
one differing in the location of the applicator brush;
three brand names (K2R, Glory, and Bissell); three price
levels; and two levels (either no or yes) for each of the
last two factors. The following table displays the
variables used in the carpet-cleaner study, with their
variable labels and values.
Variable
name
Variable label
Value label
package
package design
A*, B*, C*
brand
brand name
K2R, Glory, Bissell
price
price
$1.19, $1.39, $1.59
seal
Good Housekeeping seal
no, yes
money
money-back guarantee
no, yes
18
Conjoint Analysis
There could be other factors and factor levels that
characterize carpet cleaners, but these are the only ones
of interest to management. This is an important point in
conjoint analysis. You want to choose only those factors
(independent variables) that you think most influence the
subject's preference (the dependent variable). Using
conjoint analysis, you will develop a model for customer
preference based on these five factors.
Green, P. E., and Y. Wind. 1973. Multiattribute decisions
in marketing: A measurement approach. Hinsdale, Ill.:
Dryden Press.
19
Conjoint Analysis
The first step in a conjoint analysis is to create the
combinations of factor levels that are presented as
product profiles to the subjects. Since even a small
number of factors and a few levels for each factor will
lead to an unmanageable number of potential product
profiles, you need to generate a representative subset
known as an orthogonal array.
20
Conjoint Analysis
The “Generate Orthogonal Design” procedure creates an
orthogonal array - also referred to as an orthogonal
design - and stores the information in a data file. Unlike
most procedures, an active dataset is not required
before running the Generate Orthogonal Design
procedure. If you do not have an active dataset, you have
the option of creating one, generating variable names,
variable labels, and value labels from the options that you
select in the dialog boxes. If you already have an active
dataset, you can either replace it or save the orthogonal
design as a separate data file.
21
Conjoint Analysis
To create an
orthogonal design:
► From the menus
choose:
Data
> Orthogonal Design
> Generate
22
Conjoint Analysis
► Enter package in the
Factor Name text box,
and enter package design in
the Factor Label text box.
► Click Add
23
Conjoint Analysis
This creates an item labelled
package 'package design' (?).
Select this item.
► Click Define Values.
24
Conjoint Analysis
► Enter the values 1, 2, and
3 to represent the package
designs A*, B*, and C*.
Enter the labels A*, B*, and
C* as well.
► Click Continue.
25
Conjoint Analysis
You'll now want to repeat this process for the remaining
factors, brand, price, seal, and money.
26
Conjoint Analysis
Use the values and labels from the following table, which
includes the values you've already entered for package.
Factor
name
Factor label
Values
Labels
package
package design
1, 2, 3
A*, B*, C*
brand
brand name
1, 2, 3
K2R, Glory, Bissell
price
price
1.19, 1.39, 1.59 $1.19, $1.39, $1.59
seal
Good Housekeeping seal
1, 2
no, yes
money
money-back guarantee
1, 2
no, yes
27
Conjoint Analysis
Once you have completed
the factor specifications:
► In the Data File group,
leave the default of
Create a new dataset
28
Conjoint Analysis
Enter a dataset name.
The generated design will
be saved to a new dataset,
in the current session, with
the specified name.
► Select Reset random
number seed to and enter
the value 2000000.
29
Conjoint Analysis
Generating an orthogonal design requires a set of random
numbers. If you want to duplicate a design - in this case,
the design used for the present case study - you need to
set the seed value before you generate the design and
reset it to the same value each subsequent time you
generate the design. The design used for this case study
was generated with a seed value of 2000000. This value
is essential to ensure repeat analysis will reproduce
identical results.
30
Conjoint Analysis
► In the Data File group,
change the default of
Create a new data file
Enter a data file name
(with appropriate directory
structure for your
machine).
The generated design will
be saved to a new data file.
31
Conjoint Analysis
► Click Options
32
Conjoint Analysis
► In the Minimum number of cases
to generate text box, type 18.
33
Conjoint Analysis
By default, the minimum number of cases necessary for
an orthogonal array is generated. The procedure
determines the number of cases that need to be
administered to allow estimation of the utilities. You can
also specify a minimum number of cases to generate, as
you've done here. You might want to do this because the
default number of minimum cases is too small to be useful
or because you have experimental design considerations 34
that require a certain minimum number of cases.
Conjoint Analysis
► Select Number of holdout cases
and type 4.
Holdout cases are judged by the subjects but are not
used by the conjoint analysis to estimate utilities.
They are used as a check on the validity of the
estimated utilities. The holdout cases are generated
from another random plan, not the experimental
orthogonal plan.
35
Conjoint Analysis
► Click Continue in the Generate
Orthogonal Design Options dialog
box.
36
Conjoint Analysis
► Click OK in the Generate
Orthogonal Design dialog
box.
37
Conjoint Analysis
The syntax is
*Generate Orthogonal Design.
SET SEED 2000000.
ORTHOPLAN
/FACTORS=package 'package design' (1 'A*' 2 'B*' 3 'C*')
brand 'brand name' (1 'K2R' 2 'Glory' 3 'Bissell')
price 'price' (1.19 '$1.19' 1.39 '$1.39' 1.59 '$1.59')
seal 'Good Housekeeping seal' (1 'no' 2 'yes')
money 'money-back guarantee' (1 'no' 2 'yes')
/OUTFILE='15a.sav'
/MINIMUM 18
/HOLDOUT 4
/MIXHOLD NO.
38
Conjoint Analysis
The orthogonal design is
displayed in the Data Editor
and is best viewed by
displaying value labels rather
than the actual data values.
This is accomplished by
choosing Value Labels from
the View menu.
To retrieve your saved plan.
39
Conjoint Analysis
40
Conjoint Analysis
The orthogonal design is a required input to the analysis
of the data. Therefore, you will want to save your design
to a data file. For convenience, the current design has
been saved in 15a.sav (orthogonal designs are also
referred to as plans).
Once you have created an orthogonal design, you'll want
to use it to create the product profiles to be rated by
the subjects. You can obtain a listing of the profiles in a
single table or display each profile in a separate table.
41
Conjoint Analysis
To display an orthogonal design:
► From the menus choose:
Data
> Orthogonal Design
> Display
42
Conjoint Analysis
► Select package,
brand, price, seal, and
money for the factors.
43
Conjoint Analysis
The variables in the data file are the factors used to
specify the design. Each case represents one product
profile in the design. Notice that two additional variables,
CARD_ and STATUS_, appear in the data file. CARD_
assigns a sequential number to each profile that is used to
identify the profile. STATUS_ indicates whether a
profile is part of the experimental design (the first 18
cases), a holdout case (the last 4 cases), or a simulation
case (to be discussed in a later topic in this case study).
The information contained in the variables STATUS_ and
CARD_ is automatically included in the output, so they
44
don't need to be selected.
Conjoint Analysis
► Select Listing for
experimenter in the
Format group.
This results in
displaying the entire
orthogonal design in a
single table.
► Click OK.
45
Conjoint Analysis
Card List
Good
House
Card package
brand
keeping
ID
design
name
price
seal
1
1 A*
Glory
$1.39 yes
2
2 B*
K2R
$1.19 no
3
3 B*
Glory
$1.39 no
4
4 C*
Glory
$1.59 no
5
5 C*
Bissell $1.39 no
6
6 A*
Bissell $1.39 no
7
7 B*
Bissell $1.59 yes
8
8 A*
K2R
$1.59 no
9
9 C*
K2R
$1.39 no
10
10 C*
Glory
$1.19 no
11
11 C*
K2R
$1.59 yes
12
12 B*
Glory
$1.59 no
13
13 C*
Bissell $1.19 yes
14
14 A*
Glory
$1.19 yes
15
15 B*
K2R
$1.39 yes
16
16 A*
K2R
$1.19 no
17
17 A*
Bissell $1.59 no
18
18 B*
Bissell $1.19 no
19a
19 A*
Bissell $1.59 yes
a
20
20 C*
K2R
$1.19 yes
21a
21 A*
Glory
$1.59 no
22a
22 A*
Bissell $1.19 no
a. Holdout
money-back
guarantee
no
no
yes
no
no
no
no
yes
no
yes
no
no
yes
no
yes
no
yes
no
no
no
no
no
The output resembles the look of
the orthogonal design as shown in
the Data Editor—one row for each
profile, with the factors as
columns.
Notice, however, that the column
headers are the variable labels
rather than the variable names
that you see in the Data Editor.
46
Conjoint Analysis
Card List
Good
House
Card package
brand
keeping
ID
design
name
price
seal
1
1 A*
Glory
$1.39 yes
2
2 B*
K2R
$1.19 no
3
3 B*
Glory
$1.39 no
4
4 C*
Glory
$1.59 no
5
5 C*
Bissell $1.39 no
6
6 A*
Bissell $1.39 no
7
7 B*
Bissell $1.59 yes
8
8 A*
K2R
$1.59 no
9
9 C*
K2R
$1.39 no
10
10 C*
Glory
$1.19 no
11
11 C*
K2R
$1.59 yes
12
12 B*
Glory
$1.59 no
13
13 C*
Bissell $1.19 yes
14
14 A*
Glory
$1.19 yes
15
15 B*
K2R
$1.39 yes
16
16 A*
K2R
$1.19 no
17
17 A*
Bissell $1.59 no
18
18 B*
Bissell $1.19 no
19a
19 A*
Bissell $1.59 yes
a
20
20 C*
K2R
$1.19 yes
21a
21 A*
Glory
$1.59 no
22a
22 A*
Bissell $1.19 no
a. Holdout
money-back
guarantee
no
no
yes
no
no
no
no
yes
no
yes
no
no
yes
no
yes
no
yes
no
no
no
no
no
Also notice that the holdout cases
are identified with a footnote.
This is of interest to the
experimenter, but you certainly
don't want the subjects to know
which, if any, cases are holdouts.
47
Conjoint Analysis
Card List
Good
House
Card package
brand
keeping
ID
design
name
price
seal
1
1 A*
Glory
$1.39 yes
2
2 B*
K2R
$1.19 no
3
3 B*
Glory
$1.39 no
4
4 C*
Glory
$1.59 no
5
5 C*
Bissell $1.39 no
6
6 A*
Bissell $1.39 no
7
7 B*
Bissell $1.59 yes
8
8 A*
K2R
$1.59 no
9
9 C*
K2R
$1.39 no
10
10 C*
Glory
$1.19 no
11
11 C*
K2R
$1.59 yes
12
12 B*
Glory
$1.59 no
13
13 C*
Bissell $1.19 yes
14
14 A*
Glory
$1.19 yes
15
15 B*
K2R
$1.39 yes
16
16 A*
K2R
$1.19 no
17
17 A*
Bissell $1.59 no
18
18 B*
Bissell $1.19 no
19a
19 A*
Bissell $1.59 yes
a
20
20 C*
K2R
$1.19 yes
21a
21 A*
Glory
$1.59 no
22a
22 A*
Bissell $1.19 no
a. Holdout
money-back
guarantee
no
no
yes
no
no
no
no
yes
no
yes
no
no
yes
no
yes
no
yes
no
no
no
no
no
Depending on how you create and
deliver your final product profiles,
you may want to save this table as
an HTML, Word/RTF, Excel, or
PowerPoint file. This is easily
accomplished by selecting the
table in the Viewer, right clicking,
and selecting Export. Also, if
you're using the exported version
to create the final product
profiles, be sure to edit out the
footnotes for the holdout cases.
48
Conjoint Analysis
Perhaps the needs for your survey are better served by
generating a separate table for each product profile.
This choice lends itself nicely to exporting to PowerPoint,
since each table (product profile) is placed on a separate
PowerPoint slide.
49
Conjoint Analysis
To display each profile in
a separate table:
► Click the Dialog Recall
button and select Display
Design.
► Deselect Listing for
experimenter and select
Profiles for subjects.
► Click OK.
50
Conjoint Analysis
The information for each product profile is displayed in a
separate table. In addition, holdout cases are
indistinguishable from the rest of the cases, so there is
no issue of removing identifiers for holdouts as with the
single table layout.
Profile Number 1
Card ID
Good
Housekeeping
money-back
seal
guarantee
yes
no
…
package design
brand name
price
1 A*
Glory
$1.39
…
Profile Number 22
Card ID package design
brand name
price
22 A*
Bissell
$1.19
Good
Housekeeping
money-back
seal
guarantee
no
no
51
Conjoint Analysis
You've generated an orthogonal design and learned how
to display the associated product profiles. You're now
ready to learn how to run a conjoint analysis.
The preference data collected from the subjects is
stored in 15b.sav.
ID PREF1
PREF2
PREF3
PREF4
PREF5
PREF6
PREF7
PREF8
PREF9
PREF10 PREF11 PREF12 PREF13 PREF14 PREF15 PREF16 PREF17 PREF18 PREF19 PREF20 PREF21 PREF22
1
1
13
15
1
20
14
7
11
19
3
10
17
8
5
9
6
12
4
21
18
2
22
16
2
2
15
7
18
2
12
3
11
20
16
21
6
22
8
17
19
1
14
4
9
5
10
13
3
3
2
18
14
16
22
13
20
10
15
3
1
6
9
5
7
12
19
8
17
21
11
4
4
4
13
10
20
14
2
18
16
22
15
3
1
9
5
6
8
17
11
7
19
4
12
21
5
5
13
18
2
10
20
15
9
5
3
7
11
4
12
22
14
16
1
6
19
21
17
8
6
6
15
2
3
12
18
7
20
10
11
4
9
5
13
16
14
22
8
6
1
21
19
17
7
7
13
7
15
18
2
3
10
20
14
11
19
17
12
1
9
5
4
6
8
16
21
22
8
8
15
7
13
4
6
16
8
22
5
9
21
18
10
3
2
20
14
11
17
19
1
12
9
9
20
9
10
11
4
5
13
15
2
3
12
18
7
1
21
14
16
22
8
6
17
19
10 10
8
21
19
17
4
11
12
7
1
6
9
5
3
15
14
16
22
20
10
13
2
18
52
Conjoint Analysis
The data consist of responses from 10 subjects, each
identified by a unique value of the variable ID.
Subjects were asked to rank the 22 product profiles
from the most to the least preferred. The variables
PREF1 through PREF22 contain the IDs of the associated
product profiles, that is, the card IDs from 15a.sav.
Subject 1, for example, liked profile 13 most of all, so
PREF1 has the value 13.
ID PREF1
PREF2
PREF3
PREF4
PREF5
PREF6
PREF7
PREF8
PREF9
PREF10 PREF11 PREF12 PREF13 PREF14 PREF15 PREF16 PREF17 PREF18 PREF19 PREF20 PREF21 PREF22
1
1
13
15
1
20
14
7
11
19
3
10
17
8
5
9
6
12
4
21
18
2
22
16
2
2
15
7
18
2
12
3
11
20
16
21
6
22
8
17
19
1
14
4
9
5
10
13
3
3
2
18
14
16
22
13
20
10
15
3
1
6
9
5
7
12
19
8
17
21
11
4
4
4
13
10
20
14
2
18
16
22
15
3
1
9
5
6
8
17
11
7
19
4
12
21
5
5
13
18
2
10
20
15
9
5
3
7
11
4
12
22
14
16
1
6
19
21
17
8
6
6
15
2
3
12
18
7
20
10
11
4
9
5
13
16
14
22
8
6
1
21
19
17
7
7
13
7
15
18
2
3
10
20
14
11
19
17
12
1
9
5
4
6
8
16
21
22
8
8
15
7
13
4
6
16
8
22
5
9
21
18
10
3
2
20
14
11
17
19
1
12
9
9
20
9
10
11
4
5
13
15
2
3
12
18
7
1
21
14
16
22
8
6
17
19
10 10
8
21
19
17
4
11
12
7
1
6
9
5
3
15
14
16
22
20
10
13
2
18
53
Conjoint Analysis
Analysis of the data is a task that requires the use of
command syntax - A graphical user interface is not yet
available for the Conjoint procedure. To obtain a conjoint
analysis, you must enter command syntax for a
CONJOINT command into a syntax window and then run
it.
Source
54
Conjoint Analysis
Analysis of the data is a task that requires the use of
command syntax - specifically, the CONJOINT command.
The necessary command syntax has been provided below.
CONJOINT PLAN='15a.sav'
/DATA='15b.sav'
/SEQUENCE=PREF1 TO PREF22
/SUBJECT=ID
/FACTORS=PACKAGE BRAND (DISCRETE)
PRICE (LINEAR LESS)
SEAL (LINEAR MORE)
MONEY (LINEAR MORE)
/PRINT=SUMMARYONLY.
55
Conjoint Analysis
CONJOINT PLAN='15a.sav'
/DATA='15b.sav'
/SEQUENCE=PREF1 TO PREF22
/SUBJECT=ID
/FACTORS=PACKAGE BRAND (DISCRETE)
PRICE (LINEAR LESS)
SEAL (LINEAR MORE)
MONEY (LINEAR MORE)
/PRINT=SUMMARYONLY.
The PLAN subcommand specifies the file containing the orthogonal design - in this
example, 15a.sav.
56
Conjoint Analysis
CONJOINT PLAN='15a.sav'
/DATA='15b.sav'
/SEQUENCE=PREF1 TO PREF22
/SUBJECT=ID
/FACTORS=PACKAGE BRAND (DISCRETE)
PRICE (LINEAR LESS)
SEAL (LINEAR MORE)
MONEY (LINEAR MORE)
/PRINT=SUMMARYONLY.
The DATA subcommand specifies the file containing the preference data - in this
example, 15b.sav. If you choose the preference data as the active dataset, you can
replace the file specification with an asterisk (*), without the quotation marks. You
will have to adjust the file address.
57
Conjoint Analysis
CONJOINT PLAN='15a.sav'
/DATA='15b.sav'
/SEQUENCE=PREF1 TO PREF22
/SUBJECT=ID
/FACTORS=PACKAGE BRAND (DISCRETE)
PRICE (LINEAR LESS)
SEAL (LINEAR MORE)
MONEY (LINEAR MORE)
/PRINT=SUMMARYONLY.
The SEQUENCE subcommand specifies that each data point in the preference data is
a profile number, starting with the most-preferred profile and ending with the leastpreferred profile.
58
Conjoint Analysis
CONJOINT PLAN='15a.sav'
/DATA='15b.sav'
/SEQUENCE=PREF1 TO PREF22
/SUBJECT=ID
/FACTORS=PACKAGE BRAND (DISCRETE)
PRICE (LINEAR LESS)
SEAL (LINEAR MORE)
MONEY (LINEAR MORE)
/PRINT=SUMMARYONLY.
The SUBJECT subcommand specifies that the variable ID identifies the subjects.
59
Conjoint Analysis
CONJOINT PLAN='15a.sav'
/DATA='15b.sav'
/SEQUENCE=PREF1 TO PREF22
/SUBJECT=ID
/FACTORS=PACKAGE BRAND (DISCRETE)
PRICE (LINEAR LESS)
SEAL (LINEAR MORE)
MONEY (LINEAR MORE)
/PRINT=SUMMARYONLY.
The FACTORS subcommand specifies a model describing the expected relationship
between the preference data and the factor levels. The specified factors refer to
variables defined in the plan file named on the PLAN subcommand.
60
Conjoint Analysis
CONJOINT PLAN='15a.sav'
/DATA='15b.sav'
/SEQUENCE=PREF1 TO PREF22
/SUBJECT=ID
/FACTORS=PACKAGE BRAND (DISCRETE)
PRICE (LINEAR LESS)
SEAL (LINEAR MORE)
MONEY (LINEAR MORE)
/PRINT=SUMMARYONLY.
The keyword DISCRETE is used when the factor levels are categorical and no
assumption is made about the relationship between the levels and the data. This is
the case for the factors package and brand that represent package design and brand
name, respectively. DISCRETE is assumed if a factor is not labelled with one of the
four alternatives (DISCRETE, LINEAR, IDEAL, ANTIIDEAL) or is not included on
the FACTORS subcommand.
61
Conjoint Analysis
CONJOINT PLAN='15a.sav'
/DATA='15b.sav'
/SEQUENCE=PREF1 TO PREF22
/SUBJECT=ID
/FACTORS=PACKAGE BRAND (DISCRETE)
PRICE (LINEAR LESS)
SEAL (LINEAR MORE)
MONEY (LINEAR MORE)
/PRINT=SUMMARYONLY.
The keyword LINEAR, used for the remaining factors, indicates that the data are
expected to be linearly related to the factor. For example, preference is usually
expected to be linearly related to price. You can also specify quadratic models (not
used in this example) with the keywords IDEAL and ANTIIDEAL.
62
Conjoint Analysis
CONJOINT PLAN='15a.sav'
/DATA='15b.sav'
/SEQUENCE=PREF1 TO PREF22
/SUBJECT=ID
/FACTORS=PACKAGE BRAND (DISCRETE)
PRICE (LINEAR LESS)
SEAL (LINEAR MORE)
MONEY (LINEAR MORE)
/PRINT=SUMMARYONLY.
The keywords MORE and LESS, following LINEAR, indicate an expected direction for
the relationship. Since we expect higher preference for lower prices, the keyword
LESS is used for price. However, we expect higher preference for either a Good
Housekeeping seal of approval or a money-back guarantee, so the keyword MORE is
used for seal and money (recall that the levels for both of these factors were set to 1
for no and 2 for yes).
63
Conjoint Analysis
CONJOINT PLAN='15a.sav'
/DATA='15b.sav'
/SEQUENCE=PREF1 TO PREF22
/SUBJECT=ID
/FACTORS=PACKAGE BRAND (DISCRETE)
PRICE (LINEAR LESS)
SEAL (LINEAR MORE)
MONEY (LINEAR MORE)
/PRINT=SUMMARYONLY.
Specifying MORE or LESS does not change the signs of the coefficients or affect
estimates of the utilities. These keywords are used simply to identify subjects whose
estimates do not match the expected direction. Similarly, choosing IDEAL instead of
ANTIIDEAL, or vice versa, does not affect coefficients or utilities.
64
Conjoint Analysis
CONJOINT PLAN='15a.sav'
/DATA='15b.sav'
/SEQUENCE=PREF1 TO PREF22
/SUBJECT=ID
/FACTORS=PACKAGE BRAND (DISCRETE)
PRICE (LINEAR LESS)
SEAL (LINEAR MORE)
MONEY (LINEAR MORE)
/PRINT=SUMMARYONLY.
The PRINT subcommand specifies that the output contains information for the
group of subjects only as a whole (SUMMARYONLY keyword). Information for each
subject, separately, is suppressed.
65
Conjoint Analysis
CONJOINT PLAN='15a.sav'
/DATA='15b.sav'
/SEQUENCE=PREF1 TO PREF22
/SUBJECT=ID
/FACTORS=PACKAGE BRAND (DISCRETE)
PRICE (LINEAR LESS)
SEAL (LINEAR MORE)
MONEY (LINEAR MORE)
/PRINT=SUMMARYONLY.
You've generated an orthogonal design and learned how to display the associated
product profiles. You're now ready to learn how to run a conjoint analysis.
Try running this command syntax. Make sure that you have included valid paths to
15b.sav and 15a.sav.
66
Conjoint Analysis
Overall Statistics
package
brand
price
seal
money
(Constant)
A*
B*
C*
K2R
Glory
Bissell
$1.19
$1.39
$1.59
no
yes
no
yes
Utilities
Utility Estimate
-2.233
1.867
.367
.367
-.350
-.017
-6.595
-7.703
-8.811
2.000
4.000
1.250
2.500
12.870
Std. Error
.192
.192
.192
.192
.192
.192
.988
1.154
1.320
.287
.575
.287
.575
1.282
This table shows the utility
(part-worth) scores and their
standard errors for each factor
level. Higher utility values
indicate greater preference.
67
Conjoint Analysis
Overall Statistics
package
brand
price
seal
money
(Constant)
A*
B*
C*
K2R
Glory
Bissell
$1.19
$1.39
$1.59
no
yes
no
yes
Utilities
Utility Estimate
-2.233
1.867
.367
.367
-.350
-.017
-6.595
-7.703
-8.811
2.000
4.000
1.250
2.500
12.870
Std. Error
.192
.192
.192
.192
.192
.192
.988
1.154
1.320
.287
.575
.287
.575
1.282
As expected, there is an inverse
relationship between price and
utility, with higher prices
corresponding to lower utility
(larger negative values mean
lower utility).
68
Conjoint Analysis
Overall Statistics
package
brand
price
seal
money
(Constant)
A*
B*
C*
K2R
Glory
Bissell
$1.19
$1.39
$1.59
no
yes
no
yes
Utilities
Utility Estimate
-2.233
1.867
.367
.367
-.350
-.017
-6.595
-7.703
-8.811
2.000
4.000
1.250
2.500
12.870
Std. Error
.192
.192
.192
.192
.192
.192
.988
1.154
1.320
.287
.575
.287
.575
1.282
The presence of a seal of
approval or money-back
guarantee corresponds to a
higher utility, as anticipated.
69
Conjoint Analysis
Overall Statistics
package
brand
price
seal
money
(Constant)
A*
B*
C*
K2R
Glory
Bissell
$1.19
$1.39
$1.59
no
yes
no
yes
Utilities
Utility Estimate
-2.233
1.867
.367
.367
-.350
-.017
-6.595
-7.703
-8.811
2.000
4.000
1.250
2.500
12.870
Std. Error
.192
.192
.192
.192
.192
.192
.988
1.154
1.320
.287
.575
.287
.575
1.282
The presence of a seal of
approval or money-back
guarantee corresponds to a
higher utility, as anticipated.
70
Conjoint Analysis
Overall Statistics
package
brand
price
seal
money
(Constant)
A*
B*
C*
K2R
Glory
Bissell
$1.19
$1.39
$1.59
no
yes
no
yes
Utilities
Utility Estimate
-2.233
1.867
.367
.367
-.350
-.017
-6.595
-7.703
-8.811
2.000
4.000
1.250
2.500
12.870
Std. Error
.192
.192
.192
.192
.192
.192
.988
1.154
1.320
.287
.575
.287
.575
1.282
Since the utilities are all
expressed in a common unit,
they can be added together to
give the total utility of any
combination.
For example, the total utility of a cleaner with package design B*, brand K2R,
price $1.19, and no seal of approval or money-back guarantee is:
utility(package B*) + utility(K2R) + utility($1.19) + utility(no seal)
+ utility(no money-back) + constant
1.867 + 0.367 + (−6.595) + 2.000 + 1.250 + 12.870 = 11.759
71
Conjoint Analysis
Overall Statistics
package
brand
price
seal
money
(Constant)
A*
B*
C*
K2R
Glory
Bissell
$1.19
$1.39
$1.59
no
yes
no
yes
Utilities
Utility Estimate
-2.233
1.867
.367
.367
-.350
-.017
-6.595
-7.703
-8.811
2.000
4.000
1.250
2.500
12.870
Std. Error
.192
.192
.192
.192
.192
.192
.988
1.154
1.320
.287
.575
.287
.575
1.282
If the cleaner had package design C*, brand Bissell, price $1.59, a seal of
approval, and a money-back guarantee, the total utility would be:
0.367 + (−0.017) + (−8.811) + 4.000 + 2.500 + 12.870 = 10.909
72
Conjoint Analysis
Overall Statistics
package
brand
price
seal
money
(Constant)
A*
B*
C*
K2R
Glory
Bissell
$1.19
$1.39
$1.59
no
yes
no
yes
Utilities
Utility Estimate
-2.233
1.867
.367
.367
-.350
-.017
-6.595
-7.703
-8.811
2.000
4.000
1.250
2.500
12.870
Std. Error
.192
.192
.192
.192
.192
.192
.988
1.154
1.320
.287
.575
.287
.575
1.282
The range of the utility values (highest to lowest) for each factor provides a
measure of how important the factor was to overall preference. Factors with
greater utility ranges play a more significant role than those with smaller
ranges.
73
Conjoint Analysis
This table shows the linear regression coefficients for
those factors specified as LINEAR (for IDEAL and
ANTIIDEAL models, there would also be a quadratic
term). The utility for a particular factor level is
determined by multiplying the level by the coefficient.
For example, the predicted utility for a price of $1.19
was listed as −6.595 in the utilities table. This is simply
the value of the price level, 1.19, multiplied by the price
coefficient, −5.542.
Coefficients
B
Coefficient
Estimate
price
-5.542
seal
2.000
money
1.250
74
Conjoint Analysis
This table provides a measure of the relative importance
of each factor known as an importance score or value.
The values are computed by taking the utility range for
each factor separately and dividing by the sum of the
utility ranges for all factors. The values thus represent
percentages and have the property that they sum to 100.
The calculations, it should be noted, are done separately
for each subject, and the results are then averaged over
all of the subjects.
Importance Values
package
35.635
brand
14.911
price
29.410
seal
11.172
money
8.872
Averaged Importance
Score
75
Conjoint Analysis
Note that while overall or summary utilities and
regression coefficients from orthogonal designs are the
same with or without a SUBJECT subcommand,
importances will generally differ. For summary results
without a SUBJECT subcommand, the importances can be
computed directly from the summary utilities, just as one
can do with individual subjects. However, when a
SUBJECT subcommand is used, the importances for the
individual subjects are averaged, and these averaged
importances will not in general match those computed
using the summary utilities.
76
Conjoint Analysis
The results show that package design has the most
influence on overall preference. This means that there is
a large difference in preference between product
profiles containing the most desired packaging and those
containing the least desired packaging.
The results also show that a money-back guarantee plays
the least important role in determining overall
preference. Price plays a significant role but not as
significant as package design. Perhaps this is because the
range of prices is not that large.
77
Conjoint Analysis
This table displays two statistics, Pearson's R and
Kendall's tau, which provide measures of the correlation
between the observed and estimated preferences.
Correlationsa
Value
Sig.
Pearson's R
.982
.000
Kendall's tau
.892
.000
Kendall's tau for Holdouts
.667
.087
a. Correlations between observed and estimated
preferences
78
Conjoint Analysis
The table also displays Kendall's tau for just the holdout
profiles. Remember that the holdout profiles (four in the
present example) were rated by the subjects but not
used by the Conjoint procedure for estimating utilities.
Instead, the Conjoint procedure computes correlations
between the observed and predicted rank orders for
these profiles as a check on the validity of the utilities.
Correlationsa
Value
Sig.
Pearson's R
.982
.000
Kendall's tau
.892
.000
Kendall's tau for Holdouts
.667
.087
a. Correlations between observed and estimated
preferences
79
Conjoint Analysis
In many conjoint analyses, the number of parameters is
close to the number of profiles rated, which will
artificially inflate the correlation between observed and
estimated scores. In these cases, the correlations for
the holdout profiles may give a better indication of the
fit of the model. Keep in mind, however, that holdouts
will always produce lower correlation coefficients.
80
Conjoint Analysis
When specifying LINEAR models for price, seal, and
money, we chose an expected direction (LESS or MORE)
for the linear relationship between the value of the
variable and the preference for that value. The Conjoint
procedure keeps track of the number of subjects whose
preference showed the opposite of the expected
relationship - for example, a greater preference for
higher prices, or a lower preference for a money-back
guarantee. These cases are referred to as reversals.
81
Conjoint Analysis
Factor
Subject
Number
price
money
seal
brand
package
1
2
3
4
5
6
7
8
9
10
of Reversals
Subject 1
Subject 2
Subject 3
Subject 4
Subject 5
Subject 6
Subject 7
Subject 8
Subject 9
Subject 10
3
2
2
0
0
1
2
0
0
0
1
0
0
1
2
This table displays the number of
reversals for each factor and for
each subject.
For example, three subjects showed
a reversal for price. That is, they
preferred product profiles with
higher prices.
82
Conjoint Analysis
The real power of conjoint analysis is the ability to
predict preference for product profiles that weren't
rated by the subjects. These are referred to as
simulation cases. Simulation cases are included as part of
the plan, along with the profiles from the orthogonal
design and any holdout profiles.
The simplest way to enter simulation cases is from the
Data Editor, using the value labels created when you
generated the experimental design.
83
Conjoint Analysis
To enter a simulation case in the plan file:
► On a new row in the Data Editor window, select a cell
and select the desired value from the list (value labels can
be displayed by choosing Value Labels from the View
menu). Repeat for all of the variables (factors).
When you double left click in a cell the drop down menu
appears.
84
Conjoint Analysis
► Select Simulation for the value of the STATUS_
variable.
► Enter an integer value, to be used as an identifier, for
the CARD_ variable. Simulation cases should be numbered
separately from the other cases.
85
Conjoint Analysis
The figure shows a part of the plan file for the carpetcleaner study, with two simulation cases added. For
convenience, these have been included in 15a1.sav.
86
Conjoint Analysis
The analysis of the simulation cases is accomplished with
the same command syntax used earlier. In fact, if you
ran the syntax described earlier, you would have noticed
that the output also includes results for the simulation
cases, since they are included in 15a1.sav.
You can choose to run simulations along with your initial
analysis - as done here - or run simulations at any later
point simply by including simulation cases in your plan file
and rerunning CONJOINT.
87
Conjoint Analysis
This table gives the predicted probabilities of choosing
each of the simulation cases as the most preferred one,
under three different probability-of-choice models.
Preference Probabilities of Simulationsb
Bradley-TerryCard Number
ID
Maximum Utilitya
Luce
Logit
1
1
30.0%
43.1%
30.9%
2
2
70.0%
56.9%
69.1%
a. Including tied simulations
b. 10 out of 10 subjects are used in the Bradley-Terry-Luce and Logit methods because
these subjects have all nonnegative scores.
The maximum utility model determines the probability as
the number of respondents predicted to choose the
profile divided by the total number of respondents. For
each respondent, the predicted choice is simply the
88
profile with the largest total utility.
Conjoint Analysis
Preference Probabilities of Simulationsb
Bradley-TerryCard Number
ID
Maximum Utilitya
Luce
Logit
1
1
30.0%
43.1%
30.9%
2
2
70.0%
56.9%
69.1%
a. Including tied simulations
b. 10 out of 10 subjects are used in the Bradley-Terry-Luce and Logit methods because
these subjects have all nonnegative scores.
The BTL (Bradley-Terry-Luce) model determines the
probability as the ratio of a profile's utility to that for
all simulation profiles, averaged across all respondents.
The logit model is similar to BTL but uses the natural log
of the utilities instead of the utilities.
Across the 10 subjects in this study, all three models
indicated that simulation profile 2 would be preferred. 89
Conjoint Analysis
See the following sources for more information on conjoint analysis:
Akaah, I. P., and P. K. Korgaonkar. 1988. A conjoint investigation of
the relative importance of risk relievers in direct marketing. Journal
of Advertising Research, 28:4, 38-44.
Cattin, P., and D. R. Wittink. 1982. Commercial use of conjoint
analysis: A survey. Journal of Marketing, 46:3, 44-53.
Green, P. E., and Y. Wind. 1973. Multiattribute decisions in
marketing: A measurement approach. Hinsdale, Ill.: Dryden Press.
90
Warning
Louviere et al. (2010) briefly review and discuss traditional conjoint
analysis (CA) and discrete choice experiments (DCEs), which are
widely used stated preference elicitation methods in several
disciplines. They contrast CA with DCEs that have a long-standing,
well-tested theoretical basis in random utility theory, and show why
and how DCEs are more general and consistent with economic demand
theory. Perhaps the major message, though, is that many studies
that claim to be doing CA are really doing DCEs.
To the best of my knowledge SAS is required to perform an analysis
of DCEs, see Kuhfeld for extensive details.
Louviere, J.J., Flynn, T.N. and Carson R.T. 2010. Discrete choice
experiments are not conjoint analysis. Journal of Choice Modelling,
3(3), 57-72.
91