1. Conjoint Analysis

2. 1. Researchers frequently want to know what utility a particular product feature or service feature will have for a consumer.
2. Conjoint analysis is a multivariate technique that captures the exact levels of utility that an individual customer puts on various attributes of the product offering. It enables a direct comparison between say, the utility of a price level of SAR400 versus SAR500, a delivery period of 1 week versus 2 weeks, or an after sales response of 24 hours versus 48 hours.
3. Once we know utility levels for every attribute (and at every level), we can combine these to find the best combination of attributes that gives him the highest utility, the second best combination that gives the second highest utility, and so on.
4. This information can be used to design a product or service offering.

3. Method
1. The researcher determines a set of attributes and their levels, say 3 attributes, each at 2 levels, which he feels are critical decision-making variables for his consumers. Now, all possible combinations of these levels are listed out.
2. For example, in a readymade shirt, price could be one factor, at levels SAR 300 or SAR 350, stores could be exclusive or non-exclusive, and design could be checks or solid colors. We would then take all the possible combinations as follows -
1. SAR 300 Exclusive Store Checks
2. SAR 300 Exclusive Store Solid Colors
3. SAR 350 Exclusive Store Checks
4. SAR 350 Exclusive Store Solid Colors
5. SAR 300 Non-exclusive Store Checks
6. SAR 300 Non-exclusive Store Solid Colors
7. SAR 350 Non-exclusive Store Checks
8. SAR 350 Non-exclusive Store Solid Colors
3. These eight combination can be presented to the respondent of our survey, and he is asked to rank the combination he prefers from rank 1 to rank 8.
4. This forms the input data for conjoint analysis.

4. 5. The objective, as stated earlier, is to convert these rankings into utilities, so we know how this respondent’s utility varies with any change in the level of any of the attributes.
6. In other words, the output of conjoint analysis will generate utility levels for combinations given above. For example, the computer output after conjoint analysis may generate a utility table that looks like this :-
a. SAR 300 – Utility 5
b. SAR 350 – Utility 1
c. Checks – Utility 10
d. Solid Colors – Utility 6
e. Exclusive Stores – Utility 4
f. Non-exclusive Stores – Utility 2
7. Thus this table indicates that relatively, checks have the highest utility of 10, and solid colors, 6. Price at SAR 300 has a much higher utility than SAR 350.

5. 8. Relatively, exclusivity or otherwise of the stores has less utility
8. Relatively, exclusivity or otherwise of the stores has less utility. But exclusive stores have 4, and non-exclusive stores have 2.
9. The best combined utility can also be calculated for the original eight combinations. For example, for this consumer, the best utility combination would be a price of SAR 300, checks and exclusive stores: =19 points.
10. The second best would be =17 points. (SAR 300, checks, non exclusive stores). The third, fourth, fifth….eighth best combination and their utilities can similarly be found.

6. Number of attributes and levels
1. To avoid creating masses of data , the researcher has to be careful in selecting both the number of attributes and the number of levels of each. Only those attributes and levels must be used, which are feasible offerings from the manufacturer’s / marketer’s view point.
2. Another point of interest is that the number of combinations being offered for ranking by respondents should not be too high . For example, beyond about 35 or 40 combinations, respondent fatigue would probably induce inaccurate or disinterested responses, affecting the validity of the procedure .

7. Another Example
Let us take the example of an industrial product – a CNC machine tool which is used to perform a variety of manufacturing operations – to illustrate the application of conjoint analysis .
Similar to the brief example of a branded shirt discussed earlier, we first identify the attributes of the product which are important to customers, and then the levels for each attribute that we are willing to design and offer to a customer.
Thus, this will be an application of conjoint analysis for product design of an industrial machine tool. Let us assume that three attributes of a CNC machine tool are important :
1. Setup time in minutes: This is the time it takes to prepare or setup the machine for operations.
2. Delivery period in days: This is the time the manufacturer needs to deliver after the customer has placed an order.
3. Number of different tools the machine can accommodate: This is a measure of machine flexibility in performing different operations.

8. These are the three attributes. The levels of these attributes are
1. Setup time - 3 minutes, 6 minutes, 9 minutes, 12 minutes (4 levels)
2. Delivery period days, 22 days, 28 days (3 levels)
3. Number of tools - 4, 8 or 10 (3 levels)
These levels are the options that we (the manufacturer) are willing to consider in design and delivery of the machine.

9. Since we have 4, 3 and 3 levels of the three attributes, we get a total of 4x3x3 = 36 different combinations of attribute levels. The next stage of the input process is to collect from a respondent his ranking and arrive at the ratings, which is a reverse of ranking, for all the 36 combinations of attribute levels. This table would look like Fig . 1 .
Table contd on next slide

10. Table contd… Remaining part of Fig. 1

11. Running Conjoint as a Regression Model
It is quite easy to convert the conjoint analysis input into an equivalent regression model and run it as a regression. The coding of the attribute levels for this purpose is known as “Effects coding“ and Fig. 2 shows our machine tool example coded for a regression run. In this input data matrix (Fig. 2), which is similar to coding of dummy variables, the four levels of Setup Time recorded as shown in the following table.
Set up time in
Var 1
Var 2
Var 3
minutes S3 1 1 S6 1 S9 -1 -1 -1
S12 .
Thus, 3 Variables, Var 1, Var 2, Var 3 are used to indicate 4 levels of setup time, as per the coding scheme above. The property of this coding is that all the utilities for a given attribute should sum to 0.

12. Finally, the coding scheme for Number of Tools is as shown below:
Similarly , the coding scheme for the 3 levels of the attribute Delivery Period is as shown below:
Delivery
Period in
Var 4
Var 5
Days
D18 1 1
D22
D28 -1 -1
Finally, the coding scheme for Number of Tools is as shown below:
Number of
Var 6
Var 7
Tools 1 T4 1 T8
T10 -1 -1

13. Thus, seven variables var 1 to var 7 are used to represent the 4 levels of Setup Time (S3,S6,S9 and S12), 3 levels of Delivery Period (D18, D22 and D28), and 3 levels of Number of Tools (T4, T8 and T10). All the 7 variables are independent variables in the regression run. Var 8 is the rating of each combination given by a respondent, and forms the dependent variable for the regression run.
If the conjoint analysis is run as a regression model, the rating (which is a reverse of ranking) is used as a dependent variable. All combinations from the first to the thirty sixth were ranked by the respondent. Rank 1 can be considered as highest rating and given a rating of 36. Rank 2 can be given a rating of 35, and so on. Strictly speaking, this is not an interval scale rating, and should have only ordinal interpretation.

14. The complete input data recoded for a regression run on SPSS is in Fig
The complete input data recoded for a regression run on SPSS is in Fig. 2 (reproduced below): File: Conjoint Analysis.sav
Table contd on next slide

15. Table contd… Remaining part of Fig 2

16. Output and its Interpretation
If run as a regression model using SPSS, the partial output is shown in Fig 3:

17. Variables 1 to 7 are treated as independent variables
Variables 1 to 7 are treated as independent variables. Now, the column titled ‘B’ (the unstandardized regression coefficients column) provides the part utility of each level of attributes.
For example, Setup Time of S3 (3 minutes) is represented by variable 1 as per our coding scheme. Its utility is equal to 5.5 (looking under column B of Fig 3, for variable 1).
Similarly, the utility for variable 2 representing S6 (Setup Time of 6 minutes) is 4.16 and for variable 3 representing S9, it is –1.05. The utility for the fourth level of Setup Time (S12), is not in the table, but is derived from the property of this coding, that all the utilities for a given attribute should sum to 0. Thus, utility for S12 should be equal to –( ), or –8.61.

19. Utilities Table for Conjoint Analysis
Attribute
Level
Part
Range of
Utility
Utilities y 1
Setup Time in S3
5.5
(Max
.-Min.)
minutes S6
4.2
=5.5-(-8.6) S9
-1.1
=14.1
S12
-8.6
for Setup Time 2
Delivery Period
D18
3.3
(Max
.-Min.)
in Days
D22
1.3
=3.3-(-4.6)
D28
-4.6
=7.9
for Delivery
Period. 3
Number of T4
-10.3
(Max
.-Min.)
Tools T8
1.6
=8.7-(-10.3)
(Flexibility)
T10
8.7
=19.0
for
No.of Tools

20. Now, with the part utilities of every level of every attribute available to us, we can come to several conclusions. First, we can conclude that machine flexibility is the most important attribute for this customer.
There are two indicators for this. One, the range of utility values is highest (19.0) for number of tools (flexibility). Two, the highest individual value of utility for any level of any attribute is 8.7, for T10 (number of tools = 10). Both these figures indicate that number of tools is the most important attribute at given levels of attributes.
The Setup Time seems to be the second most important attribute, as its range of utilities is 14.1, as shown in the above table. The last attribute in relative importance is the Delivery Period, with a utility range of 7.9.

21. Combination Utilities
We can also pick up one attribute level from each attribute and combine their part utilities to calculate the total utility of the combination. For example, S3, D18 and T4 have a combined utility of = Similarly, S3, D22 and T4 have a combined utility of = -3.5.
If we want the best combination, we pick the highest utilities from each attribute, and add them. S3+D18+T10 in this case is the most preferred combination with a combined utility of = The next best combination is S6+D18+T10, with a combined utility of , or 16.2.

22. Individual Attributes
We can also check what difference in utility a change of one level in one attribute makes. For example, S3 to S6 (Setup time change from 3 to 6 minutes) induces only a 1.3 units drop in utility, but it gets progressively more at the next stage –S6 to S9 has a difference in utility of 5.3.
Similarly, increase in Delivery Period from 18 to 22 days costs 2.0 units( ) of utility drop, whereas 22 to 28 days causes 5.9 units of drop in utility (1.3-(-4.6)).
Finally, Number of tools causes a drastic change in utility of 11.9 units from T8 to T4, and a significant drop in utility by 7.1 units from T10 to T8.