## Conjoint analysis

Conjoint analysis is a method of portraying consumers' decisions realistically as a tradeoff among multiattribute products or services. Conjoint analysis helps us to understand how people develop preferences for products or services. It is based on the simple notion that consumers evaluate the utility or value of something by combining the separate amounts of utility provided by each attribute.

It is closely related to traditional experimentation. In situations where people are involved we often need to conduct experiments with factors we can control. For example, should a chocolate bar be slightly sweet to the taste or very sweet? Should it be promoted as a Slimmers' product or not? What price should be asked for the product?

In conjoint analysis the use of experimental design in the analysis of consumer decisions has two objectives. First, the experiments may try to assess how the

TABLE 10.10

Importance of factors in standard of living analysis

Factor 1 |
Factor 2 |
Factor 3 | ||

SS loadings |
1.644996 |
1.3791295 |
1.2124108 | |

Proportion variation |
0.274166 |
0.2298549 |
0.2020685 | |

Cumulative variation |
0.274166 |
0.5040209 |
0.7060894 | |

The degrees of freedom for the model is 0. | ||||

Uniquenesses | ||||

Consumption Doctors |
Infant mortality |
TV |
Cars Phones | |

0.08042417 0.7765078 |
0.3057129 |
0.3231836 |
0.1644488 0.1131866 | |

Loadings | ||||

Factor 1 |
Factor 2 |
Factor 3 | ||

Consumption |
0.755 |
0.588 | ||

Doctors |
0.108 |
0.460 | ||

Infant mortality |
-0.825 | |||

TV |
0.176 |
0.120 |
0.795 | |

Cars |
0.891 |
0.161 |
0.126 | |

Phones |
0.481 |
0.665 |
0.461 | |

Obtained with the aid of S-Plus for Windows5 using principal axis method. |

TABLE 10.10

Importance of factors in standard of living analysis sweetness of the chocolate bar contributes to the willingness of the consumer to buy it. It may also seek to assess how much a change in the willingness to buy can be accounted for by differences between levels of sweetness. Second, the experiments may seek to establish a valid model of consumer judgements that is useful in predicting the consumer acceptance of any combination of attributes, even those not originally evaluated by the consumer.

Conjoint analysis has been used in the pharmaceutical industry for product positioning close to launch where the product attributes were not changeable. However, it is now used earlier in product development to help define clinical end-points, and with input into go/no-go decisions.6

### EXAMPLE

In a furniture polish concept-testing experiment, each respondent has been told about the properties of eight dummy cans of polish to rank choices in order of preference for purchase. The responses for two respondents are shown in Table 10.11.

Size |
Properties |
Brand |
Respondent 1 |
Respondent 2 |

Small |
A |
Alpha |
1 |
1 |

A |
Beta |
2 |
2 | |

B |
Alpha |
5 |
6 | |

B |
Beta |
6 |
5 | |

Large |
A |
Alpha |
3 |
4 |

A |
Beta |
4 |
3 | |

B |
Alpha |
7 |
7 | |

B |
Beta |
8 |
8 |

For simplicity, in applying the technique we will assume an additive model is appropriate and that the overall preference for a combination of attributes is represented as:

Preference sib = PWs + PWi + PWb where the overall preference for a combination of size, properties and brand (Preference sib) is the sum of PWs, PWi, and PWb, the estimated part-worths for the levels of size, properties and brands, respectively.

In order to calculate the coefficients, we have to specify the composition rules and if the additive rule strictly holds, a simple difference from the mean (ANOVA) should apply. The average rank of the eight combinations is 4.5 and we calculate the impact of each factor. For example, the average ranks for the two levels of size

Small = (1 + 2 + 5 + 6)/4 = 3.5 Large = (3 + 4 + 7 + 8)/4 = 5.5

Figures for properties and brand are similarly calculated. Then, for respondent 1 the average ranks and deviations for each factor from the overall average rank (4.5) are as shown in Table 10.12.

Higher rank and a more preferred stimulus are usually given a smaller number so the next step is to reverse all the signs so that the positive part-worths now indicate higher preference. Coefficients are then calculated using the following method:

TABLE 10.12

Average ranks and deviations for respondent 1

TABLE 10.12

Average ranks and deviations for respondent 1

Factor level |
Average rank |
Deviation |

Small |
3.5 |
-1 |

Large |
5.5 |
+1 |

A |
2.5 |
-2 |

B |
6.5 |
+2 |

Alpha |
4.0 |
-.5 |

Beta |
5.0 |
+.5 |

• Square the deviations and find their sum (in this case the total is 10.5).

• Multiply each squared deviation by a standardising value calculated as the number of levels divided by the sum of the squared deviations, in this case (6/10.5) or 0.571.

• Take the square root of the standardised squared deviation to get the actual coefficient.

By way of illustration, for the first level of property (A), the deviation of 2 (reversing the sign!) is squared and then multiplied by 0.571 to obtain 2.284. To calculate the coefficent for this level, we then take the square root of 2.284 to obtain a coefficient of 1.511. This process yields the coefficients for each level, as shown in Table 10.13.

The part-worth estimates are in a common scale, so the relative importance of each factor can be computed directly. The importance of a factor is represented by the range of its levels. The ranges are then standardised by dividing each range by the sum of the ranges. For example, for respondent 1, the ranges are 1.512 and .756. The relative importance for size, properties and brand are calculated as 1.512/5.294, 3.022/5.294, and .756/5.294 or 29%, 57% and 14% respectively.

We can follow the same procedures for the second respondent and calculate the average ranks, deviations and coefficients for each level (Table 10.14).

To examine the ability of the model to predict the actual choices of the respondents, we predict performance order by summing the coefficients for the different

Size |
Property |
Brand | ||

Small |
Large |
AB |
Alpha |
Beta |

.756 |
-.756 |
1.51 -1.51 |
.378 |
-.378 |

Factor level |
Average rank |
Deviation |
Coefficent |

Small |
3.5 |
-1 |
.77 |

Large |
5.5 |
+1 |
-.77 |

A |
2.5 |
-2 |
1.55 |

B |
6.5 |
+2 |
-1.55 |

Alpha |
4.0 |
-.5 |
0.0 |

Beta |
5.0 |
+.5 |
0.0 |

Product description |
Predicted value | ||||

Size |
Properties |
Brand |
Part-worth total |
Predicted rank | |

Small |
A |
Alpha | |||

.756 |
+ 1. |
51 + |
.378 = |
2.644 |
1 |

Small |
A |
Beta | |||

.756 |
+ 1. |
51 + |
-.378 = |
1.888 |
2 |

Small |
B |
Alpha | |||

.756 |
+ -1 |
.51 + |
.378 = |
-.376 |
5 |

Small |
B |
Beta | |||

.756 |
+ -1 |
.51 + |
-.378 = |
= -1.132 |
6 |

Large |
A |
Alpha | |||

-.756 |
+ 1.51 + |
.378 = |
1.132 |
3 | |

Large |
A |
Beta | |||

-.756 |
+ 1.51 + |
-.378 = |
.376 |
4 | |

Large |
B |
Alpha | |||

-.756 |
+ -1 |
.51 + |
.378 = |
= -1.888 |
7 |

Large |
B |
Beta | |||

-.756 |
+ -1 |
.51 + |
-.378 = |
= -2.644 |
8 |

combinations of factor levels and rank ordering the resulting scores. The calculations for respondent 1 are shown in Table 10.15.

The predicted preference order can be compared to the respondent's actual preference order for a measure of predictive accuracy. The predictive preference orders for both respondents are shown in Table 10.16.

In the case of respondent 2, since the weights of zero were calculated for the brand name the compositional rule is unable to predict a difference between brands within the ingredient and can size combinations. Brand name may be a

TABLE 10.16

Predictive preference orders: both respondents

TABLE 10.16

Predictive preference orders: both respondents

Original rank |
Predicted rank order | |

Respondent 1 |
Respondent 2 | |

1 |
1 |
1.5 |

2 |
2 |
1.5 |

3 |
3 |
3.5 |

4 |
4 |
3.5 |

5 |
5 |
5.5 |

6 |
6 |
5.5 |

7 |
7 |
7.5 |

8 |
8 |
7.5 |

random choice, given size and properties. Moreover, when two or more stimuli have equal total-worth predictions, the rank orders are averaged.

The example illustrated assumes an additive model only as the base for the compositional rule. Original rankings assumed that no interaction effect occurs: for example, the respondent prefers Alpha and normally prefers property A over B. If interaction is thought to have a serious effect, steps have to be taken in the analysis to allow for this.

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