conjoint analysis

Conjoint Analysis

Formulate the ProblemSneaker Attribute and LevelsAttribute Level No DescriptionSole 1 Rubber

2 Polyurethane3 Plastic

Upper 1 Leather2 Canvas3 Nylon

Price 1 30 USD2 60 USD3 90 USD

CONSTRUCT THE STIMULI- PAIRWISE APPROACH

UPPER

SOLE

RUBBER POLYURETHANE

PLASTIC

LEATHER

CANVAS

NYLON

PRICE

SOLE

RUBBER POLYURETHANE

PLASTIC

30 USD

60 USD

90 USD

UPPER

PRICE

30 USD 60 USD 90 USD

LEATHER

CANVAS

NYLON

Full-Profile Approach to Collecting Conjoint Analysis

EXAMPLE OF A SNEAKER PRODUCT PROFILE

SOLE MADE OF RUBBERUPPER MADE OF NYLONPRICE 30 USD

CodingX one X two

Level 1 1 0Level 2 0 1Level 3 0 0

Sneaker Profiles and their Ratings

ATTRIBUTE LEVELSPROFILE NO.

SOLE UPPER PRICE PREFERENCE RATINGS

1 1 1 1 92 1 2 2 73 1 3 3 54 2 1 2 65 2 2 3 56 2 3 1 67 3 1 3 58 3 2 1 79 3 3 2 6

Conjoint Analysis Model

Where

For us

Sneaker data coded for Dummy Variable Regression

Preference ATTRIBUTES Ratings SOLE UPPER PRICE Y 9 1 0 1 0 1 0 7 1 0 0 1 0 1 5 1 0 0 0 0 0 6 0 1 1 0 0 1 5 0 1 0 1 0 0 6 0 1 0 0 1 0 5 0 0 1 0 0 0 7 0 0 0 1 1 0 6 0 0 0 0 0 1

The model estimated may be presented as:

where

Estimation of the parameters

1

0.667 2.333

Context of dummy variables•Given the dummy variable coding in which

level 3 is the base level, the coefficients may be reduced to part worths

•Each dummy variable coefficient represents the difference in the part worth for that level minus the part worth for the base level. For sole we have the following:

•To solve for the part-worths, an additional constraint is necessary. The part-worths are estimated on an interval scale, so the origin is arbitrary. Therefore the additional constraint that is imposed is of the form:

α11 + α12 + α13 = 0

These equations for the first attribute, Sole, are:

= -0.333

Soα11 = 0.778

α12 = −0.556

α13 = −0.222

Similarly we can solve for other attributes

RESULTSLEVEL

ATTRIBUTE No. Description Utility Importance

Sole 3 Rubber 0.7782 Polyurethane -0.5561 Plastic -0.222 0.286

Upper 3 Leather 0.4452 Canvas 0.1111 Nylon -0.556 0.214

Price 3 30 USD 1.1112 60 USD 0.1111 90 USD -1.222 0.500

Part-worthsDifference between

the highest and lowest Highest 0.778 1.334Lowest -0.556

-0.222Highest 0.445

0.111lowest -0.556 1.001Highest 1.111

0.111Lowest -1.222 2.333

sum of part-worths 4.668

Relative Importance of attributesSOLE 1.334/4.668=0.286

UPPER 1.001/4.668=0.214

PRICE 2.333/4.668=0.5

Preference for Attribute Levels

Rubber Polyurethane Plastic

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Sole

Sole

Preference for Attribute Levels

Leather Canvas Nylon

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Upper

Upper

Preference for Attribute Levels

30 USD 60 USD 90 USD

-1.5

-1

-0.5

0

0.5

1

1.5

Price

Price

Assessing Reliability and Validity•Look at the R square•Test-retest reliability•If an aggregate analysis has been

conducted, the estimation sample can be split and conjoint analysis conducted on each sub-sample. The results can be compared across sub-samples to assess the stability of conjoint analysis solution.

Sneaker data coded for Dummy Variable Regression

Preference ATTRIBUTES Ratings SOLE UPPER PRICE Y R Pl 𝑋3 𝑋4 𝑋5 𝑋6 9 1 0 1 0 1 0 7 1 0 0 1 0 1 5 1 0 0 0 0 0 6 0 0 1 0 0 1 5 0 0 0 1 0 0 6 0 0 0 0 1 0 5 0 1 1 0 0 0 7 0 1 0 1 1 0 6 0 1 0 0 0 1

Estimation of the parameters

𝑏0 = 3.889 𝑟= 1.333 𝑝𝑙 = 0.333 𝑏3 = 1 𝑏4 = 0.667 𝑏5 =2.333 𝑏6 = 1.333

These equations for the first attribute, Sole, are:

α11 − α12 = 𝑏1 = 1 α13 − α12 = 𝑏2= 0.333

Sneaker data coded for Dummy Variable Regression

Preference ATTRIBUTES Ratings SOLE UPPER PRICE Y P Pl 𝑋3 𝑋4 𝑋5 𝑋6 9 0 0 1 0 1 0 7 0 0 0 1 0 1 5 0 0 0 0 0 0 6 1 0 1 0 0 1 5 1 0 0 1 0 0 6 1 0 0 0 1 0 5 0 1 1 0 0 0 7 0 1 0 1 1 0 6 0 1 0 0 0 1

Estimation of the parameters

𝑏0 = 3.889 𝑃= −1.333 𝑝𝑙 = −1 𝑏3 = 1 𝑏4 = 0.667 𝑏5 =2.333 𝑏6 = 1.333

These equations for the first attribute, Sole, are:

α12 − α11 = 𝑏1 = −1.333 α13 − α11 = 𝑏2= -1.0