12 multidimensional conjoint

7/28/2019 12 Multidimensional Conjoint

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Multidimensionalscaling and

conjoint analysis

Dr James Abdey

Overview

Multidimensional scaling

Formulate the problem

Obtain input data

Decide on the number of

dimensions

Conjoint analysis


Construct the stimuli

Select a conjoint analysis

procedure

Overview

Multidimensional scaling allows the perceptions

and preferences of consumers to be clearly

represented in a spatial map

Conjoint analysis helps to determine the relative

importance of attributes that consumers use in

choosing products
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conjoint analysis

Dr James Abdey

Overview



Obtain input data


dimensions

Conjoint analysis




procedure


Specify the purpose for which the MDS resultswould be used

Select the brands or other stimuli to be included in

the analysis. The number of brands or stimuliselected normally varies between 10 and 20

The choice of the number and specific brands or

stimuli to be included should be based on the

statement of the market research problem, theory

and the judgement of the researcher
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conjoint analysis

Dr James Abdey

Overview



Obtain input data


dimensions

Conjoint analysis




procedure

Example: Similarity judgements on

pairs of mineral water brands

Perception data: direct approaches. In direct

approaches to gathering perception data, therespondents are asked to judge how similar or

dissimilar the various brands or stimuli are, using

their own criteria, i.e. similarity judgements

Very Very

dissimilar similar

Evian vs. Perrier 1 2 3 4 5 6 7

Volvic vs. Perrier 1 2 3 4 5 6 7...

......

......

......

...

Evian vs. Volvic 1 2 3 4 5 6 7

The number of pairs to be evaluated is n(n 1)/2,

where n is the number of stimuli
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conjoint analysis

Dr James Abdey

Overview



Obtain input data


dimensions

Conjoint analysis




procedure

Obtain input data

Perception data: derived approaches. Derived

approaches to collecting perception data areattribute-based approaches requiring the

respondents to rate the brands or stimuli on the

identified attributes using semantic differential or

Likert scales, for example:

Tastes pure Not taste pure...

...

Pleasant tasting Unpleasant tasting

If attribute ratings are obtained, a similarity

measure (such as Euclidean distance) is derived for

each pair of brands
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conjoint analysis

Dr James Abdey

Overview



Obtain input data


dimensions

Conjoint analysis




procedure

Obtain input data direct vs.

derived approaches

The direct approach has the following advantages

and disadvantages:

The researcher does not have to identify a set ofsalient attributes

The disadvantages are that the criteria areinfluenced by the brands or stimuli being evaluated

Furthermore, it may be difficult to label thedimensions of the spatial map
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conjoint analysis

Dr James Abdey

Overview



Obtain input data


dimensions

Conjoint analysis




procedure

Obtain input data direct vs.

derived approaches

The attribute-based approach has the following

advantages and disadvantages:

It is easy to identify respondents with homogeneous

perceptions

The respondents can be clustered based on theattribute ratings

It is also easier to label the dimensions

A disadvantage is that the researcher must identifyall the salient attributes, a difficult task


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conjoint analysis

Dr James Abdey

Overview



Obtain input data


dimensions

Conjoint analysis




procedure

Preference data

Preference data order the brands or stimuli in termsof respondents preference for some property

A common way in which such data are obtained is

through preference rankings

Alternatively, respondents may be required to make

paired comparisons and indicate which brand in a

pair they prefer

Another method is to obtain preference ratings for

the various brands
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conjoint analysis

Dr James Abdey

Overview



Obtain input data


dimensions

Conjoint analysis




procedure

Decide on the number of dimensions

A prioriknowledge: Theory or past research may

suggest a particular number of dimensions

Interpretability of the spatial map: Generally, it is

difficult to interpret configurations or maps derived in

more than three dimensions

Ease of use: It is generally easier to work with

two-dimensional maps or configurations than with

those involving more dimensions

Statistical approaches: For the sophisticated user,

statistical approaches are also available for

determining the dimensionality
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conjoint analysis

Dr James Abdey

Overview



Obtain input data


dimensions

Conjoint analysis




procedure

A spatial map

Each point in the spatial map represents a brand,

allowing similarities of perceptions or perceptions tobe determined

x

x

x

x

x

x

x

x

1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0

1.0

0.5

0.0

0.5

1.0

1.5

Spatial map of brands

Dimension 1

Dimension2
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conjoint analysis

Dr James Abdey

OverviewMultidimensional scaling


Obtain input data


dimensions

Conjoint analysis




procedure

Basic concepts in conjoint analysis

Conjoint analysis attempts to determine the relative

importance consumers attach to salient attributes

and the utilities they attach to the levels of attributes

The respondents are presented with stimuli that

consist of combinations of attribute levels and askedto evaluate these stimuli in terms of their desirability

Conjoint procedures attempt to assign values to the

levels of each attribute so that the resulting values

or utilities attached to the stimuli match, as closely as

possible, the input evaluations provided by the

respondents
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conjoint analysis

Dr James Abdey



Obtain input data


dimensions

Conjoint analysis




procedure

Formulate the problem Identify the attributes and attribute levels to be

used in constructing the stimuli

The attributes selected should be salient in

influencing consumer preference and choice and

should be actionable

A typical conjoint analysis study involves six or sevenattributes

At least three levels should be used, unless the

attribute naturally occurs in binary form (two levels),such as convertible and non-convertible cars

The researcher should take into account the attribute

levels prevalent in the marketplace and the

objectives of the study
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conjoint analysis

Dr James Abdey



Obtain input data


dimensions

Conjoint analysis




procedure


In the pairwise approach, also called two-factor

evaluations, the respondents evaluate two attributes

at a time until all the possible pairs of attributes have

been evaluated

In the full-profile approach, also called

multiple-factor evaluations, full or complete profiles

of brands are constructed for all the attributes.

Typically, each profile is described on a separate

index card

M l idi i l


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conjoint analysis

Dr James Abdey



Obtain input data


dimensions

Conjoint analysis




procedure

Mobile phone attributes

Assume three mobile phone attributes of interest:

battery life, screen size and weight

Assume each attribute has three different levels,

coded 1, 2 and 3:

Battery life: Long, medium, short

Screen size: Large, medium, small

Weight: Heavy, medium, light

M ltidi i lM bil h fil d h i
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conjoint analysis

Dr James Abdey



Obtain input data


dimensions

Conjoint analysis




procedure

Mobile phone profiles and their

ratings

Profile Attribute levels

number Battery life Screen size Weight Preference

rating

1 1 1 1 9

2 1 2 2 7

3 1 3 3 5

4 2 1 2 6

5 2 2 3 5

6 2 3 1 67 3 1 3 5

8 3 2 1 7

9 3 3 2 6

MultidimensionalS l j i l i d
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conjoint analysis

Dr James Abdey



Obtain input data


dimensions

Conjoint analysis




procedure

Select a conjoint analysis procedure

The basic conjoint analysis model may be

represented by the following formula:

U(X) =

m

i=1

ki

j=1

ijxij

where

U(X) = overall utility of an alternative ij = the part-worth contribution or utility associated

with the j-th level (j = 1, 2, . . . , ki) of the i-th attribute(i = 1, 2, . . . , m)

xij = 1 if the j-th level of the i-th attribute is present, 0otherwise

ki = number of levels of attribute i m = number of attributes

MultidimensionalS l t j i t l i d
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conjoint analysis

Dr James Abdey



Obtain input data


dimensions

Conjoint analysis




procedure


The importance of an attribute, Ii, is defined in

terms of the range of the part-worths, ij, across

the levels of that attribute:

Ii =

max(ij)min(ij)

for each i

The attributes importance is normalised to

ascertain its importance relative to other attributes,Wi:

Wi =Ii

mi=1 Ii

such that

m

i=

1

Wi = 1

The simplest estimation procedure, and one which is

gaining in popularity, is dummy variable

regression. If an attribute has ki levels, it is coded in

terms of ki 1 dummy variables

MultidimensionalS l t j i t l i d
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conjoint analysis

Dr James Abdey



Obtain input data


dimensions

Conjoint analysis




procedure


The estimated model may be represented as:

U = b0 + b1X1 + b2X2 + b3X3 + b4X4 + b5X5 + b6X6

where

X1, X2 = dummy variables representing battery life X3, X4 = dummy variables representing screen size X5, X6 = dummy variables representing weight

For battery life the attribute levels were coded as

follows:

X1 X2Level 1 1 0

Level 2 0 1

Level 3 0 0

MultidimensionalMobile phone data coded for d mm
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conjoint analysis

Dr James Abdey



Obtain input data


dimensions

Conjoint analysis




procedure

Mobile phone data coded for dummy

variable regression

Preference Attribute levels

ratings Battery life Screen size Weight

Y X1 X2 X3 X4 X5 X69 1 0 1 0 1 0

7 1 0 0 1 0 15 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 07 0 0 0 1 1 0

6 0 0 0 0 0 1

MultidimensionalSelect a conjoint analysis procedure
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conjoint analysis

Dr James Abdey



Obtain input data


dimensions

Conjoint analysis




procedure


The levels of the other attributes were coded

similarly. The parameters were estimated as follows:

b0 = 4.222 b4 = 0.667b1 = 1.000 b5 = 2.333b2 = 0.333 b6 = 1.333

b3 = 1.000

Given the dummy variable coding, in which level 3 is

the base level, the coefficients may be related to

the part-worths:

11 13 = b1

12 13 = b2

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scaling andconjoint analysis

Dr James Abdey



Obtain input data


dimensions

Conjoint analysis




procedure


To solve for the part-worths, an additional

constraint is necessary

11 + 12 + 13 = 0

These equations for the first attribute, battery life,

are:

11

13 = 1.00012 13 = 0.333

11 + 12 + 13 = 0

Solving these equations, we get:

11 = 0.778

12 = 0.556

13 = 0.222

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Dr James Abdey

Overview



Obtain input data


dimensions

Conjoint analysis




procedure


The part-worths for other attributes can be estimated

similarly

For screen size we have:

21 23 = b3

22

23 = b4

21 + 22 + 23 = 0

For the third attribute, weight, we have:

31 33 = b5

32 33 = b6

31 + 32 + 33 = 0

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Dr James Abdey

Overview



Obtain input data


dimensions

Conjoint analysis




procedure


The relative importance weights were calculated

based on ranges of part-worths, as follows:

Sum of ranges of part-worths

= (0.778 (0.556)) + (0.445 (0.556))

+(1.111 (1.222))

= 4.668

Relative importance of battery life = 1.3344.668 = 0.286

Relative importance of screen size = 1.0014.668 = 0.214

Relative importance of weight = 2.3334.668 = 0.500

Multidimensionalli dAssumptions and limitations of
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Dr James Abdey

Overview



Obtain input data


dimensions

Conjoint analysis




procedure

Assumptions and limitations of

conjoint analysis

Conjoint analysis assumes that the importantattributes of a product can be identified

It assumes that consumers evaluate the choice

alternatives in terms of these attributes and make

trade-offs

The trade-off model may not be a good

representation of the choice process

Another limitation is that data collection may be

complex, particularly if a large number of attributes

are involved and the model must be estimated at the

individual level
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12 multidimensional conjoint

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