Conjoint Analysis

Dr. Milne

Basic Problem

• Metric/non-metric input (preferences) converted to interval scaled output (utility)

• I like lobster more than catfish, which I like more than octopus. What does it mean to say that my liking for lobster over catfish is greater than my liking for salmon over tuna?– An interval level scale for preferences is

needed.

Parting of ways• Psychometrics: rigorous and idealistic• Marketing research: approximate and pragmatic• Conjoint is becoming very much removed from theoretical

roots– Numerical measurement of behavior– Additive– Compound stimuli– Factorial designs– Testing is rapidly ignored– Moving from non-metric to metric

• Conjoint measurement vs. conjoint analysis

Managerial Uses of Conjoint Analysis

1. Find the product with the optimum set of features

2. Determine the relative importance of each feature in consumer choices

3. Estimate market share among products4. Identify market segments5. Evaluate the impact of price changes or

other marketing mix decisions.

A Simple Example

• Scenario: a man buying a basic cartridge camera (faced with eight choices)– Major brand $80– Major brand $50– Major brand $30– Major brand $20– Store brand $80– Store brand $50– Store brand $30– Store brand $20

Respondent’s Ranking of Eight Camera BrandsPrice($) Major Brand Store Brand Average Rank20 8 6 7.030 7 4 5.550 5 2 3.580 3 1 2.0

Average rank 5.75 3.25

Note, 8 is most preferred and 1 is least preferred

Respondent’s Utility Values of Eight Camera BrandsPrice($) Major Brand Store Brand Average Rank Utility20 8 6 7.0 1.0030 7 4 5.5 .7050 5 2 3.5 .3080 3 1 2.0 .00

Average rank 5.75 3.25Utility .75 .25

Rank Order of Respondent’s Total Utilities.Price($) Major Brand Store Brand Marginal Utility20 8 (1.75) * 6 (1.25) 1.0030 7 (1.45) 4 (.95) .7050 5 (1.05) 2 (.55) .3080 3 (.75) 1 (.25) .00

Marginal Utility .75 .25

* 1.75 = .75 (major brand utility) + 1.00 ($20 utility)

Utility Values for Three RespondentsAdam Bob Carl

Brandx .60 .80 .33y .80 .35 .33z .40 .10 .33Price ($)20 1.00 .70 1.0030 .80 .60 .8050 .00 .20 .5080 .00 .00 .00Coupon Value($)2 .20 .20 .205 .75 .20 .3010 .95 .60 .80

Utility Values for Respondent Adam

Brand (x) .60 (y) .80 (z) .40Price ($30) .80 ($20) 1.00 ($50) .00Coupon Value ($2) .20 ($2) .20 ($2) .20

Total Utility 1.60 2.00 .60

Respondent’s Estimated Preferences for Three Camera Brands

Brand Price ($) Coupon Value ($)%Preferring

X 40 5 50

Y 20 2 35

Z 80 10 15

Effects of Change in Marketing Mix on Respondents’ Preferences

% Preferring Each % Preferring Each

Brand for Original Brand After X’s

Brand Situation Change in Price Change (%)

X 50 55 +5

Y 35 35 0

Z 15 10 -5

Conjoint Analysis

• Decompositional model—An individual’s overall preference or evaluation for a product (expressed as a combination of attributes) is decomposed by relating the know attributes to the evaluation.

• Best suited for understanding consumers’ reactions to and evaluations of predetermined attribute combinations that represent potential products or services.

• An applied method used in marketing research

Which of the two flights described below would you chose?

A B-707 flown by New Zealand Air that will depart within two hours of the time you would like to leave and that is often late in arriving in Sydney. The plane will make two intermediate stops, and it is anticipated that it will be 50% full. Flight attendants are “warm and friendly” and you would have a choice of multiple movies for entertainment.

A B-747 flown by Quantas that will depart within four hours of the time you would like to leave and that is almost never late in arriving in Sydney. The flight is nonstop, and it is anticipated that the plane will by 90% full. Flight attendants are “cold and curt” and only magazines are provided for entertainment.

Compositional versus Decompositional Techniques

Compositional

Y = w1 X1 + w2 W2 Collect x1 and x2 and relate it to Y.

Estimate weights to create a predictive model

Decompositional

Y = w1 X1 + w2 W2 Collect Y and relate it to X1 and X2

which are already fixed, and determine weights.

Note: computationally similar, but design and conceptually very distinct.

Unique Features of Conjoint

• Specifiying the Conjoint Variate– The only data provided by the subject is the

dependent variable. The independent variable is prespecified.

• Separate Models for Each Individual– A unique model is specified for each individual.– Predictive accuracy is made for each individual.

• Not limited to linear relationships.

Objectives

• To determine the contributions of predictor variables and their respective values to the determination of consumer preferences.

• To establish a valid model of consumer judgments useful in predicting the consumer acceptance of any combination of attributes, even those not originally evaluated by consumers.

Questions to resolve

• Defining the total worth of the object– Need to select attributes that accurately reflect

judgment process.– Need to include both potential positive and

negative factors• Specifying the determinant factors

– Attributes must also be selected so that they differentiate between the objects. These are the key to decision making.

Research ProblemDefine Stimuli (factors and levels)Basic model formData collectionFull profile Trade off PairwiseData Collection (Create stimuli)Factorial design Fractional factorialSelect preference measureForm of Survey AdministrationAssumptionsSelect estimation techniqueEvaluate resultsInterpret resultsValidateApply results

Conjoint Analysis Decision Process

This technique requires a lot of upfront work to think through the design, data collection, and analysis options.

Determining Factors and Selecting the Levels for each Factor

• Actionable measures• Communicable measures• Number of attributes• Balanced number of attributes• Rate of attribute levels• Attribute multicollinearity

Specifying Model form

• Additive – add up the values to each attribute (partworth) to obtain the overall worth of the model. This is the most common approach.

• Composition with interaction is possible –the sum may be more or less than the whole—but not as common and the prediction is not as good.

Level

Level

Level

Pref

eren

ce

Pref

eren

cePr

efer

ence

Linear Quadratic or idea

Part-worth

Selecting the Part-worth relationship

Trade-off Approach

$1.19 $1.39 $1.49 $1.69

Factor 1: Price

Generic

KX-19

Clean-all

Tidy-UPFa

ctor

2: B

rand

Nam

e

Pros: Easy, simple, few cognitive decisionsCons: Sacrifice in only see a few attributes at a time, large number of judgments, easy to get confused and pattern response, can’t use pictoral or non written stimuli, only non metric responses, can’t use fractional factorial designs.

Full Profile Approach

Brand Name : KX – 19Price : $ 1.19Form: PowderColor brightener: Yes

Shows all attributes at once

Pros: Better, more realistic, flexible scaling, fewer judgments.Cons: As the number of factors increases so does the possibility of information overload--can be overwhelming if have > 6 attributes. The order in which the factors are listed on the stimulus card may have an impact on the evaluation.

Paired Comparison

Brand Name: KX-19Price: $1.19Form: Powder

Brand Name: GenericPrice: $1.49Form: Liquid

VERSUS

A combination of approaches. Does not show all the attributes. It is similar to trade-off in that pairs are evaluated. But, like profile, the judgments are made about combinations of attributes. Approach used in adaptive conjoint analysis.

Creating Stimuli

• Factorial design – 4 variables with 4 levels each would result in 256 stimuli. (4x4x4x4).

• Fractional factorial design selects a sample of stimuli (16 in this case). Can only be used for estimating the main effects. The stimuli are chosen for orthogonality.– Designs are published. – Software can be used.

Two Fractional Factorial DesignsStimulus F1 F2 F3 F4 f1 f2 f3 f4

1 3 2 3 1 2 3 1 4

2 3 1 2 4 4 1 2 4

3 2 2 1 2 3 3 2 1

4 4 2 2 3 2 2 4 1

5 1 1 1 1 1 1 1 1

6 4 3 4 1 1 4 4 4

7 1 3 2 2 4 2 1 3

8 2 1 4 3 2 4 2 3

9 2 4 2 1 3 2 3 4

10 3 3 1 3 3 4 1 2

11 1 4 3 3 4 3 4 2

12 3 4 4 2 1 3 3 3

13 1 2 4 4 2 1 3 2

14 2 3 3 4 3 1 4 3

15 4 4 1 4 1 2 2 2

16 4 1 3 2 4 4 3 1

orgthogonal - no correlation among levels across attributes and balanced each level in a factors appears the same number of times.

Selecting a measure of consumer preference

Trade-off uses only ranking dataFull profile uses both ranking and rating dataMetric methods are easily analyzed and easily administered even by mail and allow conjoint estimation by multiple regression.For ranking data have 11 point scales for 16 or fewer stimuli and 21 point scale for greater than 16 stimuli.

Pencil and paper and computer based surveys. Computer Disks. Web pages.

Survey Administration

Assumptions

• Very few statistical assumptions• However, theory drives design, estimation,

and interpretation.

Estimation and Assessing Overall Fit

• Rank order calculated with MANANOVA or LINMAP

• Metric can be estimated with regression or special programs. The standardized betas are the part-worths.– Preference = b1 F1+b2 F2 + … + bn Fn

• Reliability can be estimated by correlating the predicted with the actual ratings for each individual.– Corr (pref, Y hat.)

Interpret Results

• Part worths are standardized Beta Weights so they can be compared.

• Relative importance of each factor should be calculated. Relative importance is the range of the partworths over the sum of the ranges across all factors.– B1H-B1L /{(B1H-B1L) + (B2H-B2L)+…+(BNH-BNL)}

Example: Packaged Soup

Factors Levels

Flavor Onion

Chicken

Veg

Calories 80

100

140

Salt Free Yes

No

Price 1.89

2.49

Dependent Variable is preference (0-10)

3x3x2x2 = 36 possibilities in a full factorial design

Model can be estimated using dummy variable regression where the estimated beta weights are utility preferences

Establish the Dummy Variables

D1 = 1 if onion, 0 = otherwise

D2 = 1 if chicken, 0 = otherwise

D3 = 1 if 80 calories, 0 = otherwise

D4 = 1 if 100 calories, 0 = otherwise

D5 = 1 if salt-free, 0 = otherwise

D6 = 1 if price $1.89, 0 = otherwise

Example: Onion, 80 calorie, Saltfree soup for $1.19 would be coded as

( 1 0 1 0 1 1)

Run Regressions for Each Individual

Y = B1 D1 + B2 D2 + B3 D3 + B4 D4 + B5 D5 + B6 D6 +

Card # Pref Dummy Coding

1 8 1 0 0 1 1 0

2 6 0 1 1 0 1 0

3 3 1 1 1 0 0 0

. . . . . . . .

. . . . . . . .

36 5 0 1 1 1 1 1

Check the fit for each regression for each individual

Calculate Ŷ for each individual

Corr ( Ŷ , Pref) for each individual

This is a measure of internal consistency to see if there is a strong relationship between the revealed preference and the stated preference. Include individuals with high correlations.

Standardized Beta weights are the part worths

Attributes Part worthFlavor onion 3.50

Chicken 0Vegetable3.58

Calories 80 2.17100 .67140 0

Salt Free Yes 1.89No 0

Price 1.19 .671.49 0

Note the partworths can be rescaled relative to each other. For example if onion = -.08, chicken= -3.58 and Veg = 0 adding 3.58 to each changes the coding to make chicken 0.

Utility for an Alternative = sum of the utilities

Utility

UtilityUtility

Utility

0

Chicken Onion Vegetable80 100 140

No Yes$1.89 $2.49

Flavor

Salt-FreePrice

Calories

Graphing Individual Part worths

Importance Weights

Attributes Range PercentFlavor 0 – 3.58 43%Calories 0 – 2.17 26%Salt 0 – 1.89 23%Price 0 - .67 8%

Total 8.30 100%

Aggregate Analysis

• Estimate market share for existing attribute combinations in the market– Simulate shifts in share with changes of existing

product combinations (Brand A with a higher price).– Estimate potential share that a new entrant might obtain

(with unique set of attributes)• Use the part worths to segment the market

with Cluster analysis.