代写 C graph statistic software Conjoint Analysis

Conjoint Analysis
MSCI581. Introduction to Management Science and Marketing Analytics
Ivan Svetunkov
LUMS, Room A58a i.svetunkov@lancaster.ac.uk
25/11/2019

Plan for the day
1. Recapfromthepreviouslectures;
2. ConjointAnalysis: 1. Introduction,
2. Assumptions,
3. Setup of the analysis,
4. Constructing models.

RECAP FROM THE PREVIOUS LECTURES

Recap from the previous lectures
From the Lecture 3:
• There are two types of data: primary and secondary;
• Collecting the primary one is more expensive, but sometimes also is more useful;
• When constructing the questionnaire, we should keep the aim in mind;
• Questions should:
• align with the aim;
• be easy to understand;
• be unambiguous;
• not lead to an answer;

Recap from the previous lectures
• Answers should:
• cover all options;
• not contain redundant options;
• be mutually exclusive;
• Use confidence interval approach for the optimal sample size determination;
• You can have other techniques if you have an appropriate rationale for them;
• We are quite aware of the limitations in the coursework, we will focus on the approach;
• In the ideal situation you should have a proper sample size;
• In our module we will accept simplifications, if they are acknowledged and properly discussed.

Recap from the previous lectures
• We have four types of scales: • Nominal,
• Ordinal, • Interval, • Ratio.
• They differ by the presence of the respective characteristics:
• Description,
• + Order,
• + Distance,
• + Origin.

Recap from the previous lectures
From the Lecture 4:
• When analysing data in different scales, we need to use different instruments;
• Graphical analysis: • Barplot,
• Tableplot,
• Histogram, • Boxplot,
• Scatterplot.

Recap from the previous lectures
• Univariate analysis:
• Mode,
• Mean,
• Median,
• Quantiles,
• Standard deviation,
• Coefficient of variation.
• What would you use for the data in nominal scale?

Recap from the previous lectures
• Multivariate analysis:
• Contingency table,
• Phi,
• Cramer’s V,
• Chi-square 𝜒2 ,
• Goodman-Kruskal’s γ,
• Kendall’s τ,
• Spearman’s correlation,
• Pearson’s correlation,
• Multiple correlation.
• Do all of these have range from -1 to 1?

CONJOINT ANALYSIS
See resources on Moodle

Conjoint analysis: Introduction
We want to launch a new product. E.g. laptops
• How do we know what specifically to produce?
• What characteristics laptops have?
• Price,
• Dimensions,
• HDD size,
• RAM size,
• OS,
• Colour, •…
How can we find out what consumers want?

Conjoint analysis: Introduction
How can we ask about the specific preferences?
• What do you prefer for the CPU of your laptop? • Intel Core i3 3.4GHz,
• Intel Core i3 4.0GHz,
• Intel Core i3 4.1GHz,
• Intel Core i5 4.0GHz,
• Intel Core i5 4.1GHz,
• Intel Core i5 4.2GHz,
• Intel Core i7 4.5GHz,
• Intel Core i7 4.7GHz,
• Intel Core i7 4.9GHz,
• Intel Core i9 4.4GHz,
• Intel Core i9 4.8GHz,
• Intel Core i9 5GHz,
Do we really need such level of detail?
How many attributes do we have for laptops?!
Can we measure all of them correctly?

Conjoint analysis: The trade-off choice
• Economic view:
• More alternatives is better than fewer,
• More sales per customer.
• Consumer psychology view:
• More alternatives overload perception,
• Less sales per customer,
• Only if:
• Products are difficult to compare,
• Products are complex,
• Consumers are uncertain or stressed.
We should be careful, when giving the alternatives

Conjoint analysis: Introduction
When we discuss product’s characteristics, we implicitly want to know their utility:
• •
If the attribute is important, it has high utility and people will pay more for it;
If it is less important, it has lower utility, lower value;
Consumers want the best features for the lowest possible price
If a company manages to measure the utility of features, it will get a competitive advantage.
Companies want to maximise their profits

Conjoint analysis : Introduction
What about price?
• Can we measure it correctly?
• Will respondents be honest about it?
• What will they select, when they have options:
We need a smarter way to estimate how important is each feature for the consumer!

Conjoint analysis: Introduction
The main idea – consumers are asked to make trade- off judgments:
• Which of the following laptops do you prefer?
• Please, rank the laptops by their attractiveness.
• etc.
Having collected such a data, we can:
• analyse it using statistics;
• construct a model of, for example, price from attributes…

Conjoint analysis: Basic assumptions
1. Theproductismadeupbyanumbersofattributes; • 𝐿𝑎𝑝𝑡𝑜𝑝 = 𝐶𝑃𝑈 + 𝑅𝐴𝑀 + 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑠 + 𝐶𝑜𝑙𝑜𝑢𝑟 + ⋯
2. Theutilityoftheproductisafunctionofthe utilities of the attributes;
• 𝑈 𝐿𝑎𝑝𝑡𝑜𝑝 = 𝑓 𝐶𝑃𝑈, 𝑅𝐴𝑀, 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑠, 𝐶𝑜𝑙𝑜𝑢𝑟, …
3. Utilitypredictsmarketbehaviour(rationality); • 𝐷𝑒𝑚𝑎𝑛𝑑 = 𝑓 𝑈 𝐿𝑎𝑝𝑡𝑜𝑝

Conjoint analysis: Advanced assumptions
1. Equalproductavailability
• We can easily buy both Macbook air and Macbook Pro,
2. Noout-ofstockconditions
• The product will not disappear from the market,
3. Consumerisawareofallalternatives
• Do you know all the options on the market when you
select a laptop?
4. Equalproductlaunchdate(orreplenishment)
• The sales of different products start at the same time.

Conjoint analysis: Setup
1. Definethelistofattributes:
• Use brainstorm, focus groups, interviews, judgment etc.
• Attributes should:
• Matter to consumers (do we need CPU frequency?);
• Be modifiable (i3 / i5 / i7 / i9);
2. Selectnumberoflevels(options)foreach attribute;
3. Definehypotheticalproductswiththeattributes:
• All combinations might be too much;
• Ideally products should have orthogonal designs.

Conjoint analysis: Setup
Orthogonal attributes
• IfiandjaretwooptionsoftheattributeAandkis
an option of the attribute B then:
• i.e. The probability of finding 𝐵 should be the 𝑘
same regardless of the selection of A.

Conjoint analysis: Setup
Orthogonal setup for laptops:
Product
Processor
Hard Drive
Monitor
1
Dual
SSD
11
2
Dual
SSD
13
3
Dual
SSD
15
4
Dual
Conventional
11
5
Dual
Conventional
13
6
Dual
Conventional
15
7
Dual HT
SSD
11
8
Dual HT
SSD
13
9
Dual HT
SSD
15
10
Dual HT
Conventional
11
11
Dual HT
Conventional
13
12
Dual HT
Conventional
15
13
Quad
SSD
11
14
Quad
SSD
13
15
Quad
SSD
15
16
Quad
Conventional
11
17
Quad
Conventional
13
18
Quad
Conventional
15

Conjoint analysis: Setup
• Products attributes must be mutually exclusive
• Example with laptop extras:
• Bonus spreadsheet software
• Bonus antivirus software
• What if we provide both?
• Attribute options should have unambiguous
meaning
Very subjective!
• Example with laptop price:
• Very cheap / Cheap / Moderate / Expensive / Very Expensive; • £300/£500/£750/£1000/…

Conjoint analysis: Setup
4. Designsurvey;
• Several options for the design:
• rank products;
• rate products (e.g. [0 – 100]);
• present products as pairs;
• In what scales the information will be measured?
• It is common to present products as different “cards”.

Conjoint analysis: Setup
Rate your preference
Laptop A
Processor: Quad Hard Drive: Conventional Monitor: 15
Laptop B
Processor: Dual Hard Drive: Conventional Monitor: 11
Laptop C
Processor: Dual Hard Drive: SSD Monitor: 15
___%
___%
___%

Conjoint analysis: Setup
Rank your preference
Laptop A
Processor: Quad Hard Drive: Conventional Monitor: 15
Laptop B
Processor: Dual Hard Drive: Conventional Monitor: 11
Laptop C
Processor: Dual Hard Drive: SSD Monitor: 15
v
v

Conjoint analysis: Setup
Tick the square to indicate your preference
Laptop A
Processor: Quad Hard Drive: Conventional Monitor: 15
Laptop B
Processor: Dual Hard Drive: Conventional Monitor: 11
#
#
#
#
#
#
#
#
I like A more than B
I like B more than A

Conjoint analysis: Setup
How much would you be willing to pay in comparison?
Laptop A
Processor: Quad Hard Drive: Conventional Monitor: 15
Laptop B
Processor: Dual Hard Drive: Conventional Monitor: 11
£850
£___

Conjoint analysis: Example

Conjoint analysis: Setup
Which of the cards is the best?
• Consider:
• What you want to collect,
• Audience,
• Efficiency,
• Ease of responding,
• Sensitivity to relevant factors,
• Insensitivity to irrelevant factors,
• Etc…

Conjoint analysis: Setup
Things to consider in the design:
• Don’t use too many levels:
• 3 to 5 should suffice;
• Too many levels will require too many observations;
• If some options are not included, you can interpolate;
• Use intuitively easy attribute levels
• E.g. avoid things like laptop noise: 25db / 30db / 35db;
• This might frustrate respondents and skew the results.

Conjoint analysis: Constructing models
5. Testsurveyandcarryitout; 6. Dotheanalysis:
• Regression, depending on the scale:
• Linear or non-linear multiple regression;
• Logistic regression;
• Multinomial logistic regression;
•…
• Hierarchical Bayes Estimation
• Machine learning techniques; •…
• But overall, use statistics!
Metric scales Nominal scale Ordinal scale
Random utility models

Conjoint analysis: Constructing models
Rating of laptops based on perception of different attributes
Item
Processor
Hard Drive
Monitor
Rating
1
Dual
SSD
11
55
2
Dual
SSD
13
60
3
Dual
SSD
15
65
4
Dual
Conventional
11
70
5
Dual
Conventional
13
80
6
Dual
Conventional
15
90
7
Dual HT
SSD
11
35
8
Dual HT
SSD
13
40
9
Dual HT
SSD
15
45
10
Dual HT
Conventional
11
10
11
Dual HT
Conventional
13
20
12
Dual HT
Conventional
15
5
13
Quad
SSD
11
80
14
Quad
SSD
13
70
15
Quad
SSD
15
50
16
Quad
Conventional
11
25
17
Quad
Conventional
13
25
18
Quad
Conventional
15
15

Conjoint analysis: Constructing models
Encode attributes into dummy variables (if n is the number of levels of an attribute use n-1 dummies):
• Processor: 2 Dummies (Dual HT, Quad – Dual not encoded)
• Hard Drive: 1 Dummy (SSD – Conventional not encoded)
• Monitor: 2 Dummies (13”, 15” – 11” not encoded)
• Too many levels, too many attributes would lead to estimation problems.
• Why?

Conjoint analysis: Constructing models
Regression model:
𝑅𝑎𝑡𝑖𝑛𝑔=𝑏 +𝑏 𝐷𝑢𝑎𝑙𝐻𝑇+𝑏 𝑄𝑢𝑎𝑑+𝑏 𝑆𝑆𝐷+𝑏 𝑆𝑐𝑟𝑒𝑒𝑛13+𝑏 𝑆𝑐𝑟𝑒𝑒𝑛15+𝑒 012345
Item
DualHT
Quad
SSD
Screen13
Screen15
Rating
1
0
0
1
0
0
55
2
0
0
1
1
0
60
3
0
0
1
0
1
65
4
0
0
0
0
0
70
5
0
0
0
1
0
80
6
0
0
0
0
1
90
7
1
0
1
0
0
35
8
1
0
1
1
0
40
9
1
0
1
0
1
45
10
1
0
0
0
0
10
11
1
0
0
1
0
20
12
1
0
0
0
1
5
13
0
1
1
0
0
80
14
0
1
1
1
0
70
15
0
1
1
0
1
50
16
0
1
0
0
0
25
17
0
1
0
1
0
25
18
0
1
0
0
1
15

Conjoint analysis: Constructing models
• Measure of importance within attributes (regression coefficients)
Processor
Mean
Lower 2.5%
Upper 97.5%
Dual
0.000
0.000
0.000
Dual HT
-44.17
-63.83
-24.50
Quad
-25.833
-45.49
-6.17
Hard Drive
Conventional
0.00
0.00
0.00
SSD
17.78
1.72
33.84
Monitor
11″
0.00
0.00
0.00
13″
3.33
-16.33
22.99
15″
-0.83
-20.49
18.83
• Any comments?
• An example of interpretation:
• SSD increases rating of the device on average by 18 points

Conjoint analysis: Constructing models
• Measure relative importance of attributes (Best – Worse)%
Processor
Mean
Lower 2.5%
Upper 97.5%
Dual
0.000
0.000
0.000
Dual HT
-44.17
-63.83
-24.50
Quad
-25.833
-45.49
-6.17
Hard Drive
Conventional
0.00
0.00
0.00
SSD
17.78
1.72
33.84
Monitor
11″
0.00
0.00
0.00
13″
3.33
-16.33
22.99
15″
-0.83
-20.49
18.83
Best
Worse
Difference
%
Processor
0.00
-44.17
44.16
66.81%
Hard Drive
0.00
17.78
17.77
26.89%
Monitor
3.33
-0.83
4.16
6.30%
Total
66.09

Conjoint analysis: Constructing models
Note that this was a model based on the answers of only one respondent!
• There are different options how to construct model for a sample:
• Construct a model for each respondent, then average out;
• Construct pool regression for all the respondents, ignoring their possible individuality;
• Construct mixed effects regression; •…

Conjoint analysis: Constructing models
What about the different types of utility functions?
• So far we have assumed the linear one. Is it realistic?
• Maybe non-linear model makes more sense…
• Also, there might be some interaction effects between
the attributes:
• Laptop with faster CPU and SSD is not the same as laptop with faster CPU + laptop with SSD…
• We can construct more advanced models, but we need more observations…

Conjoint analysis: Constructing models
Implicitly we assumed that utilities (preferences) are linearly increasing or decreasing.
• More types of conjoint models have been proposed:
Linear preference
Ideal-point preference
Highest preference
Ideal point xp Amount of attribute p
Part-worth (discreet) preference
Highest preference
Next highest
Lowest
Amount of attribute p
Amount of attribute p
j
pjp j
pjpp j
p jp
PPP
 p=1
 p=1
s= wy d= w(y−x) s= f(y)
 p=1
22
P attributes
j options with each attribute
yip desirability of pth attribute for the jth option sj respondents preference for jth option
dj2 is inversely related to sj
f is function denoting part worth p
Preference
Preference
Preference

CONCLUSIONS

Conclusions
• You should now:
• Be familiar with the idea of conjoint analysis,
• Be able to setup the conjoint analysis,
• Understand how to carry out the analysis,
• Be aware of the more advanced techniques.

Thank you for your attention!
Ivan Svetunkov
LUMS, Room A58a i.svetunkov@lancaster.ac.uk
Alisa Yusupova
LUMS, Room A48 a.yusupova@lancaster.ac.uk

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