Chapter2. CONJOINT ANALYSIS

1
Multivariate Analysis

Chapter2. CONJOINT ANALYSIS
Object
Attribute

Attribute
56
24
20
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???? ??? ??

• ??
• ????(??? ???? ??-????? 2? ??)?
• ????(?? ??)? ?? ??? ???? ??
• ????
• ????-???? ??
• ????-???? ??

Object
Attribute

Attribute

• ? Attribute ? ??? ??? ??
• ????? ??? ????
• Ideal Combination
• Optimal Combination

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???? ?? ??

• ?? ?? ?? ???? ????? Attribute ????? ??? ????
• Utility? ?????? ? ??? ??? ??? ???? ?? ??
• ????? ????? Attribute? ??? ???? ??? ? ??? ??? ?
  Attribute? Utility? ??? ? ??? Factorial Design?
  ??? ?? ?? ?
• Consider Jointly ???? ?? ?? ???? ?? ?? ??
  ???? ???? ???? ???? ??? ????? ????? ???? ??
• ???? ??? MDS
• ??? ???? ??? ????? ?? ??
• ??? ?? ??? ???? ??
• - ???? ?? ?? Attribute? Factorial
  Type?? ??
• - MDS ?? ??(?? Attribute)?? ???? ??? ??

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?? ??

• Attribute ????
• ?? (Level) ????? ??? ?
• ???? ?? ???? ?
• ???? ??? ???? ??? ?? ??? ?? ??? ????
• ?? 4?? 5?? ?? ?? ?? ??? ?? ?? ??
• Ex) ??, ??? 3???, ? ???? ??? ? ?? ?????, ??? ??
  ??? ?? 8?(2x2x2)
• ???? ??? ????
• ??? (Main Effects)
• ? ??(????) ??? ????? ????? ??? ??

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?? ??

• TFA (Two factor-At-Time-Approach) ???? ????
  Attribute? ?? ? ?
• ?? ??.
• FPA (Full-Profile Method) ????? ?? Attribute? ??
  ? ??
• ? ?? ??? ?? ???? ???
• Ex) ??, ??? 3???, ? ???? ??? ? ?? ?????, ??? ??
  ??? ?? 27?(3x3x3)
• 27? ?? ????????? ??? ???3???? ????? ??? ???
  ???? Attribute? ?? ?? ??
• ???? (Additive Model)
• ? ?? ??
• ?? ????? ??? ????? ???? ??? ???? ??
• ??? ??? ?? ??? ???? ? ? ?? ??? ???? ??
• ???? (Part-Worth)
• ???? ??? ??? ???? ???? ???? ?? ???? ? ??? ?? ??
  ??? ??? ?? ??

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?? ??

• 1???? Attribute? Level? ??? ? ? ?? ??
• ? ???? ??? ?? ?? ?, ??? ??? ??
• Fractional Fractorial Design
• ??????? ?? ????? ?? ?? ? ???? ??? ? ?? ?? ??????
  ??? ??? ???? ??? ??
• Addelman? ????? ?????, ?????? ???? ???? ??(SPSS)
• ???(Orthogonality)
• ????? ???? ?? ???? ????? ??? ??? ??? ??
• ???? ?? ? ? ?? ??? ????? ??? ?? ?? ??? ??? ?????
  ??? ????? ???? ?? ????? ?

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?? ??

• ??(Treatment) ??(Stimulus)
• ????? ????? ???? ?? ??? ??? ??
• ??? ??? ?? ???? ??? ?? ??? ???? ??? ? ??? ????
  ??? ???? ?? ???? ??? ??
• ?? ?? ??(Additive Rule)
• ????? ?? ??? ???? ???? ???? ???? ??? ??? ??
• ??? ?? ???? ?? ??? ???? ???? ???? ??? ?? ??

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???? ????
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Attribute ?? ? Level ??

• ????
• ???? ? ??/ ???/????? ?? Utility factor? ?????
• ?????? ??? ?? ??????? ?????
• ????
• Focus Group Interview, In-depth Interview, Survey
  , Kellys Repertory Grid, ???? ??
• ???? ??
• ??? ??? ??? ?
• ????? ? ?? (Attribute-Level ? ??? ??, ?? ?? ???)

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Attribute ?? ? Level ??

• ?? ????
• Additive vs. Interactive
• ?? ?? ??? ??? ??? ??? ???
• Ideal-point Model
• Vector Model
• Part-worth function Model
• Mixed Model
• ?? ??? ? ??
• ??? ???, ??? ??? ??? ??
• Factorial Design, Decision Tree, Fractional
  Factorial Design
• ?????(Orthogonal Arrays)? ???? ??? ??
• SAS/ QC

1.Attribute ?? ? Level ??
Decision Tree Fractional Factorial
Design (Orthogonal Arrays) SAS/QC
2.??? ??
???? ????
3.??? ??
??? ??(Badness of Fitting) ? Attribute ???
??? ???? ?? ? ????
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??? ??

• ????
• ???? ??? Factorial? ??-???? ???? ?? ????? ?? ??
• ???? ??
• ?? ??, ??? ??, ??
• ???? 2??? ????
• Metric ?? Nonmetric ?? ?? ????
• ????? ?? ?? Nonmetric ??? ????(??. ??) ??? ?? ??

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??? ??

• ???? ?? ??
• TFA (Two factor-At-Time-Approach) ???? ????
  Attribute? ?? ? ? ?? ??
• FPA (Full-Profile Method) ????? ?? Attribute? ??
  ? ??

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?? ? ??

• ??? ??(Badness of Fitting)
• Stress ?? ??
• - 0.1? ???? ? ??? ?? ? ??
• SAS ??????? R-square ??
• - ??? ???? ??? ?? ?? ?????? ??
• ? Attribute ??? ???
• ? Attribute? ?? ?? ?? ?? ?? ?? ?? ?? ??
• - ??? ? ?? Utility? ??? ?? ??? ?? ??
• ???? ??? ??
• ???? ?? (Ideal Combination) ? ????(Optimal
  Combination)
• ? Attribute? ??? ?? Utility? ? ??? ???? ???
• - ?? ???? ?? Utility? ? ??? ????
• ??? ??? ?? ??? ????? ????? ???? ?? ??

1.Attribute ?? ? Level ??
Decision Tree Fractional Factorial
Design (Orthogonal Arrays) SAS/QC
2.??? ??
???? ????
3.??? ??
??? ??(Badness of Fitting) ? Attribute ???
??? ???? ?? ? ????
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SAS? ??? ???? ?? ??(1)
The researchers of use three factors with two
levels each8(222)

• Factor

Level
Ingredient Form Brand name
Phosphate-free Liquid HATCO
Phosphate-based Powder Generic brand
Stimuli Description Stimuli Description Stimuli Description Stimuli Description Respondent Rankings Respondent Rankings
Form Ingredient Brand Respondent 1 Respondent 2
1 Liquid Phosphate-free HATCO 1 1
2 Liquid Phosphate-free Generic 2 2
3 Liquid Phosphate-base Generic 5 3
4 Liquid Phosphate-base HATCO 6 4
5 Powder Phosphate-free Generic 3 7
6 Powder Phosphate-free HATCO 4 5
7 Powder Phosphate-base Generic 7 8
8 Powder Phosphate-base HATCO 8 6
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SAS ??(1)

• SAS ??

Title 'Perforence ' DATA FORM INPUT FORM
Ingred Brand Rating DATALINES Liquid
Phfree HATCO 1 Liquid
Phfree Generic 2 Liquid
Phbased HATCO 5 Liquid Phbased
Generic 6 Powder Phfree
HATCO 3 Powder Phfree
Generic 4 Powder Phbased HATCO
7 Powder Phbased Generic
8 RUN PROC PRINT DATAform PROC TRANSREG
UTILITIES TITLE2 'Conjoint Analysis' MODEL
MONOTONE(RATING) CLASS(Form Ingred Brand /
ZEROSUM) RUN
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SAS ?? ? ??(1)

• SAS ??? ??

Perforence
0241 Wednesday, January
24, 2002 OBS
FORM INGRED BRAND RATING
1 liquid
phfree HATCO 1
2 liquid
phfree Generic 2
3 liquid
phbased HATCO 5
4 liquid
phbased Generic 6
5 powder
phfree HATCO 3
6 powder
phfree Generic 4
7 powder
phbased HATCO 7
8 powder phbased
Generic 8
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SAS ?? ? ??(1)

• SAS ????

Utilities
Table Based on the Usual Degrees of Freedom


Importance
Standard
( Utility Label
Utility Error
Range) Variable
Intercept 4.5000000
0.00000
INTERCEPT FORM liquid
-1.0000000 0.00000 28.571
CLASS.FORMLIQU FORM powder
1.0000000 0.00000
CLASS.FORMPOWE INGRED
phbased 2.0000000 0.00000
57.143 CLASS.INTEGRPH INGRED
phfree -2.0000000 0.00000
CLASS.INTEGRPH
BRAND Generic 0.5000000
0.00000 14.286 CLASS.BRANDGEN
BRAND HATCO -0.5000000
0.00000 CLASS.BRANDHAT
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SAS? ??? ???? ?? ??(2)
The researchers of use three factors with two
levels each8(222)

• Factor

Level
Ingredient Form Brand name
Phosphate-free Liquid HATCO
Phosphate-based Powder Generic brand
Stimuli Description Stimuli Description Stimuli Description Stimuli Description Respondent Rankings Respondent Rankings
Form Ingredient Brand Respondent 1 Respondent 2
1 Liquid Phosphate-free HATCO 1 1
2 Liquid Phosphate-free Generic 2 2
3 Liquid Phosphate-base Generic 5 3
4 Liquid Phosphate-base HATCO 6 4
5 Powder Phosphate-free Generic 3 7
6 Powder Phosphate-free HATCO 4 5
7 Powder Phosphate-base Generic 7 8
8 Powder Phosphate-base HATCO 8 6
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SAS ???? ??(2)

• Combination

data c input form ingr brand subj1-subj2 drop
form ingr brand if form 1 then nform
liquid' else if form 2 then nform
powder' if inte 1 then ninte
pho-free' else if inte 2 then ninte
pho-based' if brand 1 then nbrand
HATCO' else if brand 2 then
nbrandgeneric' average mean(of
subj1-subj2) length comb 40 combtrim(nform)
',' trim(ningr) ',' trim(nbrand)
/????3, ????(Subject 2 ?)/ ?? ???? 8??? ?? ??
/3?? ?? ???? ?? ??? ??/
/? ??? Utility? ???? ?? ? ??? Level ?? /
/2? Subject? ??? ??/
/??? ??? COMB /
/????? ?? TRIM(??) , TRIM(??) /
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SAS ???? ??(2)

• Raw Data

cards 1 1 1 1 1 1 1 2 2 2 1 2 1 5 5 1 2 2 6 6 2
1 1 3 3 2 1 2 4 4 2 2 1 7 7 2 2 2 8 8
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SAS ???? ??(2)

• Output

proc print var comb subj1-subj2 average proc
transreg model monotone(subj1-subj2 average)
opscore(nform ningr nbrand) /maxiter60
output Tstandardcenter additive id
comb proc print var comb _depvar_ t_depend
tnfont tnsiz tnlin by notsorted _depvar_ run
/??? ?????? Average??/
/???? ?? ?? ???? 2?? ????? ?? ???? ???
???? 3?? ?? ???? ??? ??? ?? ??? ???? ???
Monotone?? ??, ????? ? ??? ???? ???????
Opscore? ? /
/?? ??/
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SAS ?? ? ??(2)

Preference
Metric Conjoint Analysis 1712 Wednesday,
September 9, 1998 OBS
COMB SUBJ1 SUBJ2
AVERAGE 1 liquid,
pho-free, HATCO 1 1
1 2 liquid,
pho-free, gener 2 2
2 3
liquid, pho-base, HATCO 5
5 5 4
liquid, pho-base, gener 6
6 6 5
powder,pho-free, HATCO 3
3 3 6
powder,pho-free, gener 4
4 4 7
powder,pho-base, HATCO 7
7 7 8
powder,pho-base, gener 8
8 8
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SAS ?? ? ??(2)


Preference
Metric Conjoint
Analysis 1712 Wednesday, September 9, 1998
TRANSREG MORALS Algorithm Iteration
History for MONOTONE(AVERAGE)
Iteration Average Maximum Squared
Criterion Number Change
Change Multiple R Change
---------------------------------------------
------------------------ 1
0.00000 0.00000 1.00000
.

NOTE Algorithm
converged.
R-square ??? - ?? ???
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SAS ?? ? ??(??)

The SAS System 0318 Wednesday,
January 24, 2002 14 TRANSREG MORALS
Algorithm Iteration History for
MONOTONE(AVERAGE)
Iteration Average Maximum
Squared Criterion
Number Change Change
Multiple R Change
--------------------------------
----------------------------------------------
1
0.05336 0.34735 0.90372
.
2 0.01289 0.05080 0.97695
0.07323
3 0.00739 0.02971
0.97803 0.00108
4 0.00426
0.01694 0.97836 0.00033
5
0.00245 0.00959 0.97847
0.00010
6 0.00141 0.00543
0.97850 0.00003
7 0.00081
0.00308 0.97851 0.00001
8
0.00047 0.00175 0.97851
0.00000
9 0.00027 0.00101
0.97851 0.00000
10 0.00016
0.00058 0.97851 0.00000
11
0.00009 0.00034 0.97851
0.00000
12 0.00005 0.00020
0.97851 0.00000
13 0.00003
0.00011 0.97851 0.00000
14
0.00002 0.00007 0.97851
0.00000
15 0.00001 0.00004
0.97851 0.00000
16 0.00001
0.00002 0.97851 0.00000
NOTE
Algorithm converged.
R-square ??? - 90.0 ? 97.9
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SAS ?? ? ??(2)

• SAS Code

------------------ Dependent Variable
Transformation(Name)MONOTONE(AVERAGE)
------------------ OBS COMB
_DEPVAR_
T_DEPEND TNFORM TNINTE TNBRAND 17
liquid,pho-free,HATCO MONOTONE(AVERAGE)
-3.5 -1 -2
-0.5 18 liquid,pho-free,gener
MONOTONE(AVERAGE) -2.5
-1 -2 0.5 19
liquid,pho-base,HATCO MONOTONE(AVERAGE)
0.5 -1 2
-0.5 20 liquid,pho-base,gener
MONOTONE(AVERAGE) 1.5
-1 2 0.5 21
powder,pho-free,HATCO MONOTONE(AVERAGE)
-1.5 1 -2
-0.5 22 powder,pho-free,gener
MONOTONE(AVERAGE) -0.5
1 -2 0.5 23
powder,pho-base,HATCO MONOTONE(AVERAGE)
2.5 1 2
-0.5 24 powder,pho-base,gener
MONOTONE(AVERAGE) 3.5
1 2 0.5
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????

• ???(Goodness of Fit)??
• R-square ??? - ??100 ? 100

• ??? ???(Relative Importance)

wa
Form Ingredients Brand Total
Upper 1 2 0.5
Lower -1 -2 -0.5
?? 2 4 1 7
?? 28.571 57.143 14.286 100

• ???? (Optimal Combination)
• ??? ??(Ideal Combination) ? ???? ?? ??? ? ???
  ???? ??? ?? ?
• Form Powder, Ingredients Pho-based,
  BrandGeneric brand ?? ???? ??

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????
Cleanser ???
Form
Ingredients
Brand
28.6 Powder
75.1 Pho-based
14.3 Generic
Display? ??? ???()
Factors Form Ingredients Brand
Cleanser Preference 25.18 13.31 61.51
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?????.
CONJOINT ANALYSIS
Object
Attribute

Attribute
56
24
20
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Homework

Conjoint Analysis