david arnold

36 Pages·2013·1.1 MB·English

by  Lynsey Mccoll

20TH JUNE 2013
UNDERSTANDING CONSUMER PREFERENCE
WITH MULTIVARIATE VISUALISATION
DAVID ARNOLD
THE PRODUCT DESIGN PROCESS
MARKET CONSUMER SENSORY INSTRUMENTAL PRODUCT

Sensory Descriptive Analysis
micro-structure ingredients
External Preference
physical/chemical
Sensory molecules
Mapping
description performance
purchase Liking/in-use
formulation
behaviour perception
processing
Sensory
Internal Preference Mapping
cost
discrimination

predict
optimise
TALK OUTLINE
• Sensory description (Product Profiling)
• Trained panels
• Untrained panels

• Consumer Preference
• Preference Mapping
• Drivers Analysis
PRODUCT
PROFILING
OBTAINING A QUANTITATIVE
DESCRIPTION OF PRODUCTS
TRAINED PANELS

• Trained assessors (panel monitoring)

• Well defined scales (0-100, VAS)

• Experimental design and carry over issues (order effects)

• We want to be able to compare across panel sittings
Analysis of Variance (adjustment for multiple testing, Fisher Analysis)

Uni-variate testing, ignores dependencies between questions

Multivariate analysis of variance (multivariate normal distribution assumption)
We would also like to visualise the interdependencies in the data and preferably
on a two dimensional map...
PRINCIPAL COMPONENT BIPLOTS
X is a mean centred matrix where rows are products and columns questions
p x q p x k k x q
We would like a good two dimensional representation to graph,
that captures as much information as possible.
p x q p x 2 2 x q
Capturing,
• Groups of similar products.
• Groups of similar questions.
• The relative associations between products and questions.
• Relative sizes of the differences between the products.
Principal component analysis allows us to do this...
PRINCIPAL COMPONENT ANALYSIS
(PCA)
A PCA finds linear combinations of the questions that explain the
maximum variation in the data, with as few principal axes as possible.
The first axis explains the highest possible amount of variation on a single axis.
The next axis finds the direction explaining the maximum remaining unexplained
variation and so on.

Y  XV VTV 1 Columns of X are mean centred, so the average scores

are now zero.
 
1
 


V is chosen to produce uncorrelated  2 
 
y   
principal axes (components) Y.
 


 
 
q

1 1
v 
2 2  1 
1 1
v 
 
1 2 1
If the first two PCs explain a high proportion
of the variation then we can use Y and V to
represent X on a two dimensional plot.
REPRESENTING THE PRODUCTS IN
TWO DIMENSIONS
Individuals factor map (PCA)
0
3
5 x 2
0
2 Distances between products D
are proportional to the
)
%
Malahanobis distance
5
3 0
. 1
3
1
(

2

m
iD 0 C
A
E
B
0
1
-
-60 -40 -20 0 20
Dim 1 (83.71%)
REPRESENTING THE QUESTIONS IN
TWO DIMENSIONS
Variables factor map (PCA)
15 x 2
5 VVVVVVVVViiiiiiiiisssssssssuuuuuuuuuaaaaaaaaalllllllll.........TTTTTTTTTeeeeeeeeexxxxxxxxxtttttttttuuuuuuuuurrrrrrrrreeeeeeeee
SSSSSSSSShhhhhhhhheeeeeeeeeeeeeeeeeennnnnnnnn TTTTTTTTTooooooooonnnnnnnnneeeeeeeee.........ooooooooofffffffff.........CCCCCCCCCooooooooolllllllllooooooooouuuuuuuuurrrrrrrrr
)% DDDDDDDDDrrrrrrrrraaaaaaaaaggggggggggggggggggiiiiiiiiinnnnnnnnneeeeeeeeessssssssssssssssssCCCCCCCCCooooooooollllllllldddddddddnnnnnnnnneeeeeeeeeSSSSSSsssSSSsssssssssssssstttsttttttiiiiiiiiiccccccccckkkkkkkkkiiiiiiiiinnnnnnnnneeeeeeeeessssssssssssssssss VVVVVVVVViiiiiiiiisssssssssuuuuuuuuuaaaaaaaaalllllllll.........CCCCCCCCCooooooooonnnnnnnnnsssssssssiiiiiiiiisssssssssttttttttteeeeeeeeennnnnnnnncccccccccyyyyyyyyy
5 EEEEEEEEEvvvvvvvvveeeeeeeeennnnnnnnnnnnnnnnnneeeeeeeeessssssssssssssssss.........ooooooooofffffffff.........sssssssssppppppppprrrrrrrrreeeeeeeeeaaaaaaaaaddddddddd RRRRRRRRReeeeeeeeesssssssssiiiiiiiiiddddddddduuuuuuuuueeeeeeeee.........FFFFFFFFFeeeeeeeeeeeeeeeeeelllllllll
3 WWWWWWWWWeeeeeeeeetttttttttnnnnnnnnneeeeeeeeessssssssssssssssss
. RRRRRRRRReeeeeeeeesssssssssiiiiiiiiiddddddddduuuuuuuuueeeeeeeee.........LLLLLLLLLooooooooooooooooookkkkkkkkk
3 0 VVVVVVVVViiiiiiiiisssssssssiiiiiiiiibbbbbbbbbiiiiiiiiillllllllliiiiiiiiitttttttttyyyyyyyyy
1
(
CCCCCCCCCrrrrrrrrruuuuuuuuummmmmmmmmbbbbbbbbbllllllllliiiiiiiiinnnnnnnnnggggggggg
2

m
iD GGGGGGGGGllllllllliiiiiiiiidddddddddaaaaaaaaabbbbbbbbbiiiiiiiiillllllllliiiiiiiiitttttttttyyyyyyyyy
5
- CCCCCCCCCooooooooommmmmmmmmfffffffffooooooooorrrrrrrrrttttttttt
-10 -5 0 5 10 15 20
Dim 1 (83.71%)
Vector length approximates variance
HOWEVER THE TWO MAPS ARE
RELATED
Each element of X is represented
A
by multiplying a row of y and a row
of v.
So the projections of the rows of y
onto the rows of v give the
B > A > C
relative ordering of the product mean
B
scores on each question.
C
Y and V can be overlaid to produce a PCA biplot....
2 2