UNDERSTANDING CONSUMER PREFERENCE

WITH MULTIVARIATE VISUALISATION

DAVID ARNOLD

20TH JUNE 2013

THE PRODUCT DESIGN PROCESS

PRODUCT MARKET INSTRUMENTAL CONSUMER

micro-structure

physical/chemical

performance Liking/in-use perception

ingredients

molecules

formulation

processing

cost

purchase behaviour

Sensory Descriptive Analysis

Internal Preference Mapping

predict

optimise

Sensory description

Sensory discrimination

External Preference

Mapping

SENSORY

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

p x q p x k k x q

p x q p x 2 2 x q

We would like a good two dimensional representation to graph,

that captures as much information as possible.

Principal component analysis allows us to do this...

• Groups of similar products.

• Groups of similar questions.

• The relative associations between products and questions.

• Relative sizes of the differences between the products.

X is a mean centred matrix where rows are products and columns questions

Capturing,

PRINCIPAL COMPONENT ANALYSIS (PCA)

1

1

2

11v

1

1

2

12v

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.

XVY 1VV T

q

2

1

y

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.

Columns of X are mean centred, so the average scores

are now zero.

V is chosen to produce uncorrelated

principal axes (components) Y.

-60 -40 -20 0 20

-10

01

02

03

0

Individuals factor map (PCA)

Dim 1 (83.71%)

Dim

2 (

13

.35

%)

AB

C

D

E

REPRESENTING THE PRODUCTS IN TWO DIMENSIONS

5 x 2

Distances between products

are proportional to the

Malahanobis distance

-10 -5 0 5 10 15 20

-50

5

Variables factor map (PCA)

Dim 1 (83.71%)

Dim

2 (

13

.35

%)

Coldness

Comfort

Crumbling

Dragginess

Evenness.of.spread

Glidability

Residue.FeelResidue.Look

SheenStickiness

Tone.of.Colour

Visibility

Visual.Consistency

Visual.Texture

Wetness

Coldness

Comfort

Crumbling

Dragginess

Evenness.of.spread

Glidability

Residue.FeelResidue.Look

SheenStickiness

Tone.of.Colour

Visibility

Visual.Consistency

Visual.Texture

Wetness

Coldness

Comfort

Crumbling

Dragginess

Evenness.of.spread

Glidability

Residue.FeelResidue.Look

SheenStickiness

Tone.of.Colour

Visibility

Visual.Consistency

Visual.Texture

Wetness

Coldness

Comfort

Crumbling

Dragginess

Evenness.of.spread

Glidability

Residue.FeelResidue.Look

SheenStickiness

Tone.of.Colour

Visibility

Visual.Consistency

Visual.Texture

Wetness

Coldness

Comfort

Crumbling

Dragginess

Evenness.of.spread

Glidability

Residue.FeelResidue.Look

SheenStickiness

Tone.of.Colour

Visibility

Visual.Consistency

Visual.Texture

Wetness

Coldness

Comfort

Crumbling

Dragginess

Evenness.of.spread

Glidability

Residue.FeelResidue.Look

SheenStickiness

Tone.of.Colour

Visibility

Visual.Consistency

Visual.Texture

Wetness

Coldness

Comfort

Crumbling

Dragginess

Evenness.of.spread

Glidability

Residue.FeelResidue.Look

SheenStickiness

Tone.of.Colour

Visibility

Visual.Consistency

Visual.Texture

Wetness

Coldness

Comfort

Crumbling

Dragginess

Evenness.of.spread

Glidability

Residue.FeelResidue.Look

SheenStickiness

Tone.of.Colour

Visibility

Visual.Consistency

Visual.Texture

Wetness

Coldness

Comfort

Crumbling

Dragginess

Evenness.of.spread

Glidability

Residue.FeelResidue.Look

SheenStickiness

Tone.of.Colour

Visibility

Visual.Consistency

Visual.Texture

Wetness

REPRESENTING THE QUESTIONS IN TWO DIMENSIONS

Vector length approximates variance

15 x 2

HOWEVER THE TWO MAPS ARE RELATED

A

B

C

B > A > C

Each element of X is represented

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

relative ordering of the product mean

scores on each question.

Y2 and V2 can be overlaid to produce a PCA biplot....

PCA BIPLOT

This plot is produced using standardised X

So now product distances are Euclidean not Malahanobis.

Vectors are all the same length

Almost zero correlation between

Residual Look and Residual Feel

Almost perfect correlation between

Tone of Colour and Visual Consistency

Angles between vectors are still correlations

Projections give relative ordering of products on questions

PCA BIPLOT

• Question scoring scales are calibrated to be linear and continuous.

• Panellists are trained and checked for scoring consistency and

reproducibility.

• The intrinsic dimensionality of the data is well represented on two

(or possibly three) axes.

PCA biplots produce a good representation of this kind of data.

What if my data is not continuous

or is intrinsically higher than two or three dimensions?

We can use a general class of models termed Multidimensional Scaling

MULTIDIMENSIONAL SCALING (MDS)

Finds a configuration of points representing products

Like PCA it finds a low dimensional representation of the data.

• Better representation in 2D of intrinsically high dimensional data than PCA

• Can represent non metric data such as ordered ranks

However, unlike PCA it tries to find the best representation possible in the

chosen number of dimensions, usually two.

Distances between pairs of points no longer approximate the original

dissimilarities (distances in multidimensional space)

Instead the rank order of the distances between pairs of points

match the rank order of the dissimilarities (as well as possible)

-3 -2 -1 0 1 2

-1.0

-0.5

0.0

0.5

1.0

1.5

MDS1

MD

S2

A

BC

D

E

Coldness

ComfortCrumbling

Dragginess

Evenness.of.spread

Glidability

Residue.FeelResidue.Look

Sheen

Stickiness

Tone.of.Colour

Visibility

Visual.ConsistencyVisual.Texture

Wetness

MDS ON THE SENSORY DATA

The product relationships are

reproduced as closely as possible

in two dimensions.

Questions are overlaid as weighed

averages across the products

Its all about proximity

UNTRAINED PANELS FREE CHOICE PROFILING

FREE CHOICE PROFILING (FCP)

FCP provides an indication of which attributes are likely to be perceived by

consumers

• It uses untrained consumers

• There is no need to maintain a sensory panel

• Less resource required

WHAT’S INVOLVED?

• Develop individual vocabularies

• Incorporate individual vocabularies into score sheets

• Individuals assess samples using their personalised score sheets

• Individuals must score the same objects

• Individuals need not record the same attributes or number of attributes

Generalised Procustes Analysis (GPA) compares the differing panellist

data without disturbing the relationships contained inside the sets

Principal Components Analysis is used to produce individual assessor

configurations.

GENERAL PROCUSTES ANALYSIS

Individual's configurations are translated, rotated and scaled to minimise

the sum of squares for individual deviations

» maximises product deviations

» maximises the agreement between individuals on each product

Example

10 Spanish consumers scoring 10 washing up liquids using their own

sensory attributes

creamy/moisturizing

Spanish English

Cremoso Creamy

Suave Smooth

Deslizable Flowly

Espumosa Foamy

Pegajoso Sticky

Absorbible Absorbable

Espesa Thick

Consistente Consistent

Líquido Liquid/ Fluid

Transparente Transparent

Liviano Light

Acuoso Watery

Grasoso Greasy

Abundante Abundant/ Plentiful

Áspera Rough

Opaco Opaque

Aceitoso Oily

Denso Thick

Humectada Moisturizing

Ligero Light

Rápido Quick

Resbaladizo Slippery

Adherente Adherent

Fluida Fluid

Gelatinoso Gelatinous

Perdurable Long Lasting

Pesado Heavy

Seca Dry

Translúcido Tanslucent

...

light/smooth/opaque

thick/abundant/consistent

Absorbable/foamy

with 95% confidence

intervals

CONSUMER PREFERENCE PREFERENCE MAPPING AND

DRIVERS ANALYSIS

WHAT IS PRODUCT PREFERENCE MAPPING?

• Models of preferential choice

• The data is scores such as rank order of preference for different panellists

for a set of products

• Individuals are untrained consumers

Internal Preference Mapping

• Used to find consumer clusters

sharing a product preference

• Data consists of a products x consumer

scores

External Preference Mapping

• Predict maximum consumer

acceptance for a set of prototypes

• Uses an external data set to predict

consumer acceptance

Assumptions

• Different individuals perceive the products in the same way

• but individuals differ as to what an ideal combination of the products attributes are

INTERNAL PREFERENCE MAPPING

We try to represent products and consumers on a common

underlying scale and visually examine the relationship between them.

We locate individuals and products as points in a joint space

It says that an individual will pick the product in the set closest to their ideal point.

MULTIDIMENSIONAL UNFOLDING

1 2 A B C D E

1st 2nd 3rd 4th 5th

Judge 1 B C A E D

Judge 2 A B C E D

taken from Multidimensional Scaling, Cox and Cox (2005)

Suppose we have 2 judges and 5 essays for the judges to rank

A B

C E D

Judge 1 rankings

Unfolding (common ordering)

Judge 2 rankings

A

B C E D

We represent the consumers and

products on a two dimensional

map maintaining as accurately as

possible the ranks of each

consumer

BREAKFAST EXAMPLE

-10 -5 0 5 10

-10

-50

51

0

Joint Configuration Plot

Configurations D1

Co

nfig

ura

tio

ns D

2

toast

butoast

engmuff

jdonut

cintoast

bluemuff

hrolls

toastmarm

butoastj

toastmarg

cinbun

danpastry

gdonut

cofcake

cornmuff

12

3

4

5

6

78

9

101112

131415

16

17

18

19

20

2122

23

2425

2627

28

29

30

31

32

3334

35

3637

38

39

40

4142

42 individuals were asked to order 15 breakfast items

based on their preference.

similar preference These individuals

had a high preference for

Danish pastry

taken from the smacof R package

EXTERNAL PREFERENCE MAPPING

In addition to the consumer data (internal data), an external set

of data is present which describes the products in some way.

Sensory data should have prioritisation of the attributes based

on their importance to consumers

and have dimensions that pertain to preference.

We can use PCA to create the product sensory map.

The sensory axes are regressed onto the consumer preference

e.g. by a quadratic model using the PCs.

This data is used in some form of regression model to give meaning

to the axes on the map.

External data is usually sensory data and/or product technical data.

EXTERNAL PREFERENCE MAP FOR CONDITIONERS

DRIVERS ANALYSIS

DRIVERS ANALYSIS

We have seen some ways to represent the correlations and distances

between products, sensory attributes and consumer preference.

Can we gain further insights into the structure of the data?

Factor analysis and regression

Similar to PCA but we seek an interpretation of the components as

hidden or latent variables to explain the observed correlations

between questions

Observed questions (measurements)

Latent variables (can’t measure directly but are represented indirectly through the observed answers to our questions

Each observation has a score for each factor.

These can be regressed onto a measure of product liking.

GRAPHICAL MODELS (GM)

These are probability models for multivariate random observations,

whose independence structure is characterised by a graph.

Consist of (data, probability model) -> likelihood function

Gives a measure of the relative support the data gives for different model

formulations

x3 x1

x2

1960980

9601980

9809801

..

..

..

S

102.071.0

02.0168.0

71.068.011S

Idea of conditional independence

This holds for sets of random variables in a

joint distribution. (global Markov property)

GRAPHICAL MODELS (GM)

The correlations hide the probable structure

between the variables.

Makes my hair feel soft

Moisturises my hair

Allows my hair to move naturally

ADVANTAGES OF GRAPHICAL MODELS

Interpretation

Conditioning is the key concept underpinning GM.

Conditional independence gives a visualisation of the structure of the data

not just the correlations.

Unification

GM provides a unified framework for continuous data (correlation) and discrete data

(contingency table), and this unification suggests generalisation to mixed

variable systems.

UNDERSTANDING THE DRIVERS OF CONSUMER PREFERENCE

Products 10 (commercially available) laundry bars incomplete mixture of 9 ingredients

Sensory Data

19 panellists 32 attributes (day 1 & day 3) complete sequential evaluation

Liking Data Location 1 - soft water - 339 households Location 2 - hard water - 323 households complete sequential evaluation

Hand Wash Bars

A factor analysis was performed on the sensory data to reduce the number of attributes

FACTOR ANALYSIS

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

factor #

att

ribute

pattern loadings visualisation

Brightness1 Hardness1 Dryness1

Grip1 Rubbing1 Disintegration1

Grit1 Lather1

Soapiness1 Perfume1

Breaks1 Effort1 RinsWater1

BucketDep1 Economy1

Brightness3 Hardness3 Dryness3

Grip3 Rubbing3 Disintegration3

Grit3 Lather3

Soapiness3 Perfume3

Breaks3 Effort3 RinsWater3

BucketDep3 Economy3

1 2 3 4 5

perfume grip/economy grit/deposits

engagement

tactile feel

Highlight are the most important correlations with the factors

The factors were rotated

to align them as well as

possible with the

sensory questions.

This also induces

correlation

between them.

CONDITIONAL INDEPENDENCE (SENSORY FACTORS & LIKING)

Location 1 Liking driven by Engagement and tactile feel

Location2 liking driven by Engagement and Grip/Economy

Pref Location 1

Pref Location 2

We then related the formulation profiles of the test products

to match the preference drivers from the study.

USEFUL RESOURCES

Sensory and Preference Mapping in R

SensoMineR http://sensominer.free.fr

FactoMineR

smacof Preference mapping using unfolding (MDS)

Graphical Modelling

R packages gRim and gRain

MIM (Mixed Integer Modelling http://www.hypergraph.dk/)

Thank you