Sensory Analysis, R tools to analyze Preference liking in ... · PDF fileWhat’s Sensory Analysis Sensory analysis is a scientific discipline used to analyze reactions to stimuli

Sensory Analysis,R tools to analyze Preference liking in function of

descriptive measures.

Dhafer Maloucheessai.academia.edu/DhaferMalouche

Center of Political Studies,Institute of Social Research

University of Michigan,

Ecole Supérieure de la Statistiqueet de l’Analyse de l’Information,

University of Carthage.

12/09/2016

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What’s Sensory Analysis

Sensory analysis is a scientific discipline used to analyze reactions tostimuli perceived through the senses: sight, smell, touch, taste, andsound.It is considered one of the most important tools for the food industry,given that it can be applied in several ways.

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Aim of Sensory Analysis

Gives a comparison between several (food) products

Explains preference consumer in terms of the characteristics ofthe (food) products.

Provides the optimal (food) product: liked by a majority ofconsumers.

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Data used for Sensory Analysis

Analytic Data.X1 Physico-chemical data: measure some physico-chemical param-

eters of the product of the Study.

X2 Sensory data: rates of the products by a panel of experts accord-ing to a list of sensory a�ributes.

X3 Genetic data.

. . . .

Hedonic data: Y, rates provided by a sample of consumers.

X1,X2, . . . are analytic data.

Y is a perceptual data.

⇒ Y ≈ f (X1, X2 . . .)

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Example: A study on the Tunisian Olive Oil.

78 million olive oil trees (more than300 million in Spain and 750 millionworldwide).

6,950 square miles (10% of theTunisian Area).

1750 Oil mills

4th producer and 2nd exporter...

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Analyzing Olive Oils

Three data sets

Sensory Data: Panel of Experts

Physico-chemical Data: Several laboratories, Italy, Tunisia,

Hedonic Data: A survey in a grocery shop with 252 con-sumers who accepted to taste the samples of OO.

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R tools for Sensory Analysis

FactoMineR, SensoMineR, FactoshinyAuthors: Francois Husson, Julie Josse, Sebastien Le, JeremyMazetDescription: performs PCA, MFA, Clustering and Panel perfor-mance, External and internal Mapping . . .Webpage: http://factominer.free.fr/ andhttp://sensominer.free.fr/

sensR

Authors: Per B Brockho, Rune Haubo Bojesen.Description: Statistical tests of sensory discrimation and simi-larity data, Power and sample size computations for discrimina-tion and similarity. tests

SensMap

Authors: Ibtihel Rebhi, Dhafer Malouche.Description: Everything about sensory analysis, External andInternal mapping, Shiny UI.

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Sensory data

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Sensory data

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Sensory data

9 experts rate 21 olive oil products:

7 cultivars:Coratina (Italy),Arbequina (Spain cultivar),Chemchali (South West),Chemlali (South East),Chetoui (North),Leguim (Center)Zalmati (South).

3 extraction systems: 3P, 2P, SP.

9 a�ributes: Fruity, Bi�er, Pungent, Fusty, Musty, Winey,Muddy, Metallic, Rancid: rates from 0 to 10.

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Problem: How can we measure the quality of the collected data?

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Assessing performance of a Panel

The statistical assessment of the performance based on threeimportant qualities:

discrimination: their ability to di�erentiate the productsrepeatable: consistently.agreement: consensually.

To assess this performance we use an ANOVA: the dependentsvariables are the sensory a�ributes. The factors:

productspanelistssessions

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Assessing performance of a Panel: ANOVA Model

Let (Yiks) be the rate of the sensory a�ribute

of the ith productby the kth panelistat the sth session

ANOVA:

Yiks = µ + αi + βk + γs + [αβ]ik + [αγ ]is + [βγ ]ks + ϵiks

where∀ (i, k, s), ϵiks ∼ N(0,σ 2)∀ (i, k, s), (i′, k ′, s′), cov(ϵiks, ϵi′k′s′) = 0

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Assessing performance of a Panel: ANOVA Model

αi is the Product e�ect: it measures the ability of discrimination(if significant).

[αβ]ik is the interaction Product-Panelist. It indicates whetherthere’s a consensus among the panelists: agreement.

[αγ ]is is the interaction Product-Session. It indicates whetherthe product is perceived similarly from one session to another:repeatability.

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In practice with R

> m1<-aov(Fruity~product+panelist+session+product:panelist+product:session+jury:session,data=panel_session_data)

> summary(m1)Df Sum Sq Mean Sq F value Pr(>F)

product 20 886.3 44.31 57.652 < 2e-16 ***panelist 7 16.6 2.38 3.092 0.00372 **session 2 1.3 0.63 0.824 0.43958product:panelist 140 232.5 1.66 2.160 2.66e-08 ***product:session 40 30.8 0.77 1.001 0.47435panelist:session 14 9.6 0.68 0.889 0.57178Residuals 280 215.2 0.77---Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1

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In practice with R

With p-value < 2e − 16: (Product e�ect is significant, discrimina-tion performance. [expected]

With p-value = 2.66e − 08, Product-Panelist is significant, noconsensus. [not expected]

With p-value = 0.47, Product-Session is not significant, repeata-bility. [expected]

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In practice with R, Interaction Product-Session

arbequina(2p)

arbequina(3p)

arbequina(sp)

chem(2p)

chem(3p)chem(sp)

chemchali(2p)

chemchali(3p)

chemchali(sp)

chetoui(2p)

chetoui(3p)

chetoui(sp)

coratina(2p)

coratina(3p)

coratina(sp)

leguim(2p)

leguim(3p)

leguim(sp)

zalmati(2p)zalmati(3p)

zalmati(sp)

1

2

3

4

5

6

2 3 4 5 6Mean on the whole session

Mea

npe

rse

ssio

n

Session123

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In practice with R, package SensoMineR

>formul<-"~product+jury+session+product:jury++ product:session+jury:session"> res.panel<-panelperf(panel_session_data,firstvar = 4,+ lastvar = 9,+ formul = formul)> round(res.panel$p.value,5)

prod jury session p:j p:sFruity 0 0.00372 0.41845 0.00000 0.47435Bitter 0 0.00700 0.31445 0.00000 0.83263Pungent 0 0.00140 0.28710 0.00000 0.05473Fusty 0 0.00008 0.00013 0.00000 0.05873Moddy 0 0.87224 0.00015 0.36808 0.38847Rancid 0 0.10302 0.00001 0.00831 0.06140

j:sFruity 0.57178Bitter 0.78702Pungent 0.78932Fusty 0.09085Moddy 0.06745Rancid 0.60208

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Physico-chemical data.

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Physico-chemical data.

7 cultivars + 2 Extraction systems (sp and 3p).

3 repetitions for each measure

68 Physico-chemical parameters : Acidity, K232,...

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Physico-chemical data, Assessing repeatability

Let (Yir ) be the measure of a given Physico-chemical parame-ter.

of the ith product

by the rth repitation

ANOVA:Yir = µ + αi + βr + ϵir

where∀ (i, r), ϵir ∼ N(0,σ 2)∀ (i, r), (i′, r ′), cov(ϵir , ϵi′r′) = 0

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In practice with R,

> m1<-aov(Acidity~product+repitation,data=phch)

> summary(m1)

Df Sum Sq Mean Sq F value Pr(>F)

product 13 4.300 0.3308 45.950 1.44e-14 ***repitation 2 0.007 0.0037 0.512 0.605

Residuals 26 0.187 0.0072

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

With p-value = 1.44e − 14, Product has a significant e�ect,discrimination.

With p-value = 0.605, Repetation has not a significant e�ect,repeatability.

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Repeatability, Multivariate approach.

Perform a Principal Component Analysis on the PHCH-data.

Dimension reduction method.

Summarize the most information contained in the data with asmall number of artificial variables (principal components).

Information = Total variance of the data.

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1 Let X be the physico-chemical data: P × N numeric where P isthe number of the products and N is the number of variables:X 1, . . . ,XN the columns of X.

2 Scale and center X and consider the correlation matrix

V = X′X/P .

3 Search for F a P × 1 matrix (or vector) such that

F =N∑j=1

αjX j such that Var(F ) is maximal

Solution: F = F 1 = Xu1 where u1 is the eigen vector of Vassociated to the greater eigen value λ1 of V .C1 is called the first principal component of X.

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4 We search also a second F such that

F =N∑j=1

αjX j such that Var(F ) is maximal and Cor(F , F 1) = 0

Solution: F = F 2 = Xu2 where u2 is the eigen vector of Vassociated to the 2nd greater eigen value λ2 of V .

5 And F 1, F 2, . . . , F k , ..

6 Draw a sca�er-plot [F k , F k′] with repetition as a supplementaryvariable.

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In practice with R, Scree-plot

> library(FactoMineR)

> library(factoextra)

> res.pca<-PCA(X,scale.unit = T,

+ ncp = 5,quali.sup = 66:67,graph = F)

> fviz_screeplot(res.pca, ncp = 10) + theme_classic()

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0

10

20

1 2 3 4 5 6 7 8 9 10Dimensions

Perc

enta

geof

expl

aine

dva

rian

ces Scree plot

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0

10

20

1 2 3 4 5 6 7 8 9 10Dimensions

Perc

enta

geof

expl

aine

dva

rian

ces Scree plot

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In practice with R, Product-map

> library(ggplot2)> library(scales)> library(grid)> library(plyr)> library(gridExtra)> find_hull <- function(X) X[chull(X$PC1, X$PC2), ]>dt=cbind.data.frame(res.pca$ind$coord[,1:2],+ X$product,X$repetition)> colnames(dt)=c("PC1","PC2","Product","Repetition")> dt2=cbind.data.frame(res.pca$quali.sup$coord[1:14,1:2],+ rownames(res.pca$quali.sup$coord[1:14,]))> colnames(dt2)=c("PC1","PC2","Product")> dt2$Product=gsub("_","",dt2$Product)> hulls <- ddply(dt, "Product", find_hull)

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> p<-ggplot(data = dt,aes(x=PC1,y=PC2,col=Product,fill=Product))++ geom_hline(yintercept = 0,alpha=.4)++ geom_vline(xintercept = 0,alpha=.4)++ geom_polygon(data=hulls, alpha=.2)++ geom_point() ++ geom_text(data=dt2,aes(x=PC1,y=PC2,label=Product),col="black")++ xlab(paste("Axis 1 (",round(res.pca$eig[1,2],1),"%)",sep=""))++ ylab(paste("Axis 2 (",round(res.pca$eig[2,2],1),"%)",sep=""))> p<-p+theme_classic()+theme(legend.position = "none")> p

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arbeq(3p)

arbeq(sp)

chemch(3p)

chemch(sp)

chemle(3p)

chemle(sp)

chetou(3p)

chetou(sp)

corati(3p)

corati(sp)

leguim(3p)leguim(sp)

zalmat(3p)zalmat(sp)

-2.5

0.0

2.5

5.0

7.5

-4 0 4Axis 1 (28.1%)

Axi

s2

(12.

5%)

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In practice with R, V-test

> res.pca$quali.sup$v.test[15:17,]

Dim.1 Dim.2 Dim.3 Dim.4 Dim.5

repetition 1 0.014 -0.034 -0.034 0.265 -0.292

repetition 2 0.039 -0.071 0.019 -0.152 0.107

repitation 3 -0.053 0.105 0.015 -0.113 0.185

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-2.5

0.0

2.5

5.0

7.5

-4 0 4Axis 1 (28.1%)

Axi

s2

(12.

5%)

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C 16:1C 18:1

C 18:2

LLL

LnLO

LnLP

LLO

LnOO

PLL

LOO

LOPPLP

OOO

POP

POOAOL

SOOb carotène

polyphenols

Hexanal

1-Pentanol

Cis-3-hexenyl acetateCis-3-hexenol

Trans-2-hexenol

H- TyrDFLA

Ac-PinLA

-1.0

-0.5

0.0

0.5

1.0

-1.0 -0.5 0.0 0.5 1.0Axis 1 (28.1%)

Axi

s2

(12.

5%)

Circle of Correlations

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External Mapping

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External Mapping

Y ≈ f (X1,X2, . . .)It Aims to

give an estimation of the probability of liking of a product.derive a multidimensional representation of products basedon their sensory profile or a set of other external data such asinstrumental measures of color, texture or flavor.

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External Mapping, Danzart 1998, 2009.

1 Combine all measures X1, X2, . . . into one analytic data matrixX with dimensions P × N (products × a�ributes).

2 Perform a dimension reduction method on X: for example aPrincipal Component Analysis and let F 1 and F 2 be the firsttwo components.

3 Let Y be the hedonic matrix with dimensions P × C (products ×consumers) and with columns Y 1, . . . ,YC .

4 For all c = 1, . . . ,C, perform a regression Model

Y c = fc(F 1, F 2) + ϵc

Let fc be an estimation of fc .

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External Mapping, Danzart 1998, 2009.

5 Consider a grid in the plan ∆(C1,C2):

G ={(f 1l1, f 2

l2), (l1, l2) ∈ {1, . . . , L}2

}6 For each c and (l1, l2), predict

y(c, l1, l2) = fc(f 1l1, f 2

l2)

7 Computer the percentage of the consumers that have predic-tions higher than the average of their given scores.

ϕ(l1, l2) =1C

C∑c=1

1{y(c, l1, l2) ≥ y(c)}

where

y(c) = 1P

P∑p=1

yp(c)

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In practice with R

1 Prepare data

> x.phch=aggregate(phch[,1:65],

+ by = list(phch$product),mean)

> y.hedo=aggregate(hedonic[,1:255],

+ by=list(hedonic$product),mean)

> z.panel=aggregate(panel[,3:8],

+ by=list(panel$products),mean)

2 Merge PHCH-data and Senso-data into one data matrix.

> i=match(x.phch$Group.1,z.panel$Group.1)

> X=cbind.data.frame(x.phch[,-1],z.panel[i,-1])

3 Hedonic-matrix

> Y=y.hedo[,-c(1:4)]

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In practice with R (cont.)

4 Perform PCA on the Senso-data from SensMap package.

> library(SensMap)

> map=map.with.pca(X = X)

5 Extract the first two components of the PCA and create thegrid.

> maps=cbind.data.frame(map$F1,map$F2)

> colnames(maps)=c("F1","F2")

> nbpoints=100

> discretspace=discrete.function(nbpoints = nbpoints,

+ map = maps)

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6 Perform quadratic regression (default) and estimate the predic-tions among all the points in the grid and for each consumer

Y c = ac + b1cF

1 + b1cF

2 + b11c (F 1)2 + b22

c (F 2)2 + b12c F 1F 1 + ϵc

> x.lm=predict.scores.lm(Y = Y,discretspace = discretspace,

+ map = maps)

7 Compute percentage of Liking.

> p.lm=100*rowMeans(x.lm$preference)

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8 Draw the External-map.

> image.plot(graph.surfconso,col=terrain.colors(60))

> contour(x=graph.surfconso$x,y=graph.surfconso$y,

+ z=graph.surfconso$z,add=T,

+ levels=seq(from=0,to=100,by=5))

> text(x=maps$F1,y=maps$F2,labels=y.hedo$Group.1,pos=3)

> points(x=maps$F1,y=maps$F2,pch=20)

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-6 -4 -2 0 2 4 6

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24

68

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60

65

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arbeq(3p)

arbeq(sp)

chemch3p

chemch(sp)

chemle(3p)

chemle(sp)

chetou(3p)

chetou(sp)

corati(3p)corati(sp)

leguim(3p)

leguim(sp)

zalmat(3p)

zalmat(sp)

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Denoising the External map

Perform now a Local Polynomial Regression Fi�ing of thepercentages in terms of the (x, y)−coordinates

> dlow=cbind.data.frame(discretspace,p.lm)

> colnames(dlow)=c("x","y","z")

> m.loess<-loess(z~x+y,span=.5,data=dlow,degree=2)

> p.loess=m.loess$fitted

> graph.surfconso.loess=as.image(Z=p.loess,x=discretspace,

+ nrow=nbpoints,

+ ncol=nbpoints)

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Denoising the External map (cont.)

-6 -4 -2 0 2 4 6

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24

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55

60

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70

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arbeq(3p)

arbeq(sp)

chemch(3p)

chemch(sp)

chemle(3p)

chemle(sp)

chetoui(3p)

chetoui(sp)

corati(3p)corati(sp)

leguim(3p)

leguim(sp)

zalmat(3p)zalmat(sp)

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Denoising the External map (cont.)

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Some references

Analysis Sensory Data with R, Sebastien Lê, Thiery Worsh,CRC Press (2014)

McEwan, J. A. (1996). Preference Mapping for product opti-mization. In Multivariate analysis of data in sensory science(Naes, T., and Risvik, E. eds.). New York: Elsevier (pp. 71-102).

Danzart, M. (1998). �adratic model in preference mapping.4th Sensometric meeting, Copenhagen, Denmark, August 1998.

timesens.com by INRA Dijon, France (2016)

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Thank you

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Documents

Sensory Analysis, R tools to analyze Preference liking in ... · PDF fileWhat’s Sensory Analysis Sensory analysis is a scientific discipline used to analyze reactions to stimuli