sensory analysis, r tools to analyze preference liking in ... · pdf filewhat’s sensory...
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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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Repeatability, Multivariate approach.
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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Repeatability, Multivariate approach.
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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In practice with R, Scree-plot
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, Scree-plot
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$Product)> hulls <- ddply(dt, "Product", find_hull)
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In practice with R, Product-map
> p<-ggplot(data = dt,aes(x=PC1,y=PC2,col=Product,fill=Product))++ geom_hline(yintercept = 0,alpha=.4)++ geom_vline(xintercept = 0,alpha=.4)++ geom_polygon(data=hulls, alpha=.2)++ geom_point() ++ geom_text(data=dt2,aes(x=PC1,y=PC2,label=Product),col="black")++ xlab(paste("Axis 1 (",round(res.pca$eig[1,2],1),"%)",sep=""))++ ylab(paste("Axis 2 (",round(res.pca$eig[2,2],1),"%)",sep=""))> p<-p+theme_classic()+theme(legend.position = "none")> p
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In practice with R, Product-map
arbeq(3p)
arbeq(sp)
chemch(3p)
chemch(sp)
chemle(3p)
chemle(sp)
chetou(3p)
chetou(sp)
corati(3p)
corati(sp)
leguim(3p)leguim(sp)
zalmat(3p)zalmat(sp)
-2.5
0.0
2.5
5.0
7.5
-4 0 4Axis 1 (28.1%)
Axi
s2
(12.
5%)
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In practice with R, V-test
> res.pca$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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In practice with R, Product-map
-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, Product-map
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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In practice with R (cont.)
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$preference)
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In practice with R (cont.)
8 Draw the External-map.
> image.plot(graph.surfconso,col=terrain.colors(60))
> contour(x=graph.surfconso$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$F2,pch=20)
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In practice with R (cont.)
-6 -4 -2 0 2 4 6
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arbeq(3p)
arbeq(sp)
chemch3p
chemch(sp)
chemle(3p)
chemle(sp)
chetou(3p)
chetou(sp)
corati(3p)corati(sp)
leguim(3p)
leguim(sp)
zalmat(3p)
zalmat(sp)
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In practice with R (cont.)
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Denoising the External map
Perform now a Local Polynomial Regression Fi�ing of thepercentages in terms of the (x, y)−coordinates
> dlow=cbind.data.frame(discretspace,p.lm)
> colnames(dlow)=c("x","y","z")
> m.loess<-loess(z~x+y,span=.5,data=dlow,degree=2)
> p.loess=m.loess$fitted
> graph.surfconso.loess=as.image(Z=p.loess,x=discretspace,
+ nrow=nbpoints,
+ ncol=nbpoints)
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Denoising the External map (cont.)
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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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