Post on 14-Dec-2015
XLSTAT-ADA’s functions
Canonical correlation analysis Studies the correlation between two
sets of variables
Extracts a set of canonical variables that are as closely correlated with both tables as possible and orthogonal to each other.
Symmetrical method
Canonical correlation analysis
Recording of data on men in a training center,
Two sets of data:The physiological data:
• Weight• Waist• Pulse
The exercises the men did:• Chin-ups• Sit-ups• Jumps
Canonical correlation analysis Men doing sit-ups or chin-ups
have usually a smaller waist.
In general people training more have a smaller waist and weight.
Jumping seems to have an impact on the weight but not as much on the waist.
Redundancy analysis Redundancy Analysis is an alternative
to Canonical Correlation Analysis.
Non-symmetric method.
The components extracted from X are such that they are as closely correlated with the variables of Y as possible. Then, the components of Y are extracted so that they are as closely correlated with the components extracted from X as possible.
Redundancy analysis Same example as Canonical correlation analysis:
Recording of data on men in a training center,Two sets of data: The physiological data:
• Weight• Waist• Pulse
The exercises the men did:• Chin-ups• Sit-ups• Jumps
Redundancy analysis Same relationships are
observed:• Men doing more sit-ups or
chin-ups have usually a smaller waist.
• In general people training more have a smaller waist and weight.
• Jumping seems to have an impact on the weight but not as much on the waist.
Note that the first factor is explaining more variance than in canonical correlation analysis (93,30)
The larger the waist, the lower the pulse
Redundancy analysis It is possible to project the
observations in the same graphic.
It is easy to visualize which men are doing more exercises and the one being fitter.
Canonical Correspondence Analysis Canonical Correspondence Analysis
(CCA) was developed to allow ecologists to relate the abundance of species to environmental variables.
CCA simultaneous representation of the sites, the objects, and the variables describing the sites.
Principles of Canonical Correspondence Analysis
T1n
sites
pspecies
T2n
sites
qdescriptive variables
Contingency table
Canonical Correspondence Analysis Canonical Correspondence Analysis
can be divided into two parts:• A constrained analysis in a space which
number of dimensions is equal to q = analysis of the relation between the two tables T1 and T2.
• An unconstrained part = analysis of the residuals.
XLSTAT-ADA offers as well: • Partial CCA• PLS-CCA
Canonical Correspondence Analysis Contingency table:
• the counts of 10 species of insects • on 12 different sites in a tropical region.
A second table includes 3 quantitative variables that describe the 12 sites:
• altitude, • humidity, • and distance to the lake.
Canonical Correspondence Analysis Some insects: insects 2,
4 and 5 prefer the humid sites, such as sites 7 to 12, while some prefer dry climates such as insects 1, 6, 8 and 10.
Insect 9 prefers a climate with higher altitude
Principal coordinate analysis Principal Coordinate Analysis is aimed
at graphically representing a resemblance matrix between p elements.
The algorithm can be divided into three steps:
Principal coordinate analysis Principal Coordinate Analysis is aimed at
graphically representing a resemblance matrix between p elements.
The algorithm can be divided into three steps:
1. Computation of a distance matrix for the p elements
p
n
x11 x12 x1p
xn1 xn2 xnp
p
p
0 d12 d1p
0 0 0 0dp1 dp2 0
Principal coordinate analysis Principal Coordinate Analysis is aimed at
graphically representing a resemblance matrix between p elements.
The algorithm can be divided into three steps:
2. Centering of the matrix by rows and columns
p
n
p
p
x11 x12 x1p
xn1 xn2 xnp
0 d12 d1p
0 0 0 0dp1 dp2 0
p
p
-r1-c1 d1p-r1-cp dij-ri-cj dp1-rp-c1 -rp-cp
Principal coordinate analysis Principal Coordinate Analysis is aimed at
graphically representing a resemblance matrix between p elements.
The algorithm can be divided into three steps:
3. Eigen-decomposition of the centered distance matrix
p
n
p
p
x11 x12 x1p
xn1 xn2 xnp
0 d12 d1p
0 0 0 0dp1 dp2 0
p p
pt
t
p
p
-r1-c1 d1p-r1-cp dij-ri-cj dp1-rp-c1 -rp-cp
Principal coordinate analysis Principal Coordinate Analysis is aimed at
graphically representing a resemblance matrix between p elements.
The algorithm can be divided into three steps:
The rescaled eigenvectors correspond to the principal coordinates that can be used to display the p objects in a space with 1, 2, p-1 dimensions.
1. Computation of a distance matrix for the p elements2. Centering of the matrix by rows and columns3. Eigen-decomposition of the centered distance
matrix
Principal coordinate analysis
5 products are graded by 10 individualsNote that product 4 is preferable.
Principal coordinate analysis
The results is a map of the proximity of the 5 products.
P1 and P3 are the most similar products.
Generalized Procrustes Analysis (GPA) GPA is a pretreatment used to:
• reduce the scale effects
• and obtain a consensual configuration
on data where products have been graded by several judges.
GPA compares the proximity between the terms that are used by different experts to describe products.
Generalized Procrustes Analysis (GPA)
10 experts graded 4 cheeses for 3 sensory attributes:
• Acidity• Strangeness• Hardness
Generalized Procrustes Analysis (GPA)
The products do not have the exact same grade by each expert
Generalized Procrustes Analysis (GPA)
A consensus can be found for the position of each product
Cheese 1 and 2 are the strangest
Cheese 3 is the Hardest
Generalized Procrustes Analysis (GPA)
Strangeness is not graded in the same way by the different experts
Acidity and Hardness are quite reproducible
Multiple Factor Analysis (MFA) MFA is a generalization of PCA
(Principal Component Analysis) and MCA (Multiple Correspondence Analysis).
MFA makes it possible to:• Analyze several tables of variables
simultaneously, • Obtain results that allow studying the
relationship between the observations, the variables and tables.
36 experts have graded 21 wines analysed on several criteria:• Olfactory (5 variables)• Visual (3 variables)• Taste (9 variables)• Quality (2 variables)
Multiple Factor Analysis (MFA)
Multiple Factor Analysis (MFA) MFA groups the information on one chart
Multiple Factor Analysis (MFA) MFA groups the information on one chart
Multiple Factor Analysis (MFA)
Wine 13 is in the direction of the two quality variables and is therefore the wine of preference.
Multiple Factor Analysis (MFA)
The olfactory criteria are often increasing the distance between the wines.
Penalty analysis Identify potential directions for the
improvement of products, on the basis of surveys performed on consumers or experts.
Two types of data are used:• Preference data (or liking scores) for a product or for a characteristic of a product
• Data collected on a JAR (Just About Right) scale
Penalty analysisA type of potato chips is evaluated:
By 150 consumersOn a JAR scale (1 to 5) for 4 attributes:
• Saltiness, • Sweetness, • Acidity, • Crunchiness.
And on an overall liking (1 to 10) score scale
Penalty analysis
Mean of Liking for JAR – Mean of Liking for too little and too much
Semantic differential charts The semantic differential method is a
visualization method to plot the differences between individuals' connotations for a given word.
This method can be used for:• Analyzing experts’ agreement on the
perceptions of a product described by a series of criteria on similar scales
• Analyzing customer satisfaction surveys and segmentation
• Profiling products
Semantic differential charts 1 yoghurt
5 experts
6 attributes:• Color• Fruitiness• Sweetness• Unctuousness• Taste • Smell
Semantic differential charts
TURF analysis TURF = Total Unduplicated Reach and
Frequency method
Highlight a line of products from a complete range of products in order to have the highest market share.
XLSTAT offers three algorithms to find the best combination of products
TURF analysis 27 possible dishes 185 customers
"Would you buy this product?" (1: No, not at all to 5: Yes, quite sure).
The goal is to obtain a product line of 5 dishes maximizing the reach
TURF analysis
Product characterization Find which descriptors are discriminating
well a set of products and which the most important characteristics of each product are.
All computations are based on the analysis of variance (ANOVA) model.
Check the influence on the scores of attributes of:
• Product• Judge
• Session• Judge*Product
Product characterization
29 assessors
6 chocolate drinks
14 characteristics: • Cocoa and milk taste and flavor• Other flavors: Vanilla, Caramel• Tastes: bitterness, astringency,
acidity, sweetness• Texture: granular, crunchy, sticky,
melting
Product characterization
DOE for sensory data analysis Designing an experiment is a
fundamental step to ensure that the collected data will be statistically usable in the best possible way.
DOE for sensory data analysis Prepare a sensory evaluation where
judges (experts and/or consumers) evaluate a set of products taking into account:
• Number of judges to involve• Maximum number of products that a judge
can evaluate during each session• Which products will be evaluated by each of
the consumers in each session, and in what order (carry-over)
Complete plans or incomplete block designs, balanced or not.
Search optimal designs with A- or D-efficiency
60 judges 8 products Saturation: 3 products / judge
DOE for sensory data analysis
DOE for sensory data analysis
DOE for sensory data analysis